ADVANCING INDUSTRIAL ENGINEERING IN NIGERIA THROUGH TEACHING, RESEA RCH AND INNOVATION ■ :V. ; . . . A BOOK OF READING 'iff* .' , • ■- ■ y;fg; Edited By Ayodeji E. Oluleye Victor O. Oladokun Olusegun G. Akanbi ADVANCING INDUSTRIAL ENGINEERING IN NIGERIA THROUGH TEACHING, RESEARCH AND INNOVATION Edited By Ayodeji E. Oluleye Victor O. Oladokun Olusegun G. Akanbi ADVANCING INDUSTRIAL ENGINEERING IN NIGERIA THROUGH TEACHING, RESEARCH AND INNOVATION (A Festchrift in honour of Professor 0 . E Charles-Owaba) Professor O. E. Charles-Owaba ii Advancing Industria l Engineering in Nigeria through Teaching, Research and Innovation. Copyright © 2020 Department of Industrial and Production Engineering, University of Ibadan. ISBN : 978-078-515-9 All rights reserved. No part of this book may be used or reproduced in any form or by any m eans or stored in a data base or retrieval system without prior written permission of the publisher except in the case of brief quotations embodied in critical articles and review. Published by Department of Industrial and Production Engineering University of Ibadan. Printed by: Leading Edge Printers & Publisher Ibadan FOREWORD It gives me great pleasure writing the foreword to this book. The book was written in recognition of the immense contributions of one of Nigeria's foremost industrial engineers, respected teacher, mentor, and lover of youth - Professor Oliver Charles-Owaba. His commitment to the teaching and learning process, passionate pursuit of research and demonstration of excellence has prompted his colleagues and mentees to write this book titled - Advancing Industrial Engineering in Nigeria through Teaching, Research and Innovation (A Festschrift in honour of Professor O. E Charles-Owaba) as a mark of honour, respect and recognition for his personality and achievements. Professor Charles-Owaba has written scores of articles and books while also consulting for a medley of organisations. He has served as external examiner to various programmes in the tertiary educational system. The topics presented in the book cover the areas of Production/Manufacturing Engineering, Ergonomics/Human Factors Engineering, Systems Engineering, Engineering Management, Operations Research and Policy. They present the review of the literature, extension of theories and real-life applications. These should find good use in the drive for national development. Based on the above, and the collection of expertise in the various fields, the book is a fitting contribution to the corpus of knowledge in industrial engineering. It is indeed a befitting gift in honour of erudite Professor Charles-Owaba. I strongly recommend this book to everyone who is interested in how work systems can be made more productive and profitable. It represents a resourceful compilation to honour a man who has spent the last forty years building up several generations of industrial engineers who are part of the process to put Nigeria in the rightful seat in the comity of nations. Congratulations to Professor Charles-Owaba, his colleagues and mentees for this festschrift. Professor Godwin Ovuworie Department of Production Engineering University of Benin IV TABLE OF CONTENTS Page CHAPTER 1 Quantitative Approach to Organisational Design in Project Management Office 1 By B. O. Odedairo and I. O. Raji CHAPTER 2 Options for the Nigeria Electricity Tariff Review: Cost or Service Reflective Tariff? 18 By Akinlabi, K.A., Oladokun, V.O. and Alexander A.O CHAPTER 3 Development of an Artificial Neural Network-Fuzzy Markov Model for Industrial Accidents Forecasting 3 8 By I. E. Edem and O. A. Adebimpe CHAPTER 4 Ergonomics/Human factors training and research in Nigeria: Early years and current efforts 71 By Olanrewaju O. Okunribido CHAPTER 5 Some Developments in Scheduling Algorithms 92 By Ayodeji E. Oluleye, Elkanah O. Oyetunji and Saheed Akande CHAPTER 6 An Integer Linear Programming Model of a University Soccer Timetabling Problem 123 By Okunade Oladunni S.and Ogueji Kelechi J. CHAPTER 7 The Role of Renewable Energy in Nigeria's Energy Transformation 171 By MojisolaA. Bolarinwa CHAPTER 8 Application of Deep Learning in Disease Prediction 195 By S. C. Nwaneri and C. O. Anyaeche v CHAPTER 9 New Normal: Ergonomic Awareness for Telecommuters in Nigeria 220 By Ezekiel Olatunji and Ebenezer Olowolaju CHAPTER 10 Model-Based Systems Engineering: Relevance and Applications in Contemporary Systems Design 247 By Ebenezer Olowolaju and Ezekiel Olatunji CHAPTER 11 The Impact of Covid-19 Pandemic on Sustainable Supplier Selection Process 254 By Chukwuebuka .M. U-Dominic CHAPTER 12 The Traveling Salesman Problem: Algorithms, Sub-tours and Applications in Combinatorial Optimization 287 By V.O. Oladokun, B.O. Odedairo and O.S. Atitebi CHAPTER 13 On Safety, Health, Productivity and National Development 305 By A Kolawole and A A Opaleye CHAPTER 14 Garment Sizing System: A Critical Review of the Past, Present and Future 321 By Adepeju A. Opaleye and A Kolawole CHAPTER 15 Comparison of Compromise Constraint Bi-objective LP Method and Three Traditional Weighted Criteria Methods 342 By Adeyeye, A. D., Arise, O. T. and Charles-Owaba, O. E. CHAPTER 16 Preventive Maintenance Interval Prediction: Application of a Cost-Based Approach with Lost Earnings Consideration in a Manufacturing Firm 360 By O.A. Adebimpe and O.E. Charles-Owaba vi CHAPTER 17 Supply Chain Modelling: A Discrete Event Approach 386 By Ajisegiri G.O, Ajisegiri, A. //. and Akande S. CHAPTER 18 Evaluation of Mechanical Strain Resulting from Working with two Locally -abricated Engine Powered Stationary Grain Threshers 405 3y O.G. Akanbi1 and B. O. Afolabi CHAPTER 19 Team-based Material Selection for a DC Machine Armature Design Using Compromise Programming Optimization 421 By Odu, O. Godwin CHAPTER 20 A review of the effect of Industry 4.0 on Supply Chain Systems 463 By Modestus Okwu, C.M. U-Dominic, Ifeyinwa J. Orji, Victor Mbachu, and Ayomoh Michael CHAPTER 21 Computer Aided Design (CAD) of a Vertical Transportation System in High- rise Building: Case of Ivory Tower, University of Ibadan Ibadan 493 By Odunfa, K.M, Taiwo, O. I, Odunfa V.O., Abu, R CHAPTER 22 A Synopsis of Major Classical Inventory Management Models 510 O. Ibidapo-Obe, F. O. Ogunwolu and O. F. Odeyinka CHAPTER 23 Redesign of Organisational Structure of a Manufacturing Firm 549 By Anyaeche C. O. and Akindele J. O. CHAPTER 24 Anthropometric Evaluation of Bus Drivers and their Workstations 590 By S. O. Ismaila, S.A Odunlami, S.I Kuye, A. I. Musa, T. M. A. Olayanju, A. P Azodo and O. A. Adeaga v:: CHAPTER 1 Quantitative Approach to Organisational Design in Project Management Office B. O. Odedairo1 and I. O. Raji1,2 'Department of Industrial and Production Engineering, University of Ibadan, Ibadan, OYO 200284. Nigeria. E-mail: bo.odedairo@ui.edu.ng (corresponding author) 2 School of Industrial Engineering, LIUC - Universita Carlo Cattaneo Castellanza 21053 (VA). Italy. E-mail: iraji@liuc.it Abstract In a competitive and dynamic business environment, project management is an efficient framework to ensure flexibility and to manage beneficial change. In the design of a project organisation structure, the use of a quantitative approach to model contingency variables and human dynamics challenges have received limited attention. In this chapter, the basic concepts of projects, organisation design and structure, and Project Management Office (PMO) was discussed. Thereafter, the applicability of operations research paradigm to structure a PMO using the methodology developed by Professor Charles-Owaba were highlighted. Keywords: Project, Project management, Organisation structure, Project-based organisation, Modeling, Charles-Owaba. 1. Introduction An organisational structure is rooted in different organisational design theories and provides the required platform to drive organisation strategic goals. Although different organisational structure exists, the effect of competition and an uncertain business environment often leads to organisational restructuring. In this chapter, the applicability of quantitative methods in project organisational structure will be discussed from sections 1.1 to 1.6. 1 1.1 Projects and Project Management: Concepts and Definitions As agents of beneficial change, projects are conceptualised and executed within the established schedule, resource and performance parameters to achieve organisation strategic goals. Therefore, in a dynamic and competitive environment, the pace of change offered by projects is one of the ways to remain relevant. Projects constitute 30% of the world economy as commented by Anbari et al. (2008). Projects are characterised by their uniqueness, temporary and transient nature, urgency, unitary, resource usage, novelty, complexity, integration, level of risk, flexible structure, modularity of design, and predefined objectives (see Bard et al., 1994; Atkinson, 1999; Turner & Muller, 2003; Bredillet, 2007; Reiss, 2007; Gray & Larson, 2008, p.100; Moleli, 2012; Project Management Book of Knowledge (PMBOK) Guide, 2017, p.4; Odedairo & Olenloa, 2021). These inherent attributes of projects differentiate it from another business process; for example, the transient nature ot projects refers to different stages in the project management processes. Hence, project management is an efficient framework to ensure flexibility and handle changes. Project Management (PM) as defined by Association of Project Management (APM) is “a process by which projects are defined, planned, monitored, controlled and delivered such that the agreed benefits are realized” (APM Book of Knowledge, 2006, p.2). Project Management Institute (PMI), view PM as the “application of knowledge, skills, tools and techniques to project activities to meet the project requirements” (PMBOK, 2017, p.10). While the core of PM methodologies is adaptable and universal, an effective project life-cycle ensures smooth transformation from vision to reality. Project life-cycles can be characterised along level (i.e. degree) of change and delivery frequency. A project life-cycle is agile if it offers a high degree of change and high delivery frequency, while the predictive, iterative and incremental life-cycles lies within these two extremes. The project management team (or the organisation) must identify the peculiarity of 2 the project before selecting the preferred life-cycle. Also, the project organisational structure and needs (e.g. time, resources, communication links, etc.) should be appraised continually during the life-cycle. 1.2 Organisations: Design and Structure An organisation is developed “whenever the pursuit of an objective requires the realization of a task that calls for the joint effort of two or more individuals” (Hax & Majluf, 1981 p. 417). In essence, organisations can be characterised based on type and size. Greenwood and Miller (2010) commented that most organisation types are confronted with arrays of design and decision challenges. Eames (1969) defines design as a plan for arranging elements effectively to accomplish a purpose. Most design efforts present flexibility to gather multiple choices and offer opportunities to compare alternatives. Organisational design is an approach that holistically integrates people, processes, structure and other core organisation elements to enable an organisation to actualise its strategic goals. Any organisational design method should be responsive to the ability to adapt to new strategies and future changes. This responsiveness will enable the organisation to respond to disruption arising from the environment, political and economic pressure, technology, and culture. Organisation design has rich and established literature on different design frameworks such as classical, neoclassical and modem theories (Charles- Owaba, 2002; Greenwood & Miller, 2010; Van de Ven et al., 2013; Food and Agriculture Organisation). However, the complexity and malleability inherent in almost all types prohibit a “one-size-fits-all” organisational design framework. Although, an in-depth discussion of these design theories is beyond the scope of this chapter; however, a summary will be provided. The components of the classical theory are Taylor’s scientific management (scientific selection, management and training of workers), Weber bureaucratic approach (structure, specialization and democracy) and administrative theory by Fayol (discipline, unity of command, and equity). The neo-classical approach consists of human relation and decision-making theories. The modem 3 theories include the following approaches: (i) system-view (ii) socio- technical and (iii) contingency or situational. Irrespective of the design theory adopted, a carefully designed organisation is expected to reduce confusion in the choice of a structure. Organisation structure (OS) rooted in organisational design theories is one of several elements in any business. OS provides the necessary platform to conceptualise and drive the strategic plan. Some of the elements to consider in the selection of an OS include decision positions and levels, supervisory positions, cost, physical locations, operation positions, communication lines, and span of control (Charles-Owaba (2002); PMBOK, 2017 p.46). An efficient structure provides an enabling environment for rapid transformation of decisions into actions. Usually, to arrive at an acceptable structure, a trade-off among several elements is unavoidable. Since organisation structure is expected to work in tandem with organisation design, some of the constraints associated with the preferred design theory have to be addressed before a working structure can be achieved. An organisation may adopt more than one structure across its business functions e.g. the sales/fulfilment function may require a different structure from the purchasing function. Once the design and structure of an organisation support its business objectives; ultimately, organisational effectiveness will be actualized. In Table 1, different structures are compared along with several factors. Table 1 Comparison of some organisation structures Structure type Factors Functional Divisional Matrix Network Cluster 1 Strategic goal Specific Multiform Reactive Innovative Competitive 2 Environmental Stable Heterogeneo Complex Volatile Fast-paced conditions us 3 Division of By inputs By outputs Inputs Knowledge Skills and Labour and knowledge Outputs 4 Co-ordination / Hierarchic By division- Dual Cross­ Centralised Reporting al General purpose functional manager and teams Corporate staff 4 ; 5 Decision Centralised Separated Shared Decentralise Internal making d 6 Boundaries Core Dual- Multiple Unstable Multiple Internal/ external 7 Mode of Functional/ Management Required Use of Combinatio authority Positional Skills and negotiatin knowledge n of responsibility g skills expertise and resource usage 8 Resource usage 4 1 2 3 4 9 Time usage 1 3 2 4 4 10 Responsivenes 1 2 3 4 4 s 11 Adaptability 1 3 2 3 3 ; 12 Accountability 3 4 1 3 3 Legend: 1-Poor, 2-Moderate, 3-Good, 4-Excellent Source: Adapted from Guide to Organisation Design (Stanford, 2007, P -66 ) 1.3 Organisation Structure in Project Management The term ‘temporary organisation’ is one of the characteristics of a project. Lundin and Soderholm (1995) highlighted the difference between a permanent and temporary organisation using the concept of task, time, team and transition. Permanent organisations are preoccupied with goals (rather than tasks), the need to survive (not time-based), functioning organisation (not a team concept) and continuous production (rather than a transition). The question ‘what is the most suitable organisation structure in project management is somehow complicated due to inherent characteristics of projects. A project organisation structure (POS) is expected to support, maintain and ensure balance among the following criteria: resource allocation, authority, division of work, communication lines, etc. Invariably, a poor POS can result in a failed project; for example, a report submitted in 2011 by the presidential projects assessment committee in Nigeria revealed a huge number totalling 11,886 of ongoing and abandoned federal infrastructural projects (Premium Times Newspaper, 2012). Lack of direction in project management was cited as one of the several reasons for the problem. Usually, a good direction in project management aligns the selection of 5 the project, organisation structure/culture, and the project management process with corporate strategy. Similarly, Dai and Well (2004) suggested that while project failure rates are on the increase, more research into improved organisation structures such as the Project Management Office (PMO) should be encouraged. 1.3.1 Typology of Project Organisation Structure In organisation theory, based on environmental conditions (i.e. internal and external factors) surrounding an organisation the need for typology arises. Project-based organisation (PBO) has its mixture of desigr choices and contingency features. The idea of developing a generalised typology will be useful in modelling different types of organisations. In literature, researchers have discussed project organisation by multiple nomenclatures as presented in Table 2. Table 2. T apology of Project Organisation Structures Authors Description/ Characteristics Nomenclature/ Names 1 Hobday, 2000; Description: 1. Project-Based Pemsel and Project is the primary unit of Organisation (PBO) Wiewiora, 2013; production, innovation, and competition. Characteristics: Standalone, subsidiary of a big corporation and role defined by the parent organisation 2 Oliviera, 2017; Description: 1. Project Management PMBOK, 2017; (i) An organisation unit with the Office (PMO). Babaeianpour and responsibility of coordinating 2. Project Office projects in a PBO. (ii) PMO is 3. Organisational project Zohrevandi, 2014; implemented to standardise, office Kerzner, 2003; improve, administer and control Hurt and Thomas, project management processes, (iii) 2009. PMO may be in stages depending on the maturity of an organisation. (iv) PMO referred to as Project Office Characteristics: Diverse, transient (can be created and closed when not needed), an organisation within an organisation 6 3 Monteiro et al (2016) (i) Identified 47 PMO models 1.Enterprise PMO (ii)Number of models sharing the 2. Project Management same name reduced to 25. Centre of Excellence (ii) Common nomenclature across (PMOCE) models reduced to 4 3. Project Office 4. Project Support Office 1.3.2 Project Management Office In recent years, several organisations have embraced PMO as a formal organisational structure to ensure a good direction in project management, eliminate trial and error in project administration and efficient resource management. A PMO (also called the Centre of Excellence or Center of Expertise) is a governance strategy and a control layer between an organisation and its project management efforts. Project management institute defined a PMO as: an organizational structure that standardizes the project-related governance processes and facilitates the sharing of resources, methodologies, tools, and techniques. The responsibilities of a PMO can range from providing project management support functions to the direct management of one or more projects (PMBOK, 2017, p.48). In the third edition of its PMBOK (2004), PMI highlighted other nomenclature for PMO as “project office” or “program office”. Some of the functions of a PMO includes: storing of proprietary information, defining and maintaining project standards, facilitating and provision of resources, consulting and knowledge sharing, and to conduct training. Ward and Daniel (2013) consider a PMO as an organizational entity designed to offer supports on strategic decisions and proper implementation of project management principles; to project managers, project and management teams. As an entity, Montero et al (2016) commented that a PMO could be a unit or department in a matrix or PBO. Babaeianpour and Zohrevandi (2014) identified the project office, basic PMO, standard PBO, advanced PMO and centre of excellence (CoE) as stages a PMO may transform through in an organisation. Just like projects, PMOs are complex and due to variability in different project 7 management firms, their design may be difficult. However, Hobbs and Aubry (2008) through their rigorous empirical study proposed three (3) classifications for PMOs using three variables; namely, number of projects (NP), number of project managers (NPM) and level of decision­ making authority (DMA). The three classifications are (i) PMOs with many NP and NPM with considerable high DMA (ii) PMOs with few NP, few NPM with less DMA and (iii) PMOs with few or zero NPM with a moderate level of DMA. 1.4 Organisation Design and Project Management Structure: Current Issues Miterev et al. (2017) commented that despite limited studies on the interaction between project management and organisation design, PBO presents promising research opportunities. The contingency features and human dynamics challenges of elements such as decision positions and levels, supervisory positions, cost, physical locations, operation positions, communication lines, and span of control in a PBO is worth researching. 1.5 Organisational Design Approaches in Project management Office Several organisation models (e.g. Galbraith’s Star Model, 7-S model) derived from different organisational design theories form the basis of many organisational structures. Hax and Majluf (1981) identified three forms of organisational structures widely used. These are the functional, divisional and matrix derived from well-proven design theories. The advantages and disadvantages of these design structures are widely published. For example, the matrix structure is mostly preferred in project management; however, its use is characterised by conflicts bothering on authority, reporting and resource management (Thiry, 2007). 1.5.1 Quantitative methods With quantitative research design, it is possible to observe, assess, diagnose, generate a hypothesis, and estimate interaction among system 8 components. Quantitative methods emphasize the mathematical and numerical analysis of data to enhance better communication. Hax and Majluf (1981) suggested the use of operations research (OR) paradigm in organisational design. OR methods can evaluate and determine optimal choice among several courses of action. Charles-Owaba (2002) not only accepted the idea of studying the applicability of OR in organisational design, the author further suggested the adoption of the engineering design process in organisational design. The author highlighted 24 benefits of using engineering design methodology in organisational design studies to show that OR methods can handle mechanistic tendencies in different organisation design theory. Some of the benefits include (i) adoption of quantitative procedures for the design (ii) ability to mathematically model an organisation structure (iii) quick modification of an organisation structure (iv) provision for comparative evaluation of different types of structure (v) combination of suitable design tools from mathematics, physical sciences, social sciences, industrial and systems engineering opportunities (vi) ability to choose appropriate design criteria (vii) identification of design variable and parameters required to define an organisation structure, etc. 1.6 Modeling PMO with Personnel Utilisation as the organisational design objective An organisational design problem using OR approach will aim to optimise a pre-defined design objective such as personnel utilisation, redundancy and their associated cost; subject to the satisfaction of a set of organisation design variables and constraint functions parameters within sets of variables limiting values (Charles-Owaba, 2002). Since the organizational design of PMO using quantitative approach is an emerging research area, the design methodology proposed and developed by Charles-Owaba (2002) will be adopted. Consequently, an employee utilisation design approach to PMO and the relevant solution procedure to ensure an optimal business organisational structure will be highlighted further in the next section. 9 1.6.1 Notations and Terminologies The basic notations and their definitions are presented in Table 3. Table 3. Notations and Definitions Notation Definition Notation Definition i Index for Work level j Index for decision-making (Decision-making authority) centre (Number of project managers) " a The utilisation of personnel of M Number of decision levels decision making centre j at work level i K i i The span of control for a N< Number of decision position decision-making centre with available at work level i index j and i t h work level W i j Average waiting time(hours) a p u The amount of time a project case is available to receive manager has no case attention from the project requiring his/her attention manager The subordinates arrive to A i j The time required (in hours) consult the superior (project for work scheduled in a day manager) at this rate N o Number of operation positions % The subordinates are which perform terminal activities attended to by a superior at (number of the lowest cadre of decision-making centre j and staff) work level at this rate 4>h Set of functions (i4y,/ty_ N 0 , Ay) L i ! The average number of cases available for a project manager to attend to in one day H Personnel utilisation function for entire organisation structure which contains a set of functions (K l j . N i , M, 0 From equation 1, is expressed as: Kij+1 (4) total number of cases at position (i,j) total time (hours)for study at the position (5) total completed cases at position (i,j) time (hours)spent to treat all completed cases (6) P i j = hL u < pv (7) 1.6.5 Applicability To use the model represented from equations 1 to 7, a PMO (a sample structure presented in Fig.l) organisational goals will be converted to the 12 volume of work and personnel requirements. This involves the determination of terminal activities, skill identification, determine the amount of available work per skill, determination of the number of operations positions, determine the number of project managers and number of decision making authority. Also, the values of Atj, Ai;-,/qy Kij and N0 have to be determined. A chronological review of organisation structure design algorithm to obtain an optimal design and compare to an existing design is contained in Charles-Owaba (2002, p. 223-225). It is expected that the number of projects (NP), number of project managers i'NPM) and level of decision-making authority (DMA) that will reduce redundancy will be obtained. 1. Director, 2- Marketing Department, 3- Human Resources, 4-Finance and Administration, 5 - Legal, 6- Project A, 7- Project B Fig.l Project Organisation Structure for a sample Project management office 1.6.6 Summary In this chapter, projects, project management, and components of project organisation structure were discussed. In the selection of a project organisation structure, some of the elements to consider include, the number of projects, number of project managers, level of decision­ making authority, physical locations, operation positions, 13 communication lines, and span of control. Therefore, due to inherent characteristics of projects, organisations have embraced project management office as a formal organisational structure to eliminate trial and error in project administration and to ensure efficient resource management. From the organisational design framework proposed by Professor Charles-Owaba through operations research paradigm, the modeling structure for a project management office was presented. References Anbari, F. T., Bredillet C.N., & Turner, J. R. (2008). Exploring research in project management: the nine schools of project management. Retrieved on October 2, 2020. Available at https://www.academia.edu/3294985/Exploring research in project management Nine schools of project management research Pa rt 2 Association for Project Management (2006). APM Body o f knowledge (APMBOK) (5th ed.) Somerset: Butler and Tanner Atkinson, R. (1999). 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The Impact of Project Management on Road Construction and Maintenance at Emfuleni Local Municipality. Retrieved October 2, 2020, from https://repository.nwu.ac.za/handle/10394/10317 Monteiro, A., Santos, V., & Varajao, J. (2016). Project Management Office Models - A Review. Procedia Computer Science, 100, 1085-1094. DOI: 10.1016/j.procs.2016.09.254 Odedairo, B.O., & Olenloa, O.E. (2021). Scheduling of Post-Flood Recovery Project with Flexible Project Structure. Journal o f Engineering, Project, and Production Management, 11(2), 118-126. https://doi.org/10.2478/ieppm-2021-0012 Oliveira, R.R & Martins, H.C (2018). Strategy, People and Operations as influencing agents of the Project Management Office performance: an analysis through Structural Equation Modeling, Gest. Prod. 25(2), 410-429. http://dx.doi.org/10.1590/0104-530X2294-16 Pemsel, S. & Wiewiora, A. (2013). Project management office a knowledge broker in project-based organisations. International Journal o f Project Management. 31( 1), 31-42 Premium Times Newspaper (2012) The Tragedy of Abandoned Projects by Nasir El-Rufai Retrieved September 15, 2020, https://www.premiumtimesng.com/opinion/98468-the-tragedy-of- abandoned-projects-by-nasir-el-rufai.html 16 Project Management Institute (2004). A Guide to The Project Management Body o f Knowledge (PMBOK®) (3rd ed.) Newtown Square, PA Project Management Institute (2017). A Guide to The Project Management Body of Knowledge (PMBOK®) (6th ed.) Newtown Square, PA Reiss, G. (2007). Project Management Demystified (3rd ed.). Routledge Stanford, N. (2007). Guide to Organisation Design: Creating high- performing and adaptable enterprises. London: Profile Books. Thiry, M. (2007). From PMO to PBO: the PMO as a vehicle for organizational change. Paper presented at PMI Global Congress North America, Atlanta, GA. Newtown Square, PA: Project Management Institute. Turner, J. R., & Muller, R. (2003). On the Nature of the Project as a Temporary Organization. International Journal o f Project Management, 27(1), 1-8. Van de Ven, A.H., Ganco, M. & Hinings, C.R. (2013). Returning to the Frontier of Contingency Theory of Organizational and Institutional Designs. Academy of Management Annals, 7(1), 393^440. https://doi.org/10.5465/19416520.2Q13.774981 Ward, J. & Daniel, E. M (2013). The role of project management offices (PMOs) in IS project success and management satisfaction. Journal o f Enterprise Information Management, 26(3),316 - 336. http://dx.doi.org/10.1108/17410391311325252 17 CHAPTER 2 Options for the Nigeria Electricity Tariff Review: Cost Or Service Reflective Tariff? Akinlabi, K.A.1, Oladokun, V.O.1, Alexander A.O.2 1 Department of Industrial and Production Engineering. University of Ibadan, Ibadan Nigeria 2 Centre for Petroleum, Energy Economics and Law, University of Ibadan, Ibadan Nigeria Corresponding emails:tundelabi@yahoo.com. vo.oladokun@mail 1.ui.edu.ng, akolo.xander@gmail.com Abstract: The improvement in the Nigerian electricity value chain has not been visible after seven years of partial privatization of the sector as the government continues to subsidize tariffs to avert the total collapse of the sector. The electricity distribution companies tagged the weak link in the value chain, have been challenged with inherited dilapidated infrastructure and poor revenue generation. The Nigeria Electricity Supply Industry is currently considering service reflective tariff options after her inability to implement a cost-reflective tariff in the sector since privatization in 2013. The electricity value chain is presently challenged with poor cash flow due to customer payment apathy, perceived corruption in the system, unavailability of a cost-reflective tariff which resulted in poor remittance to the value chain by the distribution companies. This paper reviews the power sector evolution and the reforms in the sector, the performance of Nigeria Electricity Regulatory Commission regulations, the concepts of the cost, and service reflective tariff. The paper recommends a cost-reflective tariff option with strict regulatory performance monitoring of all the value chain participants in the sector. Keywords - electricity value chain; privatization; service reflective tariff, cost-reflective tariff, electricity distribution, Nigeria power sector 18 1.0 INTRODUCTION The level of infrastructural development of a country will determine her rate of attainment of sustainable development and economic growth (Elum & Mjimba, 2020). A good understanding of infrastructural service performance, especially electricity, is critical for planning and policymaking to achieve vibrant economic development. Nigeria is a developing nation with a population of 203 million over the 923,768km2 area it covers (CIA, 2019). The International Energy Agency and the World Bank reported in 2017 that 58% of Nigeria’s population is connected to electricity through the national grid. In 2019, the United States Agency for International Development (USAID) estimated the installed electricity generation capacity in Nigeria to be 12,522MW with daily generation hovering above 4,000MW. Oyedepo (2012) opined that the instability of electricity supply from the national grid resulted in 80% of consumers being underserved with only a few hours of supply daily. Thus, consumers have resulted in self-generation of electricity from renewable and non-renewable sources to be able to meet their energy needs. There are many issues with electricity supply which make the distribution from the national grid epileptic and cover only about 40% of the country’s population (Aliyu et al., 2013). According to Seymour, (2012) and Titus et al., (2013), service outages could arise from transmission lines failure, traffic accidents, switching problems at injection substations, heavy start-up loads, background electrical noise, faulty distribution components, and lack of scheduled preventive maintenance. However, a very critical issue that determines the sustainability of the power sector, especially a deregulated power sector, is the tariff (Oladokun & Asemota, 2015). Recovery of cost in the value chain and avoidance of cross-subsidies by customers are two critical issues for consideration when setting right price in transition economies (Reneses et al., 201 l).Meanwhile, there are no policy consensus on the tariff regime that is most suitable for Nigeria viz a viz cost and service reflectivity of the regime (Nwangwu, 2019). The current tariff being charged electricity users in Nigeria is neither service nor cost-reflective and this is hurting the entire value chain. The section 2 of this paper 19 reviews the history of electricity in Nigeria, the power sector reform and the electricity distribution company. The Nigeria electricity value chain is discussed in section 3 while section 4 details the electricity tariff building blocks in Nigeria. The section 5 explains the difference between the cost and service reflective tariff in Nigeria context while the authors’ recommendation and conclusion can be found in the last section. 2.0 HISTORY OF ELECTRICITY IN NIGERIA Nigeria started generating electricity in the Lagos colony with two small generators in 1886. A 60kW generator was introduced to power Lagos in 1896, after fifteen years of electricity introduction in England (Niger Power Review, 1985; Sambo, 2010; Onochie et. al. 2015). The foremost utility company that started operations in 1929 was the Nigeria Electricity Supply Company (NESCO), with a hydroelectric power station located in Kurra, near Jos. In 1964, the Nigerian Government Electricity Undertaking (NGEU) was established as part of the Public Works Department, to oversee both liabilities and assets of electricity distribution in Lagos. An act of Parliament was enacted in 1951 to create the Electricity Corporation of Nigeria (ECN). ECN was responsible for the integration of both privately-owned and government-owned power generating systems (Awosope, 2014). In February 1956, the Ijora power station was launched to increase accessibility and supply quality to Ikorodu, Shagamu, Ijebu-ode, and more cities in the Ibadan-Ijebu bloc leading to remarkable improvement in the economic activities in southwest states. In 1962, another act of parliament was enacted to establish the Niger Dams Authority (NDA), and the first 132KV line was constructed to link Ijora generating plant to Ibadan generating plant. NDA was responsible for the development of hydroelectricity generation through the building and preservation of dams on the Niger River and beyond, improving navigation, supporting fish brine, and irrigation activities (Manafa, 1995). The renowned Kainji dam was constructed between 1962 and 1968. The Niger Power Review (1989) stated that the combined contribution of defunct NDA and ECN led to the commencement of the 20 operations of the national grid in 1966. The grid power transmission system linked Lagos with Kainji. The connection between Kaduna and Kainji was increased up to Kano and Zaria. In the same vein, the construction grid network of the Benin-Onitsha-Afam and Oshogbo- Benin-Ughelli were done in the Nigerian southern region. The NDA was the generating company while ECN was the distribution company selling electricity to customers. The National Electric Power Authority (NEPA) was established from the merger of NDA and ECN on the 1st of April 1972. The merger commenced with the appointment of the first manager for NEPA in January 1973. ECN was primarily in charge of sales and distribution and the NDA established to construct and operate transmission lines and power generating stations. The major reason for the merger is vesting authority for power production and distribution throughout Nigeria in one company which would also be accountable for the financial obligations. It will also lead to the useful utilization of resources available, financial, human, and other resources available in the industry across Nigeria. Okoro &Madueme (2004) stated in their study that despite annual network expansion since the inception of NEPA, the electricity supply is not regular, and the current electricity connection access rate at 45% (USAID, 2019). Meanwhile, the federal government, between 1978 and 1983, established two committees to develop templates for restructuring NEPA into an efficient and autonomous entity in readiness for its unbundling and privatization. In 2005, NEPA was renamed as Power Holding Company of Nigeria (PHCN) and takes responsibility for the entire power sector in readiness for the reforms (Sambo, 2008). 2.1 Nigeria Power Sector Reform Nigeria's power sector is responsible for the supply of quality and reliable electricity for residential, commercial, and industrial activities. In 2002, the Federal Ministry of Economy affirmed that the Power sector is a vibrant and important part of the economic value chain playing a very strategic role in the remaining sectors of the economy. Oyedepo et al., (2012) opined that inadequate power supply will impede commercial and industrial activities, the establishment of infrastructural facilities, and 21 other social amenities. To this end, continuous improvement in power generation and distribution should be the utmost priority for all the participants in the power sector to achieve the desired growth. To have continuous growth in the sector, there has been an evolution to search for the way forward in resolving the enormous issues facing the sector over the last decades. The Nigeria government embarked on massive power infrastructures rehabilitation from 1999 to 2004 in response to the pathetic state of the electricity supply (Lawal, 2008). This phase of the reform is known as the National Integrated Power Project (NIPP). Power plants were established at different parts of the country to improve power generating capacity through NIPP projects across the nation (REMP, 2005). In furtherance of the power infrastructure expansion program, licenses for power generation were granted to various Independent Power Producers (IPPs). The IPPs sell their generated electricity to private utilities and the public through the distribution companies (Adedayo & Yong 2010). In 2005, the Federal Government of Nigeria enacted the Power Sector Reform Bill into law with the key objective of deregulation of Nigeria Electricity Supply Industry (NESI) within two years of implementation. A major notable achievement of the reforms is the successful unbundling of PHCN into 18 succession companies - 11 DISCOs - distribution companies, 6 GENCOs - generation companies, and TCN - Transmission Company of Nigeria. The unbundling of PHCN is in readiness for privatization which was delayed due to change in government, policy inconsistency, administrative bureaucracy, and opposition by the workers’ union (Onochie et al., 2015). Other achievements include the setting up of institutional framework and regulatory bodies such as the Nigeria Electricity Regulatory Commission (NERC), the Nigeria Bulk Electricity Trading Company (NBET), and the implementation of a Multi-Year Tariff Order - MYTO regime designed to achieve a cost-reflective tariff. The NERC was inaugurated on November 1st, 2005, as a regulatory body overseeing activities in the power sector including tariff regimes (Okafor, 2017). Other regulatory 22 bodies created are the Nigeria Bulk Electricity Trading Pic (NBET) which oversees buying and selling of electric power and provision of ancillary services for the successor generation companies and the independent power producers. The Nigeria Electricity Liability Management Company (NELMCO) was established to take over the remaining PHCN assets and liabilities while the Rural Electrification Agency (REA) was created to ensure the expansion of electricity to the unserved area, oversees the development, and uphold transparency in the sector (Idemudia and Nordstrom, 2016). The Federal Government sold 80% and retain 20% of the GENCOs. The GENCOs are Afam, Egbin, Kainji, Sapele, Shiroro, and Ughelli. There are some Independent Power Producers (IPPs) which are connected to the grid under the auspices of the Niger Delta Power Holding Company (NDPHC), while other IPPs are still under construction. The Nigerian Electricity Supply Industry (NESI) currently has 23 grid-connected power generation stations in operation with a total installed capacity of 12,522 MW (USAID, 2019) and an available capacity of 6,056 MW as of 10th of May 2019. The peak energy is 109,372.01 MWH and peak generation to date is 4602.4 MW (Okafor, 2017; Sambo, 2018). The thermal-based plant is prevalent with an installed capacity of 10,142 MW (81% of the total) and an available capacity of 4,996 MW (83% of the total). The total installed capacity of the three Hydropower generation stations is 1,938MW with an available capacity of 1,060MW. According to IEA, the Gas Thermal Plant with 64%, Hydro with 23%, and Steam Thermal Plant with 13% made up the total installed electricity generation in Nigeria. Figure 1 shows the Nigeria Power Sector Structure with the main participants. 23 Fig. 1: Nigeria Power Sector Structure Source: Energy Sector Management Assistance Program - ESMAP (2017) The Federal Government still fully owned the Transmission Company of Nigeria (TCN) out of 18 successor companies unbundled from PHCN. The transmission asset was managed on a 4-year contract, on behalf of the government by Manitoba Hydro International (MHI Canada) whose responsibility is to revamp the network and wheel power from generating plants to distribution companies’ infrastructure without system failure. MHI contract ended in August 2016 without achieving its objective and the government did not renew the contract. TCN is now being managed by the Federal Government and Nigerians. TCN has three operational departments: System Operations (SO), Transmission Service Provider (TSP), and Market Operations (MO). The System Operations is responsible for electricity flow from generation to distribution systems, control of electricity on the grid, dispatch, system operations planning, and grid reliability. Transmission Service Provider is responsible for transmission infrastructure development, operations, and maintenance. The Market Operations overseethe administration of the NESI market rules, the wholesale electricity market, and promoting efficiency (Onochie et al., 2015). 24 TCN grid network of 20,000km transmission lines has anoverall theoretical) wheeling capacity of about 7,500MW. The transmission system footprint does not cover every area of Nigeria (Sambo, 2010). A new generation and transmission peak of 5,375MW was achieved on Thursday 7th February 2019 at 2100hrs (TCN, 2019). There are acute infrastructure and operational challenges on the grid network. The network infrastructure is radial without redundancies consequently leading to an unreliable and technically weak grid with frequent failure due to major disturbances. The transmission losses on the network are approximately 7.4% which is higher than the 2 - 6% benchmark for emerging countries. 2.2 Electricity Distribution in Nigeria A major outcome of the reform in the electricity sector was the unbundling of PHCN into eleven distribution companies - DISCOs, one transmission company - TCN, and six generation companies - GENCOs. The Federal Government sold 60% of the eleven electricity distribution companies (DISCOs) to the private investors and retains 40% ownership. The eleven DISCOs are EKEDC - Eko Electricity Distribution Company, Ikeja Electric (IE) in Lagos State, IBEDC - Ibadan Electricity Distribution Company covering the Southwest States, BEDC - Benin Electricity Distribution Company with franchise across the mid-western states, the eastern states were covered by Enugu Electricity Distribution Company - EEDC, KEDC - Kaduna Electricity Distribution Company, KEDCO - Kano Electricity Distribution Company, YEDC - Yola Electricity Distribution Company, JEDC - Jos Electricity Distribution Company covering the northern states, AEDC - Abuja Electricity Distribution Company for the federal capital territories and its environ and PHEDC - Port-Harcourt Electricity Distribution Company for the southern states. The available electricity on the grid is allocated to all the distribution companies as seen in Table 1 that shows the percentage Load Allocation for each DISCO. TheNigeria Electricity Distribution Network Map in Figure 2 shows the coverage area of each distribution company. 25 Table 1: Load Allocation for DISCOs. Source TCN (Oct. 2013) s/n 1 2 3 4 5 6 7 8 9 10 i i DISCOS PortAbuja Benin Eko Enugu Ibadan Ikeja Jos Kaduna Kano Yota Harcourt % Load 11.5 Allocation 9 11 9 13 15 5.5 8 8 6.5 11.5 Fig. 2:Nigeria Electricity Distribution Network Map Source:https://www.nbet.com.ng/ 3.0 NIGERIA ELECTRICITY VALUE CHAIN Electricity is generated from different fuel sources like coal, hydro, natural gas, solar, wind biomass, and other renewable and unconventional sources. Natural gas is responsible for 80% of electricity generation in Nigeria (UNDP 2016), therefore the value chain would be incomplete without the gas suppliers. The electricity value chain comprises gas suppliers (producers and transporters), generation (independent power producers - IPPs), transmission and distribution companies, and the end-user - customers. The cost of gas (in the US dollar) is a key determinant in the pricing unit of electricity. The generating company signs a gas supply agreement with the natural gas supplier while NBET reviews the contract for risk allocation. The electricity flow commences from transporting gas to the generation 26 companies to fire their turbines. The generation companies (IPPs) sign a power purchase agreement (PPA) with NBET while the latter issues bank guarantees for bulk electricity purchased from IPPs. The electricity produced is wheeled by TCN -transmission company of Nigeria to the eleven DISCOs - distribution companies through high voltage 330kv and 132kv cable network spanning several kilometers. TCN sends data to NBET for IPPs invoice verification and invoices to DISCOs. The DISCOs distribute electricity to the customers from their injection substations through low voltage 33kv and llkv lines to various distribution transformers. Monthly bills (invoices) are issue to customers for settlement or purchase energy for their meters (Pre-paid) before consumption. Figure 3 shows the Nigerian electricity supply industry NESI) value chain with participants' roles. The industry average collection efficiency is currently 60% with residential customers responsible for the highest default in bills payment. The market operator issues invoices to all distribution companies for energy received from the grid monthly. The invoices are for market operators and NBET bills. The market operator’s invoice is for the transmission tariff paid to TCN. The NBET bill is for the power purchase agreement (PPA) and capacity-energy charge for the month paid to the generation companies. DISCOs also pay regulatory charges to NERC while retaining only 26% of collections from the customers. GENCOs pay for gas supply and transportation in US dollars to the -gas producers and transporters while the producers settle royalties and hydrocarbon taxes. All payments in the value chain are made in Naira except for gas supply and transportation. Figure 4 shows the electricity and cash flow in the value chain. 27 Fig. 3: Nigeria Electricity Supply Industry (NESI) Value Chain Source: Nigeria Bulk Electricity Trading Company 831 _________________________ Ekctncrty flow Cashflow Fig. 4: Electricity and Cashflow in Value Chain 28 4.0 NIGERIA ELECTRICITY TARIFF BUILDING BLOCKS Nigeria's government did not allow both minor and major tariff review since 2016. The current electricity tariff is due for a change because the last minor review was done in February 2016. There have been changes in macroeconomic indexes such as gas price, exchange rate, and inflation but tariff remains because most customers are against it due to poor supply and services. This has great implications on the market as revenue shortfall is being rammed up with a total of N 1.1 trillion tariff shortfall in 2019 and 2020 (EMRC, 2020). The situation is further worsened because of poor revenue collection from the residential and government rustomers is causing the distribution companies to accumulate huge lebts. lie Act which sets the background for the Nigerian power industry is ailed the Electric Power Sector Reform Act (EPSRA) 2005.Section 32 d) of this Act highlights the mainresponsibilities of the NERC. One of he NERC’s responsibilities is toguarantee that the prices charged by licensees are fair to customers whilst allowing the licensees to finance their activities and obtainingrational profits. In agreementwith Section 76 (2) of the Act, the NERC set a frameworktoset electricity prices which arecalled the Multi-Year Tariff Order (MYTO). The MYTO aims to reward stakeholders that perform above certain thresholds, whilst also reducing the aggregate technical commercial and collection losses, hence leading to the recovery of costs and an overall performance standards improvement. The NERC uses the MYTO to fix the bulk and retail prices for electricity in the NESI by using anintegratedmethod to ascertain the revenue requirement for the power sector. The objective of the MYTO is to fix tariffs that are cost-effective thereby causing the NESI to be self-sufficient. It delivers a tariff path for a period of 15-years for the NESI, with two minor reviews every year and a major review every 5 years. These reviews are conducted when it has been determined that there are fluctuations or changes in the macroeconomic variables used in tariff computation (for exampleexchange rates, inflation, interest rates, and generation capacity). All the variables will be appraised by the market participants during the reviews. The intents of the MYTO are: 29 • Recovery of costs and viability of the NESI to guarantee a realistic rate of returns on investment by the participants • Provision of Key Performance Incentives that are modest and achievable • Certainty and Steadiness of the pricing methodologythat boosts an effective capital injection into the industry • Risk Allocation is efficiently done among the participants In setting the tariffs for the NESI, the MYTOemploys the building blocks approach.This methodallows a combined advantage of the incentive- based regulations and price capping. The MYTO is premised on combining all costs in a dependable accounting methodology. The MYTO is built on three building blocks below to allow the returns on capital in achieving the following: - (a) A fair rate of returns on capital invested (b) Recovery of capital over the depreciation period of assets (c) Well-managed overheads and operating costs. Some macroeconomics indices that were considered in arriving at the tariff are exchange rate, inflation, invested capital, return on capital, generating capacity, load forecasts, aggregated technical, commercial & collection (ATC&C) losses, fuel costs, operating and maintenance costs, other technical data, customer population, etc. The minor tariff reviews have been scheduled for June and December of every year by NERC while a major review of the industry’s pricing structure comes up every five years. 30 5.0 COST REFLECTIVE TARIFF VERSUS SERVICE REFLECTIVE TARIFF Cost Reflective Tariff (CRT) regime is when the tariff charge for electricity have put into consideration all the inputs and parameters in the value chain before arriving at the pricing in a way that aligns electricity tariff with the cost of providing network services to customers (Passey., Haghdadi, Bruce, & MacGill, 2017). On the other hand, Service Reflective tariff (SRT) is based on availability hours of supply to incentivize the distribution companies toward improving their service by investing in network rehabilitation and upgrade. The CRT is the same for all customers while SRT is not the same across the board. Customers have been categorized using the electricity network feeders and distribution transformers. This makes it easy to track the availability hours of supply and thus determine the tariff. In the SRT regime, tariff increases according to the number of hours of supply. Nigeria as a transition electricity market has plans to achieve CRT gradually and in phases. However, the NERC failed to adjust the macroeconomic indices to achieve cost reflectivity in the Nigeria Electricity Supply Industry since 2016. The Power Sector Recovery Plan makes provision for a steadychange to cost-reflective tariffs with protections for the lesserincome earners in the country. NERC proposed atransitional review in consumer tariffs on January 1, 2020, and a gradual transition to full cost-reflective tariffs shall be attained by July 2020. The review of basic assumptions in the MYTO is highlighted in the 2016 -2018 Minor Review of MYTO 2015 and Minimum Remittance Order for the Year 2019. This review covers changes to these parameters: loss target, Nigerian Inflation Rate, US$ Exchange Rate, Daily Generation Capacity, Transmission & Administrative Costs, Tariff and Market Shortfalls, etc. Thus, it aimed to provide some certainty about revenue shortfall that might have arisen due to tariff misalignment between the MYTO tariff and Cost Reflective Tariff. Table 4 below provides a summary of the actual and projected indices for 2015 to 2021. 31 Table 4: Macro-Economic Indices of MYTO and Non-Cost- Reflective Tariffs MYTO 2015 MYTO Indices Assumptions The Reality % Variance Nigerian Inflation 8.80% 12.20% 30% U.S. Inflation 0.20% 1.54% 650% Debt Interest Rate 9.70% 20% 107% Naira Vs USDS Exchange Rate (N) 198.97 361 54% Generation (MW) 5.465 4,369 -20.0% Source: NERC Website Due to the prevalence of the COVID-19 pandemic across Nigeria, the NERC suspended the implementation of the cost-reflective regime in July 2020, thereby invariably creating a further tariff shortfall in the electricity market. Under this regime, customer tariff classes were categorized into residential (Rl, R2, R3, R4), commercial (Cl, C2, C3, C4), industrial (Dl, D2, D3), special (Al, A2, A3), and Street Lighting (SI). Conversely, on September 1, 2020, the Nigerian Electricity Regulatory Commission published the MYTO 2020, which introduced the Service Reflective Tariff (SRT) regime across the country. This became necessary due to the high number of complaints received by the Commission at the public hearings held across the country, in the first quarter of 2020, during the Commission’s consideration of the DISCOs’ application for an extraordinary tariff review. The Service Reflective Tariff (SRT) regime categorizes electricity customers into five (5) Service Bands based on the daily availability hours of supply. The service bands are: - • Band A - a minimum of 20 hours supply daily • Band B - minimum of 16 hours supply daily but less than 20 hours daily • Band C - minimum of 12 hours supply daily but less than 16 hours daily • Band D - minimum of 8 hours supply daily but less than 16 hours daily 32 • Band E - minimum of 4 hours supply daily but less than 8 hours daily The new tariff regime further collapses the tariff classes into three (3) classes namely lifeline (LFN), non-maximum demand (NMD), and maximum demand customers (MD1 and MD2). The rate methodology is directly tied to the hours of electricity supply by associated feeders. The Commission aimed to incentivize the DisCos to invest in their networks to earn more by charging higher tariffs when availability hours improves. By implication, DisCos can meet their revenue requirements when they invest in their network rehabilitation and upgrade to achieve an increase in supply. The difference between the old tariff regime and the new SRT is shown in Table 5. Table 5: Differences between the old tariff regime and the Service Reflective Tariff INDICES OLD TARIFF SERVICE REFLECTIVE TARIFF _ . Rates/tariff designed at Disco level Ratestarif designed at feeder level ... R ate Design without regard to hours of supply m the recognizing the hours of supply on each . different locations covered feeder Feeder Clnstering Not Applicable Basis of rate design is clustering of feeders by Hours of Supply into 5 clusters Customer base classified by type into 14 Customer base classified by type into 3 Dituaoer oi laru i classes (Residential, Commercial, classes (Lifeline, Maximum Demand and C lasses Industrial, Special) Non-Maximum Demand) 6.0 RECOMMENDATION AND CONCLUSION The power sector reforms are guided by government policies and regulations to ensure the success of the program. Unfortunately, there are extensive regulatory and policy changes as the government keeps given directives that are not in favour of the participants in the electricity sector. The commitment signed by both the government and investors at privatization is not adhered to and the government cannot hold investors 33 for not fulfilling their obligations since they are equally guilty. This policy inconsistency is a great disservice to the sector as it discourages local and foreign investors. A good example is the non-implementation of the Multi-Year Tariff Order as required while the government continues to subsidize the unit cost of electricity. This review has shown that inappropriate pricing of electricity in Nigeria is a major challenge to the progress that the reforms in the power sector are supposed to have gained in the past. The tariff shortfall created by the lack of cost-reflective tariff led to a dearth of required investment in the sector because of its liquidity problems. This is evidenced in the level of the dilapidated network infrastructure as DISCOs’ investment in network rehabilitation is very low compared to requirements. New GENCOs and IPPs are not coming in despite the huge energy gap that is available for new investors. It is also very difficult to get loans from the financial institution due to the poor and risky nature of the participants' balance sheets. This liquidity crisis in the sector is expected to be relieved with the implementation of a cost-reflective tariff. This will encourage investors and private developers to invest in the sector. Prepaid metering is a good strategy as customers will have to pay for supply before consumption thus eliminating debt accumulation. A true cost-reflective tariff will be shocking to consumers but the further delay in implementing this will be more aching when it is eventually done. The new service reflective tariff introduced on September 1, 2020, was halted barely one month after introduction because the workers’ unions gave notification of a nationwide strike to ground the economy. Government and workers’ unions will negotiate to bring down the SRT pricing and pay for the shortfall. Conclusively, we recommend regular annual tariff review to make up for changes in macroeconomic indexes until a cost-reflective tariff is reached. This will restore confidence in the industry and encourage both foreign and local investors to invest in the power sector. Customers will be willing to pay a cost-reflective tariff if there is a remarkable increase in supply. The service reflective tariff is a fallacy because the cost of 34 lkwh of electricity is the same whether customers get the supply for 20hours or just 1 hour. It is like robbing Peter to pay Paul as a customer living in a location with better supply will be paying far higher tariff than customers where supply is not sufficient, which is not the customer’s making. Finally, the recent agreement signed by Nigeria and German governments for Siemen's electrification roadmap should be taken business-like. This program is funded by the government for upgrades and development of generation, transmission, and distribution capacities with the target of 25000MW. The government should ensure that projects are not abandoned but completed to standards and specifications. REFERENCES Adedayo, Z. & Yong, L. (2010). “Impact of Domestic Natural Gas Pricing on Electricity Tariffs in Nigeria” IEEE Trans. Power system. Aliyu, A., Ramli, A., Saleh, M., (2013). Nigeria electricity crisis: Power generation capacity expansion and environmental ramifications. Energy, 61(8), pp. 354-367 Awosope C.A. (2014). 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International Association for Energy Economics. Fourth Quarter, pp 32 - 36 Seymour, J. (2012). The Seven Types of Power Problems, s.l.: Schneider Electric - Data Center Science Center. Transmission Company of Nigeria (2019): Transmission Company of Nigeria, www.tcnorg.com Titus Koledoye Olugbenga., Abdul-Ganiyu A. Jumah., Phillips D. A., (2013). The current and future challenges of the electricity market in Nigeria in the face of the deregulation process. African Journal o f Engineering Research. Vol. 1(3), pp. 33-39 UNDP Nigeria 2016 Annual Report (2017). United Nations Development Programme Nigeria media.ng@undp.org www.ng.undo.org USAID (2019): NIGERIA - Power Africa Fact Sheet, www.usaid.gov. 37 CHAPTER 3 Development Of An Artificial Neural Network-Fuzzy-Markov Model For Industrial Accidents Forecasting *' I. E. Edem and 20 . A. Adebimpe '^Department of Industrial and Production Engineering, University of Ibadan, Ibadan, Nigeria. “̂ Corresponding Author. E-Mail: 1ie.edem@maill.cdu.ng, 2oa.adebimpe @ mail 1 .edu.ng Abstract Industrial accidents possess the potential of causing physical, psychological and even fatal consequences when they occur. In that regard, Industrial accidents forecasting aid stakeholders in properly managing and improving workplace safety by anticipating accident occurrences to prevent or minimise their consequences. Due to the high variation, random and fluctuating characteristics of industrial accident occurrences, machine learning and Markov based models methods have become increasingly popular as a tool for understanding their occurrence patterns and detecting their vibrational directions. However, little investigation has been made towards combining the positive characteristics of these methods for industrial accidents forecasting. This study is concerned with the development of a neuro-fuzzy-Markov model for the prediction and forecasting of industrial accident occurrences. The methodology employed essentially involves the implementation of the Artificial Neural Network (ANN) model through the development of structured control methods to enhance improved forecast candidate generation potential. Further, an analysis of the model's residual was undertaken to obtain an ANN forecast correction factor by using a combination of fuzzy and Markov techniques. Based on this, 38 investigations were then carried out to determine the direction of vibration of the ANN predictor model. Subsequently, results were generated from the prediction mechanism. The model was validated by comparing its one window ahead (OWA) forecast potential with those of the ANN model using secondary industrial accident data based on the mean absolute percentage error (MAPE) and the Root Mean Square Error (RMSE). Also, an evaluation was done by comparing the forecast performances of the model with those of two traditional (Autoregressive moving average [ARIMA] and exponential smoothing [EXPSM]) models and two non-traditional (Mao and Sun grey-Markov (MSGM) and Grey-Fuzzy-Markov Pattern Recognition GFMAPR) models. The forecast performance results obtained on the model's application showed that it possessed the capability to correct and improve ANN forecasts. The MAPE and RMSE results obtained for the ANN-fuzzy- Markov model were 15.39 and 26.39, while those produced by the ANN were 20.13 and 30.57 respectively. The model produced more superior forecast when compared with ARIMA and EXPSM, and compared well with the MSGM and GFMAPR. The obtained results indicate that the model possesses the capability of carrying the predictions of industrial fire accident to an acceptable degree of accuracy. 1.0 Introduction Accident occurrences are an important component of industrial activities. Every occupational activity is inherent with potential accidents which if manifested can lead to accidents. Industrial accidents are undesired occurrences that can occur in forms such as bums, cuts, lacerations, radiation and amputations and even fatalities. Industrial accident occurrences can negatively impact the physical and psycho-social health conditions for workers and their families on the one hand, and potentially affect the fortunes and continuity of businesses on the other. As a result, understanding the dynamics of their occurrences with a view to anticipating and effectively managing them becomes imperative. 39 Forecasting accidents ahead of their occurrences is a popular practice adopted by organisations as part of their management processes (Xiaoping & Liu, 2009; Mock, Nugent, Kobusingye, & Smith, 2017). Accident forecasting is a guess at the safety state of a system (Xiaoping & Liu, 2009). In most cases, this guess is made by the mathematical or statistical characterisation of a prediction mechanism based on available information and observations (Shmueli, 2011). Generally, forecasting involves the deployment of single or multiple input dependent models (Bontempi, 2008; Manaloto & Balahadia, 2017; Makridakis, Spiliotis, & Assimakopoulos, 2018; Mapuwei, Bodhlyera, & Mwambi, 2020) to produce outputs based on the mathematical or algorithmic rules governing the deployed model. Single input forecasting models are used particularly in situations where the accident occurrence causal variables are sparse, unavailable, or difficult to extract as is the case with accident occurrences (Aidoo & Eshun, 2012; Ratnayaka, 2017), or when a simple model in terms of input data is desired (Aksoy & Dahamsheh, 2009). In this regard, traditional time series (TS) models such as Auto-Regressive and Moving Average (ARIMA), exponential smoothing and regression models find relevance and are still prevalently deployed (Ghedira, Kammoun, & Saad, 2018; Svs, 2018; Urrutia et al., 2018; Malysa, 2020). The non-traditional forms of TS models such as Artificial Neural Networks (ANN), Markov models and Fuzzy Time Series Models (FTSM) based models have become more popular in the last decade as a result of their ability to handle imprecise, ambiguous and incomplete data (Zhang, Qu, Wang, & Zhao, 2020). ANNs are computing systems that learn without formal statistical training, and possess the ability to detect complex nonlinear relationships between dependent and independent variables (Tu, 1996; Xiaoping & Liu, 2009), Fuzzy logic is used for the detection, description and representation of uncertainties (Pabu?cu, 2017) while the Markov methods possess the characteristic of detecting fluctuations and the vibrational direction of TS occurrences (Wang, Mehrabi, & Kannatey-Asibu, 2002). In their pure forms, these models have been found to perform satisfactorily from their successful 40 application in various industrial areas including weather forecasting (Voyant, Muselli, Paoli, & Nivet, 2011), health emergency preparedness (Mapuwei et al., 2020), crude oil production (Boaisha & Amaitik, 2010), stock price forecasting (Javedani Sadaei & Lee, 2014) and tool wear monitoring rolling bearings (Liu, Youmin, wu, Wang, & Xie, 2017). Furthermore, the hybrid forms of these models have also been frequently applied. For example, Ali, Yohanna, Ijasini, and Garkida (2018) applied a Neuro-Fuzzy (NF) model in electricity load forecasting and the results of the study indicated a forecast accuracy greater than 98 %. Ganesan, Annamalai, and Deivanayagampillai (2019) used the fuzzy cognitive maps Markov chain model in the prediction of stock market behaviour. Das, Naik, and Behera (2020) developed a NF and fuzzy reduction model and successfully applied it to solving problems of data classification in data mining. In addition, a fuzzy neural network-Markov model was developed by (Shi, Hu, Yu, & Hu, 2016). The results obtained from the studies mentioned show that the hybrid forms of the non-traditional, non­ linear models can be implemented in TS forecasting to produce outputs of high accuracies. Some studies have been carried out concerning the use of single and hybrid forms of the ANN, Markov and FTSM models for industrial accident prediction and prevention. Lan and Zhou (2014) applied a variant of the grey-Markov model in carrying prediction and out a single step ahead forecast of annual coal mining deaths in China. A forecast of the number of occupational accidents, death and permanent incapacitation was made by (Ceylan, 2014) using models developed by ANN models. Results obtained showed that the aim for which the models were developed was achieved. Also, Edem, Oke, and Adebiyi (2018) developed a high variation tolerant grey-fuzzy-Markov model for a one- window ahead (OWA) forecast of industrial accidents. Sarkar, Vinay, Raj, Maiti, and Mitra (2019) observe that although some efforts have been made concerning carrying out studies in this area, the literature is sparse with the domain still slowly developing. As such, more research is required in this area for improved understanding. 41 Two major problems of utilizing the ANN for TS analysis is that of the choice of ANN architecture (R. Adhikari & Agrawal, 2013; Sanchez- Sanchez, Garcia-Gonzalez, & Coronell, 2020) and overtraining minimization (Faraway & Chatfield, 1998). Both of these problems have reduced the popularity of ANN for TS prediction. Two common attempts at overcoming this problem involve the use of model comparison criteria and cross-validation experiments (Ratnadip Adhikari, 2015). The use of the Markov technique as a tool for detecting TS vibrational directions and correcting model prediction anomalies is popular and has been successfully applied in various industrial areas (Yarmohammadi & Safaei, 2012; Liu et al., 2017; Wilinski, 2019). However, little effort has been made at applying this technique in ANN TS prediction to correct and redirect forecasts that have been produced from inadequate architectures. This study is aimed at the development of an ANN-Fuzzy-Markov model for OWA forecasting of industrial accidents. The objectives include the building of the model and its subsequent evaluation with other existing models currently utilised for the same purpose. The study seeks to demonstrate the effectiveness of the Markov technique in producing accurate ANN TS forecast without consideration given to the processes of optimal network architecture development. It is hoped that the model developed will serve as an approach for accident forecasting as well as present stakeholders with an effective accident management tool. The rest of the work is presented as follows: Section 2 contains a brief presentation of the theoretical concepts of the model, a detailed description of the methodological steps undertaken in the development of the model is presented in section 3. Section 4 contains information regarding the application of the developed model and the discussion of the results obtained from its analysis and evaluation. The conclusions made from the study are presented in section 5. 2.0 Theoretical Background for the Model Development 42 The ANN-fuzzy-Markov industrial accidents (AFMIA) forecasting model is essentially founded on four concepts namely, ANN prediction procedure, fuzzy classification scheme, Markov transitions and the fuzzy-Markov probabilities determination. The ANN prediction procedure describes the method of setting up the ANN structure for industrial accidents TS prediction. The fuzzy classification scheme is concerned with capturing the imprecision detected from the prediction anomalies of the ANN while the Markov transitions are concerned with the re-direction of the prediction anomalies. The concept of the fuzzy- Markov probabilities determination is usually required in analysing situations where systems characterized by Markov properties also exhibit imprecise properties. These four concepts are subsequently discussed in this section. 2.1 General concept of Artificial Neural Network ANN forecasting is a deep learning method employed for TS analysis. Unlike linear TS models, ANNs readily learn different types of relationships between variables in the absence of do not require complex mapping function assumption functions (Brownlee, 2018). Although different variants of ANN models such as the feed-forward network (FNN) or Multi-Layer Perceptron (MLP) network, as well as the back- propagation (recurrent Neural networks [RNN]) such as Convolutional Neural Networks (CNN) and the Long-Short Term Memory (LSTM) network, exist, the general architecture for all ANN models is essentially the same. A typical ANN model is primarily made up of layers of nodes or neurons. The simplest ANN model must possess at least three neuron layers namely, not more than one input layer (responsible for receiving and processing input information), at least one hidden layer (concerned with the further processing of information received from the input layer) and not more than not output layer (which conveys the results of the information processed by the previously mentioned layers) [see Figure 1]. The key to the workings of the ANN is that within a layer, information processed, weighted and distributed to the next layer is made possible by the firing of biological system emulated signals arising from 43 mathematically derived activation functions (MacLeod, 2013). Thus at the end of the process, the output layer makes a decision or produces an inference based on the values computed in the hidden layers. The major difference between the FNN and the RNN variants is that in the FNN, information once weighted, cannot be modified as information flow is unidirectional while for the RNN, there is bi-directional information flow as the results received by the output layer can be communicated back to the hidden layer for weight readjustment towards improved learning. Input Layer First Hidden Layer Second Hidden Layer Output Layer Figure 1: Illustration of a typical ANN architecture 2.2 Neural network model structure for forecasting The procedure for the deployment of ANN for forecasting involves firstly the preparation of a set of historical data X [X\ x^i: l ,2 ,3 ,...,x E)} into the input vector form M and output vector form Y (Equations 1 and 2). M is a trajectory matrix made up of L lagged row vectors m ^i: 1,2,3,..., L) each of width N made up of a sequence of occurrences following each other. N (1 < N < xE_y) is referred to as the forecast window length. Y is a column vector made up L rows for which each row value yi(i: 1,2,3,..., L) is mapped to m* for learning and prediction. 44 It is worth noting that xE does not constitute the entire historical data, but the portion of data set aside for building the model. M and Y are subsequently fed into the built network and a supervised learning process involving setting the process to the desired number of iterations (epochs) and learning rates (Kriesel, 2010) is executed to obtain forecast. Due to the time and computational complexities involved in the manual development and implementation of the process, the use of soft computational solutions such as Keras TensorFlow (in R and python programming) have become quite popular (Brownlee, 2018; Lewis, 2018) f**1 *2 * 3 ■ X N - 1 X N \ ™ 1 *2 * 3 X 4 . X N X N + 1 m2 * 3 * 4 X 5 , X N + 1 X N + 2 M = (x f \ = ( 1) v l)'i=l,j=l ’ -x (2) yi y2 y3 Y l - 1 Y l LY — ( X N + 1 X N + 2 X N + 3 • ■X E - 1 xe y 2.3 Fuzzy set classification A fuzzy set T is defined by a set (Equation 3). Hm (x ) is called a membership function of the set and represents a discrete or continuous function that specifies the extent to which the element s, a member of crisp set M, belongs to M . s is associated with a fuzzy value that exists between 0 and 1 describing the extent in which it belongs to or satisfies some property attributed to M. Fuzzy values can be described using triangular, quadratic or exponential numbers (Bojadziev & Bojadziev, 2007). 7 = G £ [0,1] )} (3) 2.4 Markov chain probabilities Let 5 be a discrete sample space S = fo : i = 1,2,3, A Markov chain can be defined as a random variable sequence Xt (t: 1,2,3,..., 7) that takes values in X such that the probability of an event Ps.^ occurring 45 is dependent on the probability the event s t occurs at time t + 1 conditioned on the probability that event st occurred at time t (Dobrow, 2016). With consideration given to a Markov chain of finite-state (Equation 4), the probability of event st occurring for n number of step transitions is described in equations 5 and 6. Sta tes (s^ 1 2 3 . . . N - 1 N 1 pix P l2 Pl3 ■ ■ ■ P lN - l Pin 2 P i 1 P2 2 P2 3 ■ • P2N-1 Pin 3 P-n P3 2 P3 3 ■ • P3 N -I P3 N rP S;S■ j = * ’ ' N - 1 P-n-11 Pn- 1 2 Pn - 1 3 • ■ •Pn-1N—1 Pn- 1 N Pn- 1 1 Pn- 12 Pn- 13 ■ ■ -Pn-lN - 1 Pn-1 PlA = P(Xt+1) = st\P(.Xt) = st {Si, i t e S, t > 1} (5) 2.5 Fuzzy Markov probabilities Fuzzy Markov probabilities (FMB) are the probabilities of events that exhibit Markov properties. However, the precision of the state properties cannot be accurately estimated. FMB of events is determined from the combination of the concepts earlier presented in sections 2.3 and 2.4. Here, the FMB determination procedure of (Pardo & de la Fuente, 2010) is presented. Suppose a set of fuzzy states T k{k = 1 , 2 , 3 is defined such that each represents an event in the initial Markov chain (Equation 4), then the probability of a single step transition from a fuzzy initial state Tv to a fuzzy final state Tw is expressed in equation 6. P = P (T JT v) = P{Xx = w |J?0 = v) = 46 Where, PTv(i)- Fuzzy membership value for initial Markov event i, Ps Initial state probabilities; P(!FV): Fuzzy initial state probabilities; P: The single-step transition probability to the final fuzzy state Tw given the initial state event. P{TV) and P are further described in equations 7 and 8. P(Fv) = StL 1 P{Xo = (7) P = P ( ^ = w | * 0 = S i ) = s f =1 P s ^ P t J s , ) (8 ) Equation 6 can be conveniently solved to obtain P by adopting the following stepwise procedure (Pardo & de la Fuente, 2010) Step 1: Create the initial Markov chain (crisp set) transition matrix P = Ps $ of the events (Equation 4) Step 2: Create the matrix of the initial Markov chain states versus their corresponding transition fuzzy state components Q as well as that of the initial Markov chain states versus their corresponding initial fuzzy state components H Step 3: Obtain P = PQ via matrix multiplication Step 4: From H, determine PSiPTv(si) f°r Vi, P(TV) for V/c, then obtain (H*)t containing the values of • Step 5:The fuzzy transition probability matrix P for the event is finally obtained using equation 9. P = (H ')t P (9) 3.0 Methodology In this section, the APMIA forecasting model is presented. Section 3.1 gives an overview model development process. The notations and definitions employed are presented in Section 3.2. Section 3.3 contains a detailed description of the methodological steps deployed in developing AFMIA. 47 3.1 Overview of the model development process The development of the AFMIA involves the collection and preparation of industrial accidents, then deploying the prepared data in the development of the ANN prediction model. The model is used to generate various predictions and forecast which are subsequently screened based on certain performance criteria. Predictions that satisfy the screening conditions are deployed in carrying out a direction of vibration analysis to correct the ANN forecast producing a modified value in the process. If the desired ANN forecast population level and corresponding corrections are met, then a procedure for determining a single value forecast is implemented if not met, then the model proceeds to regenerate more forecast candidates. Figure 2 presents a summary of the key activities involved in the AFMIA development process while Table 1 lists the symbols and notations employed in the work. 3.2 Description of the AFMIA development In this section, each phase of the forecast model development is described in detail in the following subsections. 3.2.1 Development and implementation of ANN prediction model Given a set of industrial accident historical data D(£> = {Dt : t = 1,2,3,..., K}), the OWA forecast process aims to forecast DK+1. The first step taken towards achieving this step was to convert D into the input and output vector forms described in equations 1 and 2 with the input vector window width N set. To guide the decision on the choice of N, a partial auto-correlation analysis was carried out on D to determine the extent of the lagged relationship that exists between the data points N steps apart. Subsequently, the CNN neural network model was deployed. The CNN was built using Keras python 3.7 model with TensorFlow backend. Table 2 shows the parameters that were defined in building CNN and their corresponding values. The model was subsequently implemented by training D at different epoch values £ to obtain the vector of predictions De {Dt£: t = N + 1, N + 2, N + 3, ...,K - 1,K) and corresponding forecast D£+1. 48 Table 1: Symbols and notations CK: ANN Forecast residual CNN: Convolutional Neural Networks D f : ANN prediction made at time t N-. Swing window width Ct : Cumulative residual at time t CE: cumulative error Fc : Fuzzy correction span vector TS: Time series fi: Fuzzy membership OWA: One window ahead D \ Vector of Industrial accident historical data D c : Vector of AFMIA predictions Forecast residual direction of vibration range (VBR) M A P E : Mean absolute percentage error AS1, AS2: Accidents datasets 1 and 2. /? : Residual swing magnitude MMFCR : Method of the most frequent cumulative residual a . Residual quality RELU: Rectified Linear Activation Function /?, a \ Residual swing control parameters AdaM: Adaptive moment estimator optimiser | r t£+1|)} = * ct- i + \nE\ {(p{rt£} = p{rt£+1})A(|rt£l < | r te+1|)} (13) l\r tE\ {(p(rt£} ^ p { r t£+1})} . - 1 lr '« - rtE 1 {p[rtE} = P{rt\ i)} (14) fe + 1 - (Ct-i + |rt£| {otherwise} 3.3.2 Fuzzy classification of span residual errors The residual error spans 1), were subsequently classified on basis of their span magnitudes (SM). Three lingustic crisp SM classes namely, 52 Low {L: (0,0.330)}, Medium [M: (0.330,0.670)} and Large .//: (0.670,0)} were defined. The fuzzy membership of 0 t t+1in the defined classes were determined using triangular membership functions equations 15-17). f 1 _ 1 — 0.5/,} h = = ] l-M {0.5L < Asm{SM}u = A l m A m m A h m (19) A l h A m h A h h 3.3.3 Determination of correction span for ANN forecast The frequencies of as they occur in the different SM classes were determined, recorded and used to develop the crisp Markov transition matrix (P) as discussed in section XX (equations 18 and 20 ). Also, the fuzzy partition which shows the corresponding fuzzy states of 53 the system (Q = /X5M{5M}i;) [equations 19 and 21] was also determined. p[SM]ij = z U n X i j > 0} (20) U sASM hj = max(KASM{SM]ij) (21) It is worth noting that ASM{SM}ij is the set containing for all (ptlt+i whose fuzzy membership falls within that set. Based on P and Q and their derivatives, fuzzy-Markov transition probability matrix P was then derived using equation 9. Let R be the vector containing the upper bounds of the SM classes, then the correction span vector was obtained as, Fc = £y=i P ijR j > 0; R j = {0.330,0.679,0}} (2 2 ) Finally, the ANN forecast correction span (cPk,k+i ) was obtained as, # 0 ‘ } Gtf+l - (39) l i f j {#D& > #Da) •Vhere, Da = {D(k+l)i {C(K+l)i = £(/f+i)i}]l (40) Db = (^(K+l)£ {Q/C+l)i = ^0f+i)i}} (41) predictions D t{ t: l . . . ,K } were also corrected using a modified form of equation 38. The correction factors for the predictions were taken as the mean of their respective S[{rce} (equation 42) Df = Dt (42)( l - 0 . 0 1 S i { r t£ } ) 4. Model implementation, validation and evaluation Given the computational complexity of the model, its process routines were implemented via a computer program developed using the Keras package with the Tensorflow backend of Python 3.7 environment. The model's prediction and forecasting capability was investigated by applying it to two secondary industrial accident data obtained from the literature (Bureau of Safety and Environmental Enforcement, 2018; Gov.UK, 2020). In both cases, the datasets were split into a training set and a testing set using a 70-30 ratio format. The model’s relative performance was investigated by comparing its outputs with those of two traditional models (exponential Smoothing [EXPSM] and ARIMA). The EXPSM and auto-ARIMA feature of the SPSS software was used for the traditional models' analysis. Also, AFMIA's performance was also compared with two non-traditional models Markov based models (Grey-Markov model (GMM) and the grey-fuzzy-Markov and pattern recognition model (GFMAPR). Computer programs were developed for the GMM and GFMAPR based 59 on the theoretical principles provided by Zhan-li and Sun (2011) and (Edem et al, 2018). 4.1 Prediction and forecast accuracy In a bid to ascertain the predictive capability of AFMIA, the industrial accident data (referred here as Accident data sets AS1 and AS2 respectively) were characterized to determine their suitability for TS prediction (Table 3). It was observed in both industrial accident data sets that. This observation helped to reaffirm the observation that although dependent on organisation’s safety philosophy, industrial accidents occurrences are random, exhibiting fluctuating tendencies and non­ seasonality characteristics. These characteristics fit the data profile for which the AFMIA was developed. Table 3: Characteristics of fire accidents data to which the AFMIA was applied Industrial Characteristics of data Accidents Data Variation Fluctuation Randomness AS1 0.2462 89% 114.61% AS2 0.2162 78% 76.81 4.2 Expected performance of the model Given that the model was developed to obtain improved forecasts from the neural network predictor, the results obtained on the application of the model showed forecast superiority over the CNN-ANN base. It can be observed from Figures 3 and 4 that AFMIA exhibited'good tracking and anticipation capability notwithstanding the level of variation observed within the two data sets. A summary of the MAPE and RMSE performances of the base and corrector models (Table 4) were observed to be 18.44 and 3.48 compared to 19.68 and 4.08 of the ANN. Similarly for AS2, 15.39 and 26.39 were the respective method of evaluation outcomes obtained from AFMIA application, while the ANN forecast evaluation results were 20.13 and 30.57. From the results and based on 60 the data used, it is clear that the AFMIA is capable of correcting ANN thus improving the potential of improved occurrence monitoring. Key Actual -A- afmia -* ann Data Source: www.Gov.UK Key Actual -A- AFMIA - * ANN 61 Accidents Table 4: MAPE and RMSE of Industrial accidents prediction by the ANN and AFMIA model AS1 AS2 Industrial In -s am p le Fit O u t-o f-sa m p le In -s am p le F it O u t-o f-sa m p le Accidents Data Type Evaluation A F M IA AN N A F M IA A N N A F M IA A N N A FM IA ANN Results MAPE 19.50 15.35 18.439 19.679 8.052 7.171 16.828 21.012 RMSE 26.54 7.12 3.483 4.080 9.557 7.683 26.803 31.389 However, regarding the fitted or trained model results, Table 4 and Figures 5 and 6, show that although both models performed reasonably well, the ANN predictor results were more superior. This infers a greater degree of deep learning over the AFMIA. This tendency to overleam has been one of the problems that have hampered the progress of ANN as a TS predictor and as such a more accurate fitting may lead to an inaccurate forecast of data that was not used in the model development. Further, the fitted data is only an end to a means in itself and is only recognized in situations of little or no information regarding future occurrence accidents. As such it is not considered relevant in this study as the OWA technique used in the validation process provides a more reliable approach at determining the validity of future occurrences. 4.3 AFMIA relative performances with the traditional and non- traditional models The evaluation of the performance of the model with some of the existing models was also done. MAPE and RMSE results obtained from the application of the non-traditional model forms on AS1 were 49.94 and 10.20 for ARIMA and 20.20 and 3.92 for ESM. Given the degree of variation in AS1, the less accurate results produced by ARIMA is expected due to its inability to handle strong non-linearity situations. However, the ESM produced results that were comparable in accuracy to 62 the AFMIA (Table 5). However, for AS2, both models produced less accurate forecasts in comparison to the AFMIA (Table 5). Mxfefc ♦ k x u .k a s w s ± Afma.lt •§ ANN.lt Figue 5: ANN fitted predidions tof acddenl data AS1 and conesponding AFMlft correction R g t« 6 AW fBBd piwScSons kx acddert data AS2 and cxiroapontJ fQ AFM^ carrecllon This result indicated that the non-traditional forecasting model types may be more accurate in industrial accident prediction. This view was strengthened by the results obtained from the non-traditional models MSGM and GFMAPR (Table 4). Table 5: MAPE and RMSE of industrial accidents prediction by evaluated traditional and non- traditional forecasting models AS1 AS2 Industrial Accidents Data Type Out-of-sample Out-of-sample Evaluation ARIMA ESM MSGM GFMAPR ARIMA ESM MSGM GFMAPR Results MAPE 49.936 20.204 14.818 20.208 20.129 21.051 21.138 16.756 RMSE 10.20 3.917 2.943 4.216 31.794 30.800 32.789 27.633 It was observed that for AS1, the MSGM forecasts with MAPE of 14.82 and RMSE of 2.94 were more accurate than those of the AFMIA (MAPE 63 of 18.44 and RMSE of 3.48) although slightly so. Similarly with respect to AS2, the performance evaluation results of the GFMAPR (MAPE = 16.76; RMSE = 27.63) generally matched those of the AFMIA (MAPE = 16.83; RMSE = 26.80). This could indicate the capability of the fuzzy and Markov component of the AFMIA, MSGM and GFMAPR to capture more accurately the imprecision that exists in industrial accident data. Generally, the AFMIA performed well as an industrial-accidents forecasting tool when compared with existing forecasting models. 5. CONCLUSIONS This study developed a hybrid model (AFMIA) for industrial accident forecasting based on the use of neuro-fuzzy-Markov methods. The model was tested and validated using fitted and out-of-sample data from secondary sources. Also, the model’s capability and accuracy were evaluated against existing traditional and non-traditional forecasting models. Results obtained showed that the developed model produced more accurate forecasts than the ANN model as well as all the traditional models considered. However, AFMIA produced less accurate predictions in some cases when evaluated against the non-traditional models. AFMIA relative prediction superiority ranges evaluated in terms of the MAPE were 6 - 25%, 9-170%, and 20 - 26% over the ANN, traditional models and non-traditional models respectively. The developed model’s relative prediction inferiority range was 0 - 1 2 . Thus based on the limit of the quantitative evaluation done, the model is can be used in carrying predictions without the need for complex ANN architectural development processes. In addition, the obtained results make the model effective and adequate for the prediction, anticipation and management of industrial accidents. This work aims to present a perspective on the potential of combining machine learning techniques and related soft computing methods in the development of models with new and better capabilities through the development of the novel ANN-fuzzy-Markov industrial accident forecasting model. Further, the study increases the scope of industrial accidents forecasting as it opens up the window of the potential of 64 combining machine learning techniques and Markov based techniques in industrial accidents investigation and management. The field of machine learning in forecasting is still unfolding. 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Introduction The industrial revolution saw the rapid development of manufactured machines and production systems as well as the introduction of several consumer products that made living more interesting and bearable. For production and work systems, the main objective was to realise working prototypes of physical machinery. Once in service, the need to improve the efficiency of the systems soon arose, mainly for economic reasons. The work activities of the human operator, considered to be components of the production systems, were subject to analysis and strict control (Industrial engineering). However, while the analysis later demonstrated improved economic value, a considerably high number of work-related accidents and worker deaths also tended to be recorded. The initial effort to understand the causes of these incidents and minimise their occurrences contributed to the development of the ergonomics as an engineering discipline. This chapter provides first, an overview of my early interactions with Professor O.E. Charles-Owaba and my training and development as an ergonomics/human factors specialist. Secondly, it provides an overview 71 of ergonomics and human factors research in Nigeria, from three main perspectives: i. The current research focus, i.e., domains of ergonomics application and issues being studied. ii. Utility of the findings for solving human performance problems, within industrial and social work settings. iii. Effective development of ergonomics practice and research. 2. Interactions with Professor Charles-Owaba, training and development 2.1 Initial career development Having graduated with B.Sc. (Hons) degree in Mechanical engineering, I was convinced to pursue specialist ergonomics training after I was faced with a “fit the product to the person” type design problem, which defied my engineering design knowledge and understanding, and became clear after I stumbled and read the classic textbook “Human factors in engineering and design” by McCormick and Sanders (1982). The problem was design and construction of a consumer golf clubs cart. At this time, I was employed at Ogun State Polytechnic (Now Moshood Abiola Polytechnic), Abeokuta as a lecturer and took on the project as a private venture. My quest to pursue further studies in the subject area led me to the department of Industrial and Production Engineering, University of Ibadan (UI), to enquire about registering for the M.Sc. Industrial Engineering course, as ergonomics was identified as a specialist component of the course. Professor O.E. Charles-Owaba was the Head of Department at the time (1987). He gave me more detailed insights about the ergonomics components of the M.Sc. course, including how I could best develop myself in the subject area. The clear and detailed explanation that he provided encouraged me to register for the course. One module of the course that I found most interesting was Systems Engineering, which presents ideas that are relevant to any work systems (engineering, social, medical, etc.). In simple terms, the system thinking 72 supposes that every system (engineering, social, medical, economic, etc.) consists of two or more interconnecting elements that influence one another to determine the final state(s) of the system. Best control is gained through understanding of the inter-element influences. This thinking, I later discovered, is a key foundation to the development of the science of ergonomics. On successful completion of the M.Sc. course, I joined the department at the University as a Lecturer II in 1990 and two years later, started on the Ph.D. programme with focus on human factor engineering research under the supervision of Professor Charles-Owaba. As part of my lecturing role, I led the supervision of ergonomics related undergraduate projects, including: • Anthropometer design and construction • Maintenance manpower requirement in a depressed economy • Ergonomic investigation of an industrial task in relation to the time study • Anthropometric relationship between industrial workers and workplace-Case study • Visual abilities of people under different lighting conditions: A comparative study • Analysis of work procedures in workshop settings, e.g. auto­ repairs. The elements of my Ph.D. research included design / construction of anthropometric instrumentation, development of anthropometric databases and ergonomics - based procedures for assessment / evaluation of equipment, products and workplace designs. In those days, there were very few ergonomics text books available in Nigeria bookshops and few persons with working knowledge of ergonomics on ground. Also, as the special options of the M.Sc. course were not yet on offer, I visited other faculties to register for and attend courses which my supervisor had identified as relevant to the line of research (e.g. Statistical Methods, Human Kinetics, etc). The consequence was that my research progressed quite slowly. Notwithstanding however, under the research study, and 73 with my supervisor’s support, I secured a university research grant and undertook an anthropometric survey of female hands in relation to design and use of some traditional farming and food processing tools. I was also able to interact with lecturers in the other faculties whose interests included ergonomics. 2.2. Further training and career development The slow pace of the research, though personally frustrating, became a catalyst to look for opportunities abroad where the subject was more developed and I proceeded to the University of Nottingham to pursue the M.Sc. Human Factors in Manufacturing Systems programme, and a Ph.D. degree in ergonomics. These study programmes gave me a good grounding in the systems engineering analysis concept underlying thej ergonomics discipline, more appreciation of risk assessment principles and developed my research ability to investigate and identify solutions tc ergonomics - related engineering and social problems. I noted that, though the course was offered in an engineering faculty, it was a unique postgraduate programme with little or no input from the other engineering departments in the faculty other than to deliver modules a' designed. This structure encouraged us as students to de-emphasise thinking gained from our primary previous disciplines (e.g. engineering, psychology, etc) and adopt the unique ergonomics approach. 3. Overview of ergonomics research in Nigeria 3.1. Identification of literature for review Studies were identified through web-based searches using the Google and Google Scholar engines, using the following key words: Ergonomics, Awareness, Practice, and Nigeria. Sixty studies were selected and were mainly published research articles / papers. The studies are listed in Appendix. 74 3.2.Findings Majority of the studies (n=34) were published between 2013 and 2016, ten between 2000 and 2012, and sixteen of the studies were published between 2017 and 2020. 3.2.1. Affiliation of authors, stage settings and issues of the studies The distribution, according to affiliation of the authors, is presented in Table 1, and the distribution, according to stage setting, is illustrated in Figure 1. The specific issues addressed are presented in Table 2 The authors of majority of the studies had engineering affiliations (n=24); nine studies had authors with management science affiliations, and fourteen studies with health science (Table 1). Table 1 Distribution of the studies retrieved according to affiliation of the authors. Researcher affiliation Frequency Engineering 24 Health Sc. 14 Management Sc. 9 Education 4 Computer Sc. 3 Forestry/Env Sc. 3 Library Sc. 3 Stage setting here refers to the focus (i.e. main issues addressed) of studies in relation to humans in work situations: object / thing, human conditions, and work method / task. In the main, the focus of the ergonomist is work method / task and optimising human performance in the process, which consequently requires that the object / thing and human condition are also addressed. Engineers tend to focus on objects / things, i.e., physical artefacts (e.g. hand tools, work machines, furniture, software programmes, etc.) and achieving a functional objective. Practitioners in most other career groups (health-care providers, psychologists, sociologists, educators, etc.) are generally concerned with 75 the human conditions and how this can be changed to improve human performance. Physical Artefacts (n=6) Human Work Method Condition ............. Task (n=9) mmJBM Figure 1: Distribution of the studies according to the main issues (focus) Only nine of the studies include consideration for work method / task, which was mainly as a generic activity, or in terms of job designation (Figure 1). Asaolu and Itsekor (2014), for example, obtained information from library staff concerning ergonomics design of the computer workstations (item / object), which included recording of total time and time spent before taking a break from working on the computer (work method / task) and Musculoskeletal Disorders (MSD) type symptoms experience while working (Human conditions). Labeodan and Olaseha (2012) surveyed a group of secretarial staff at a university about their 76 awareness / level of knowledge of computer ergonomics (human conditions), and use (work method / task) of computers (thing / object). Use of computer was evaluated in terms of hours spent daily and tasks performed. Across the studies, prevalence and nature of musculoskeletal and disorders suffered by workers (and the workplace hazards) and awareness/level of implementation of interventions and policies were the most investigated issues, n=33 and n=32 respectively (Table 2). Workstation design, furniture design (including anthropometric data considerations), and working conditions / environment, were each addressed by an appreciable number of studies (n=23, n=18, n=10 respectively). None of the studies was specifically concerned with understanding the work task. Table 2: Distribution of the studies according to physical artefacts, human condition, work method/task._____________________________ Issues investigated___________________ Frequency__________ Physical artefacts (Thing/object) • Workstation design 23 • Work conditions 18 • Furniture design 10 • Machine/Equipment design 8 • Sustainable development 2 • Curriculum design 2 • Labour regulation/compliance 1 Human condition • Musculoskeletal disorders-MSD 33 • Awareness/implementation 32 • Training & competence 3 • Energy demands of work 2 • Visual acuity 1 • Job satisfaction 1 • Motivation 1 77 • Heat stress 1 Work method/task • Use of PPE 5 • Human computer work/human 6 machine work • Participatory intervention 3 • Situation awareness 1 • Manual handling-carrying, 1 patient • Job role-causal worker, designer 1 • Knowledge management________ 1_ 3.2.2. Methodologies applied The distribution of the studies according to the methodology applied and main issues investigated is presented in Table 3. Table 3 Distribution of the studies according to the applied methodology Applied methodology Frequency Field survey (FS) 17 Cross-section (CS) 24 Literature review (LR) 5 Mixed-CS and FS 13 Mixed-CS and LR 1 Majority of the studies applied cross-sectional methodologies (n=24); seventeen studies applied field surveys, five studies were literature reviews and thirteen studies involved both field study and cross-section methodologies. Field studies generally enable the most reliable results compared to cross-sectional and reviews, particularly when quantitative measures of observed phenomena are obtained. 78 3.3.Discussion 3.3.1 Current focus of research All the studies reviewed were published post 2000 and majority were post 2012. Secondly, prevalence and nature of MSD, awareness / level of implementation, workstation design, and/or working conditions / environment, was the focus of the majority of studies. Only few studies addressed organisational and cognitive issues such as Training & competence, Job satisfaction, Motivation, and situations. These observations suggested growing interest across Nigeria in ergonomics as a researchable subject (studies from the three main regions were found), and that much of the ergonomics related research is centred on the physical domain of application and characterising awareness. This also is not surprising as many work activities being undertaken are done at specific work stations and / or generally require physical effort. However, in spite of the general physical nature of many work activities undertaken in Nigeria industry sectors, organisational and cognitive issues need to be given greater prominence. 3.3.2 Utility of the findings for human performance problems With respect to providing solutions to human performance problems, research findings need to have been generated from studies that included investigation of specific aspects of a task performance, and / or provide clear insights about performance by user trials. Less than a third of the studies reviewed (n=18) included consideration for work method / task in one form or the other; 12 of these studies applied cross-sectional methodologies, which only enable associations between variables to be established and not causal relationships. Furthermore, work method/task was often investigated in qualitative terms, e.g., workers’ job roles or designated office, underlying management policy (compliance with labour standards/regulations, sustainability), and as a generic activity. The studies that included quantitative investigations were generally focused on one specific feature e.g. work posture, pattern of performance (time spent) and the impact of the task on the worker. Such studies provide only broad (non-specific) insights about tasks. In view of the fact 79 that majority of the studies were about structural fit of workplaces or equipment to workers, and/or the human physical condition effects of work, the indications are that the findings have limited utility for solving human performance problems. 3.3.3. Towards a research and agenda Majority of the studies approached the problem addressed as “a fitting the task to the man issue” (Grandjean, 1998) with bias towards the disciplines of the authors. This is seen in the fact that majority of the studies were undertaken by researchers with engineering, medical science, management sciences and education affiliations, and they mainly concerned themselves with issues related to the physical work equipment, machinery and environments, and the human condition. None of the studies was focused on work method / task. In view of the summary given above, two factors that will need to be addressed for effective development of the ergonomics discipline, particularly when it sits in an engineering department, are: • A functional / operational definition; and • The uniqueness. The definition and characteristics o f ergonomics Wojciech Jastrz?bowski coined the word 'ergonomics' in 1857 in his book "An outline of Ergonomics, or the Scjence of Work" (Zunjic, 2017). He derived the term from the Greek words: Ergon (work) and Nomos (laws) to indicate it as a science. Since then, various operational definitions have been proffered to characterise ergonomics as a professional discipline (for example: Grandjean, 1998; Wilson, 2000; Karwowski, 2012; Dempsey et ah, 2006; Zunjic, 2017). Dempsey et al. (2006) noted that the breadth of the field could be considered constrained because the “Ergo” of ergonomics means work. According to the authors, while many people may indeed limit “work” to mean activities associated with employment. The term “work” can however be interpreted broadly to include most types of activities that humans do, e.g. recreational sports 80 and social interactions. Wilson (2000) considered that ergonomics should be regarded as one of the first truly multi-, inter- and cross-disciplinary subjects that the world requires if we are to understand and improve the lives of people and societies going into the 21st century. Five common characteristics of most of the definitions proffered are: • Focus on solving human performance problems • Interactions between humans and the work environment • Design related-provides information about humans and conceptual models of artefacts • Systems-oriented • Holistic approach A clear and unambiguous definition of ergonomics is therefore needed to guide its practice and development in Nigeria, and to which all practitioners should ascribe. The engineering content and uniqueness As ergonomics is concerned with accomplishment of tasks and thereby is human centred, the discipline has drawn on knowledge from non­ engineering (human centred disciplines) such as psychology and human biology, and developed its own set of rules and investigation procedures which do not follow usual engineering protocols. However, having originated from engineering (industrial and manufacturing engineering particularly), the discipline is often practiced by engineers and sits within engineering departments of universities. The fact that ergonomics is a design related discipline means the practitioners exercise a range of skills for effective practice, which are shared with engineering. It is the exercise of such skills, particularly logical reasoning and systems approach to problem solving, that qualify the discipline to continue under the engineering banner. However, being multi-disciplinary in nature, ergonomics is uniquely different from engineering in how these skills are applied. The practitioners and researchers need to ensure that, while they seek to solve one problem, they are not inadvertently introducing new problems. For example a researcher who sets out to provide structurally fitting work 81 furniture may introduce new health and safety related problems if consideration is not given to behaviour during work. This demonstration should be the basis of all research projects undertaken. 4. Conclusions The current ergonomics research in Nigeria seems to be focused on structural fit of furniture, workstation, work environment and how the human condition is affected. Other issues, such as organisational (training & competence, job satisfaction, motivation) issues and cognitive issues (situation awareness, perception and interpretation of information) have received much less attention. Thus, much of the findings from the current research have limited utility for solving human performance problems. For ergonomics to grow with impacting effect in Nigeria, departments housing the discipline in universities and colleges need to consider making it an independent postgraduate training unit (M.Sc. and Ph.D.) with its own defined courses. Offering ergonomics as a sub-specialism of a mainstream discipline (industrial engineering, for example) at best helps to produce engineering graduates with knowledge of ergonomics (frontline practitioners), and not specialist ergonomist (strategic developers and thinkers). As a starting point, a clear and unambiguous definition of ergonomics is needed to guide the practice and development for Nigeria, and to which all practitioners and researcher should ascribe. 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In Proceedings of the first Ibadan ACM International Conference on Computer Science Research and Innovations. 90 Yisa, M. G., (2002). IT—Information Technology and the Human Interface: Ergonomics of Tractors Assembled in Nigeria. Biosystems engineering, 81(2), 169-177. 91 CHAPTER 5 Some Developments In Scheduling Algorithms *Ayodeji E. Oluleye1, Elkanah O. Oyetunji2 and Saheed Akande3 1. Department of Industrial and Production Engineering, University of Ibadan, Oyo State 2. Department of Mechanical Engineering, Lagos State University, Lagos State 2. Department of Mechanical and Mechatronics Engineering, Afe Babalola University, Ado Ekiti * Corresponding author: ayodeji.oluleye@ui.edu.ng 1.0 Introduction It is widely acknowledged that time is a resource. Particularly in today’s world, it is a critical metric of competitiveness. For designers of products and services the first to the market is key. When establishing production plans; the first to deliver is also key. The sequence of tasks is important in optimizing time metrics. Also, for effective deployment of resources, the start and finish times of the tasks in sequence aid in determining the schedules. In many respects, sequencing and scheduling are sometimes used interchangeably. While sequence represents the ordering of tasks, timetabling the sequence results in schedules. The use of time as a surrogate cost factor is due to the varied nature. Costs influences are many but time is considered at the top of the leader board. Work systems are replete with sequencing and scheduling examples. They are encountered in transport, computer, manufacturing, aviation, and banking systems among others. Even individual tasks and chores require that forethought be given to effective time management. Deciding sequences and schedules to adopt can be confounding given the many combinations possible. The challenge of scheduling is how to sift through the many feasible schedules and make good choices in good time since time is a resource and metric of competitiveness. 92 Determining optimal sequences and hence schedules have preoccupied many researchers for decades. The challenge is in the manner in which real-life problems present. The problems may be encountered in varied settings such as : a. Optimising single criterion b. Optimising multiple criteria c. Flow operations structures d. Job shop operational structures e. Single-channel inputs f. Multi-channel inputs These represent just a few of the settings, which sometimes could be a combination (hybrid). With the COVID-19 pandemic and subsequent disruptions to supply chains, scheduling systems need re-examination to enable a reconfiguration for organisations to remain going concerns. This work is an attempt at reviewing the evolution of some scheduling solution approaches. 1.1 Exact and enumerative algorithms Generally, solution methods for scheduling problems may be classified into two: Exact methods and approximation methods. In this section, the exact methods are discussed. Exact methods are solution methods that can find an optimal solution to an optimization problem (of which scheduling problem is one). Exact methods have been found to always solve an optimization problem to optimality. The following solution methods may be classified under the exact methods: 1.1.1 Enumeration methods: Enumeration methods involve the complete listing of all the items in a collection. Also, it involves the listing of all of the elements of a given set. Enumeration methods are often used to solve combinatorial optimization problems such as scheduling of machines in production planning, aircraft rotation/crew 93 scheduling in airlines as well as transport routing/scheduling in logistics. Enumeration methods lead to lots of possible solutions with the difficulty of selecting and finding optimal solutions. The number of outputs of an enumeration method may be exponential in the size of the input. Generally, enumeration methods may be classified into two: complete enumeration methods and incomplete enumeration methods. 1.1.1.1 Complete enumeration methods: Complete enumeration methods systematically consider all possible solutions. They are also called total or explicit enumeration methods. This method involves enumeration of all possible alternatives and a comparison of all of them to pick the best solution. Complete enumeration methods can be very expensive or even impossible for more complicated problems. 1.1.1.2 Incomplete enumeration methods: This can also be called an implicit or partial enumeration method. This method involves excluding parts of the solution space that are known to be sub-optimal.The method also involves the selection of alternatives by only considering parts of the solution space.This leads to a reduction in computation efforts because only the most promising solutions are often considered. Methods such as Branch & Bound (BB), and Dynamic Programming (DP) can be classified under implicit/incomplete enumeration methods. 1.1.2.2 Dynamic Programming method Dynamic programming (DP) is a mathematical optimization method which breaks problems into smaller parts. It uses recursion to break and assemble them. The focus is mainly on simplification to enable traction. The method was developed by Bellman Richard around the 1950s. Although similar to divide and conquer in terms of the breakdown of the problem into smaller sub-problems; however in the DP method, the resulting sub-problems are not solved independently. The DP method remembers the results of the smaller sub-problems and then used the same for similar sub-problems. The dynamic programming approach is 94 used to solve problems that can easily be divided into similar sub- problemsto re-usethe results obtained from these sub-problems. In the dynamic programming method, referring to the output of the previous solution is cheaper (concerning CPU cycles) than re-computing it.The DPmethod avoids repeated work by remembering previous partial results.The DP approach trades space for time. This means that instead of calculating all the states thereby taking a lot of time but no space, space is taken up to store the results of all the sub-problems to save time later. 1.1.2.3 Branch and Bounds method The branch and bound (BB) method is an enumeration technique in which schedules are discarded because they are worse off than established lower bounds. These could be single schedules or set of schedules. There are two important elements in the use of the branch and bound procedure. These are the search (branching) procedure and the bounding at nodes. The BB procedure, if well implemented, assures optimality (Oyetunji and Oluleye, 2008). i. Search Procedures There are two types of search procedures. These are depth-first and frontier search methods (French, 1982). The depth-first search procedure starts at the root node and explores the branches as far down as possible. They backtrack when better schedules are not feasible down the line. Essentially, it traverses the depths of the branch and uses a stack to determine the next vertex to begin a search, when improvements are infeasible (Fig. 1). 95 Fig. 1. Hypothetical search tree On the other hand, the frontier search procedure is a novel approach applicable to wide classes of trade-offs between runtime and program size. Frontier search reduces the memory requirement by storing only the Open nodes while deleting closed nodes once they are expanded. The depth-first procedure has the advantage of working with fewer variables at each node and thus requiring less storage while the frontier search procedure requires less calculations thereby obtaining solution quickly. ii. Bounding At every node, lower bounds must be computed for the objective function. The way the lower bound is obtained determines the efficiency of the branch and bound procedure. The lower bound gives an idea of what the value of the objective function is likely to be at the node. The typical way to develop a bound is to relax the original problem to an easily solvable problem. The relaxed problem solution bounds the original problem (Olafsson, 2002). The lowestbound nodedetermines branches to be explored. When all the jobs have been assigned, the solution is the node with the lowest value. 96 1.1.3 Johnsons’ 2-machines algorithm Johnson's 2-machines algorithm is a method of scheduling jobs in two work stations or machines. Johnson’s 2-machines algorithm seeks to find an optimal sequence of jobs to minimize makespan (the completion time of the last scheduled job). The rule also reduces the amount of idletime between two workstations. To apply Johnson’s rule, the following conditions must be met: i. Processing time ofeach job must be constant. ii. Processing times of jobs must be mutually exclusive of the job sequence. iii. All the jobs must be processed through the first work station before going through the second work station. iv. All the jobs have the same priority. Johnson's rule for the 2-machine problem can be described as follows: Step 1: List all the jobs and their processing times on each machine. Step 2: Select the job having the shortest processing time. If that processing time is on for the first machine, then schedule the job first. If that processing time is on the second machine then schedule the job last. Break the ties arbitrarily. Step 3: Remove the scheduled job from the list of unscheduled jobs. Step 4: Repeat steps 2 & 3until all the jobs have been scheduled.Johnson (1954) Illustrating Johnson’s 2-machine algorithm Suppose we have a five-jobs two machines scheduling problem as shown in Table 1. Each of the five jobs needs to go through machine 1 and 2. We are required to find the optimum schedule of the jobs using Johnson's rule for a 2-machine problem. 97 Job Processing times (mins) Job Machine 1 Machine 2 1 3.20 4.20 2 4.70 1.50 3 2.20 5.00 4 5.80 4.00 5 3.10 2.80 Solution 1. Since Job 2 has the smallest processing time (1.5 mins) and it is on machine 2, schedule job2 last.Remove Job 2 from the set of unscheduled jobs. X X X X 2 2. Job 3 has the next smallest processing time (2.20mins) and it is on machine 1, therefore schedule job 3 first.Remove Job 3 from the set of unscheduled jobs. 3 X X X 2 3. Job 5 has the next smallest processing time (2.80mins) and it is on machine 2, schedule job 5 last.Remove Job 5 from the set of unscheduled jobs. 3 X X 5 2 4. Job 1 has the next smallest processing time (3.20 mins) and it is on machine 1, schedule job 1 first. Remove Job 1 from the set of unscheduled jobs. 3 1 X 5 2 98 5. Schedule the only remaining job (4) to the only available space. 3 1 4 5 2 So, the jobs must be processed in the order 3 —*• 1 —* 4 -+ 5 —> 2 and must be processed in the same order on the two machines. 1.1.4 Johnson’s 3-machine algorithm Johnson’s 3-machine algorithm is similar to his 2-machine algorithm. Johnson extended his algorithm for the 2-machine problem to solve a variant of the 3-machine problem. Johnson (1954) considered a special structure case (i.e. problems in which the minimum processing time on the first or third machines is greater than or equal to the maximum processing time on the second machine). Mathematically, • The smallest processing time on machine 1 is greater than or equal to the largest processing time on machine 2, i.e., Min Pii > Max Pj2, Vi, j, • The smallest processing time on machine 3 is greater than or equal to the largest processing time on machine 2, i.e., Max Pj2< Min Pk3, V j, k At least one of the above two conditions must be met. Where Ptm= processing time of t* job on mm machine. 99 When the above conditions hold, Johnson (1954) forms an artificial (machines a and b) 2-machine problem by letting Pia — Pil + Pi2 Pib = Pi2 + Pi3 The artificial (2-machine) is solved by applying Johnson’s 2- machinealgorithm. 1.2 Approximation algorithms These are efficient algorithms that yield effective solutions to problems with provable guarantees on its closeness to the optimal one. The concept of complexity gives perspective on solution techniques concerning the computation requirements (Baker and Tritsch, 2013). The order-of- magnitude notation is used to measure the computational effort required by a solution method. For example, a scheduling problem of size m (mrepresents a quantum of information needed to specify the problem), the number of computations required by the algorithm is bounded by a function of m. For example, if the function has an order of magnitude m2, represented by 0{m2), then the algorithm is polynomial. However, if the function is 0(2m), the algorithm is nonpolynomial. For a function of the form,0(2m), it is called an exponential algorithm. Polynomial-time algorithms are more efficient than exponential-time algorithms given that the execution times grow rapidly with problem size. Numerous scheduling problems in practice belong to a class of optimization problems called Non deterministic Polynomial time- complete (NP-complete) problems. For these classes of problems, no efficient solution has been established (Weisstein, 2015). A problem is NP if its solution can be estimatedand verified in polynomial time. Nondeterministic implies that no specific rule is adoptedfor the estimation. If two or more problems of the same class are NP and are polynomial-time reducible to each other, such problems are called NP- 100 complete problems. Therefore, finding an efficient algorithm for a given NP-complete problem implies that an efficient algorithm can also be found for all other problems belonging to the same class since the problem can be restructured or modified to yield one another. However, many years of research in optimization has not yielded a single polynomial-time algorithm for problems in this class, and the surmise is that no such algorithm exists. This class of problem is thus called NP- hard (Non-deterministic Polynomial-time hardness) problems. Therefore, it is unlikely to obtain optimal solutions to NP-hard problems efficiently, i.e. by polynomial-time algorithms. An optimal solution can be found for an NP-hard problem either by complete enumeration or implicit enumeration techniques. In both cases, for real-life problems of practical interest, only small-sized problems can be solved due to the time complexity (exponential increased) involved. However, in real-life like industrial setting, production workshop, hospital, school among others where scheduling problems is a challenge, there is always the need to solve large problem-sized NP-hard problems. This practical importance necessitates relaxations to achieve tractability. A very fruitful approach has been to relax the notion of optimality and settle for an efficient and effective (or near-optimal) solution. It is desired that solutions be within a small multiplicative factor of the optimal value (approximation ratio). Approximation algorithms provide a provably good approximation ratioto the optimal. While there are numerous (good) approximation algorithms for several NP-Hard problems in the literature, scheduling problems of certain classes remain indistinguishablein the theory of NP- Completeness. They behave very differently when subjected to approximation algorithms (Brucker, 2007). Furthermore, there exist numerous NP-hard scheduling problems thatrequire lesser time to execute the work in the workshop using approximation algorithms than to solve the problem optimally using the fastest available computing machine. Therefore, the reliance on approximation algorithms is often the rule in practice.Furthermore, the closeness of the generated solution (approximation ratio) of an approximation algorithm to the optimum is usually established analytically either in the worst-case or on the average (Akande, 2017). 101 Experimental analyses of heuristicsare usually through several runs (via simulation) against benchmarks. Examples of approximation algorithms are dispatching rules, heuristics, and metaheuristics or evolution Algorithms. Heuristics are constructive approximation algorithms that start with no jobs scheduled and gradually construct schedules by adding jobssystematically.Over the last four decades, sequencing and scheduling problems have been solved using heuristics in the form of dispatching or priority rules. The priority or position of a job in the schedule is determined by the job or machine parameter as well as the shop characteristics. Al- Harkan (2013) classified scheduling dispatching rules into local rules, global rules, static rules, dynamic rules among others. Several Dispatching rules have been developed, investigated, and implemented by researchers and practitioners. These include; The Shortest Processing Time (SPT) rule (Smith, 1956; Bansal and Kulkarni, 2015).Modified Due Date (MDD) rule (Baker and Bertrand, 1982; Naidu, 2002), HR9 and HR10 (Oyetunji and Oluleye, 2010), Heuristic AA (Akande, 2018) among others. Special structure problems have also been explored with the aim of using the features to converge to good solutions (Oluleye and Charles-Owaba (1999), Oluleye and Jolayemi, (2000)). Furthermore, approximation algorithms that are initialized with a complete schedule with the exploration of systematic improvementsachieved by manipulating the current schedule are called metaheuristics or evolution algorithms. Some authors use heuristics and metaheuristics interchangeably. 1.3 Evolutionary Algorithms Evolutionary Algorithms are based on computational intelligence. They are also called metaheuristics. Metaheuristics are designed to provide good solutions to optimization problems with limited computation capacity (Bianchi, et a l, 2009). Methods explorean existing schedule 102 making improvements through manipulations of the optimization problem being solved (Blum and Roli, 2003). Much like heuristics, metaheuristics do not guarantee optimality though they yield better solutions over and above the initially selected schedule (seed). Evolutionary Algorithms explore local search procedures. The desire is to find a better schedule in the neighborhood.. Two schedules are neighbours, if one can be obtained by modifying the other. The method is performed through iteration. Many neighborhood solutions are generated by modification of the current solution by iteration. The method of modifying the current solutions to form a new neighbor, the acceptance-rejection criterion as well as the termination of the iterations are the basis for the classification of metaheuristics. Examples of metaheuristics include Tabu Search (TS), Simulated Annealing (SA), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Water Waves Optimization (WWO), League Championship Algorithm (LCA), and Variable Neighborhood Search (VNS) among others. (Interested readers can read more about different heuristics and metaheuristics approaches from the literature) 1.4 Some illustrative examples Some selected algorithms are to be applied to some real-life/random problems In this section, two scheduling problems; Single Machine Total Tardiness Problem (SMTTP) with zero release date and the Single Machine Total Flowtime Problem (SMTFP) with non-zero release date are considered. Some existing problems and the corresponding proposed heuristics found in the literature were explored. 1. Single Machine Total Flowtime Problem (SMTFP) with a non-zero release date Problem Definition: Given a single machine scheduling problem with a set of n jobs with minimize of the total flowtime as a performance 103 measure. It is assumed that the problem is deterministic and only one job can be processed at a time.For ^,?ry job Ji, parameters like t/ierelease time, rt the processing time pt are known. Also,the start time denoted as 5jis given by: St > rt ( 1) Also, the completion time of each job (Q) is defined as: Cj= + Pi (2) The flow time of each job defined as the time the job spent in the shop is given as the difference between the completion time and the release date: Fi= Ci - n (3) Oyetunji (2009) defined the total flow time (Ftot) as Ftot = Z U F , = F\ + F2 + F3 + . . . + Fn (4) For the problem of minimizing the sum of flowtime on a single machine with releasedatesOyetunjie/ al, (2012), proposed the KSA 1 heuristic. The steps are as follows: KSA1 Algorithm Steps STEP I : Initialization Job_Set_A = f J-J2J3 • • ■ /nL set of given jobs Job_Set_B = [0], set of schedules job Job_Set_C = [J'-rf'd'z • ■ • J'n]> set of unscheduled jobs,]'i = ]t n = number of jobs STEP 2: Find index = pt + r t for all jobs in Job_Set_A, i = 1,.., n STEP 3: List jobs in the Job_Set_A in increasing index order and put the jobs in Job_Set_C. To break ties, select first the job with the lowest n, else break tie arbitrarily.STEP 4: Add the first job in Job_Set_A, to Job_Set_B and remove it from Job_Set_C. STEP 5: Compute the Completion time, (Q) of the job scheduled in 104 step 4 STEP 6: Compute AWj = \Rj- Cj\ for all the remaining jobs in the Job_Set_D. Where Rjis the release date of each of the remaining jobs in Job_Set_D and (Cj is the completion time of jobs scheduled prior to the next target position (i-1) in Job_Set_D, j= 2, 3, ... n-1,1 = 1, 2, 3 ,..., n. STEP 7: Re-arrange the remaining jobs in Job_Set_D in the order of their increasing d^com puted in Step 6 and schedule the job with the lowest AWj in the next unscheduled position STEP 8: Repeat step 6and 7 until all the jobs have been scheduled STEP 9: Append Job_Set_D to Job_Set_B STEP 10: Stop Application Consider a 4 xl scheduling problem with the problem parameter in Table 1. Determine the total flowtime using the KSA 2 algorithm. Compare the results to the optimal value. Table 1: A 4x1 Scheduling Problem S/N R P 1 15 10 2 30 4 3 4 12 4 20 30 Solution. Optimal value can be obtained by complete enumeration or implicit enumeration. In this case, we want to explore complete enumeration. Number of Feasible Schedule = 4 1 = 4 x 3 x 2 = 24 The 24 schedule will be analyzed using the Gantt chart. 105 [ 1 234] 25 30 34 46 The Sum of flow time = 10 + 4 + 42 + 56 = 112 (NOTE: Fi= C, - r{ ) [1 2 43] 1 1 n 15 25 30 34 64 The Sum of flow time = 10 + 4 + 44 + 76= 134 [1 4 23] I I I 110 i i ii 30 ■Hi 4 li 15 25 55 59 The Sum of flow time = 10 + 35 + 29 + 67 = 141 [1 432 ] 15 25 55 67 The Sum of flow time = 10 + 35 + 63 + 41 = 149 [1 3 4 2] 15 25 37 67 106 The Sum of flow time = 10 + 33 + 47 + 41 = 131 [ 1 3 2 4] HI pass m m Hi 410 III u 30 1 1 1 15 25 37 41 71 The Sum of flow time =10 + 33 + 11+51 = 105 [ 2 1 3 4 ] I ' l l 11 12 liS il 30 34 44 56 86 The Sum of flow time = 4 + 29 + 52 + 66 = 151 [ 2 1 4 3 ] 30 34 44 74 86 The Sum of flow time = 4 + 29 + 54 + 82 = 169 o [ 2 4 1 3 ] IT l|g p&333|||||||1 10 BBM 12 iff 30 34 64 74 86 The Sum ot tlow time = 4 + 44 + 09 + 8 2 = 199 107 [2 4 31] 30 34 6 4 76 86 The Sum of flow time = 4 + 44 + 72 + 71 = 191 [2 3 41] ; m u mass 30 34 46 76 The Sum of flow time = 4 + 42 + 56 + 71 = 173 [2 3 1 4] KSSS n * 1 ■ 30 34 46 56 The Sum of flow time = 4 + 42 + 41 + 66 = 153 3 124] ŜSHH 10 16 26 30 34 The Sum of flow time = 1 2 + 11+4 + 44 = 71 [3 1 4 2] 16 26 56 60 108 The Sum of flow time = 12 + 11 + 36 + 30 = 89 [3 2 41] p a s s I 12 4 16 The Sum of flow time = 12 + 4 + 44 +59 =119 [ 3 2 1 4 ] 1 1 1 1 30 IBlil 4 16 30 34 44 The Sum of flow time = 12 + 4 + 29 + 54 = 101 [ 3 4 1 2 ] 4 16 20 50 60 64 64 The Sum of flow time = 12 + 30 + 45 + 34 = 131 109 [ 3 4 2 1] 30 111 16 20 50 54 64 The Sum of flow time = 12 + 3 0 + 24+ 49 =111 20 50 60 72 76 The Sum of flow time = 30 + 45 + 68 + 46 = 189 [42 1 3 ] 20 50 54 64 76 The Sum ot tlow time = 30 + 24 +49 + 72 = 1/3 110 [ 4 2 3 1 ] 20 50 54 64 76 The Sum of flow time = 30 + 24+60 + 61 = 175 [43 21] 20 50 62 66 The Sum of flow time = 30 + 58 + 36 + 61 = 185 [ 4 3 1 2 ] 20 50 62 The Sum of flow time = 30 + 58 + 51 + 46= 185 From the complete enumeration, the optimal schedule is [ 3 1 2 4 ] with the optimal value (total flowtime) of 71 The Proposed Approximation Algorithm: K.S.A1 ALGORITHM STEP 1: Initialization . Job_Set_A = [ 1 2 3 4], set of given jobs Job_Set_B = [0], set of schedules job Job_Set_C = [ l 2 3 4], set of unscheduled jobs,J'i =Jt n = 4 111 STEP 2: Compute the index - p t + rt for each of the jobs in Job_Set_A, i = 1, n S/N R P P+r 1 15 10 25 2 30 4 34 3 4 12 16 4 20 30 50 STEP 3: Job_Set_C = [3 2 1 4 ] STEP 4: Job_Set_C = [ 2 1 4 ] Job_Set_B = [ 3------- ] STEP 5: Completion time of job 3, (C*) = (4+12) = 16 STEP 6 : (Job_Set_C = [ 2 1 4 ] explore) : For job 2, AW j = | 16-30|= 14 For Job 1 , AWi = | 16—15| = 1----------- Minimum (Selected) i+3 = Job 4, AWj = | 16-20| = 4 Then; Job_Set_C = [ 2 4 ] Job_Set_B = [ 3 1 - - ] Completion time of job 1, (Q)= (16 + 10 ) =26 STEP 6: (Job_Set_C = [ 2 4 ] explore) : For job 2, AW j = | 26—30| = 4 ------------Minimum (Selected) For Job 4, AW j = | 26—20| = 6 112 Job_Set_C = [ 4 ] Job_Set_B = [ 3 1 2 4 ] KSA 1 gives = [ 3 1 2 4] the optimal schedule. 1. Single Machine Total Tardiness Problem (SMTTP) with zero release date Problem Definition: Given a single processor scheduling problem, where a set of n jobs have to be sequenced on a processor to minimise the total tardiness. Taking into consideration the following assumption; i . only one job can be processed at a time i i . the problem is deterministic that is the processing time (pf) and the due dates (d*) i i i . the release dates ( ) is zero A job is said to be late or tardy if it is completed after its due date. The tardiness of jobi is given by: 7) = max (0, C; — D*) The total tardiness is Ttot — 21i=i T'i The SMTTP has been established to be NP-hard. One of the most tested effective and efficient heuristics for the problem is the Modified Due Date (MDD) algorithm. Consider the five-job problem of minimizing total tardiness. Use the MDD solution method and compare the result to the optimal. (Source: Baker and Trietch, 2013) Job i 1 2 3 4 5 Pi 4 3 7 2 2 Di 5 6 8 8 17 113 SOLUTION In this case, the number of feasible schedules is = 51 = 5 x 4 x 3 x 2 = 120 This will take a prohibitive computation time using the complete enumeration. Thus, Branch and Bound implicit enumeration Techniques will be employed to find the optimal.The branching tree is as in Figure 2 Fig. 2: The branching Tree 114 Analysis of the branching tree At the step 1, the tree consists of P(0), with no job schedule. At the step 2, the problem p(0) was partitioned into n subproblems, p(l), p(2), . p(3), p(4), p(5), by assigning the last position in the sequence to each of the nodes in the first level of the branching tree. For the subproblems, put each associated job in the last position sequentially. That is, for p(l), put job 1 last, for p(2) put job 2 last, etc. The tardiness for each job at the last position is computed as follows: For p [ ------1],: Ti = max ( 0, C, — Dt ) = max (0 ,1 8 — 5 ) =13 For p [ ------2\ :Ti = max (0, Ct — D* ) = max (0 ,1 8 — 6 ) =13 For p [ ------3],: Tt = max (0, C, — Dt ) = max (0, 18 — 8 ) =10 For p [ ------4],: Tt = max (0, Ct — ) = max (0 ,1 8 — 8 ) =10 For p [ ------5],: 7j = max (0 , C, — D; ) = max (0 ,1 8 — 17 ) =1 NOTE (The completion time will be the summation of all the processing time since the last position of the job is assigned) To eliminate some redundant branches, only the branch with the minimum tardiness value is explored further.At the next stage, the remaining jobs (1,2, 3 ,4) are assigned the position,n - 1. The tardiness of each of the sub-problem is computed as follows For p[— 45],: 7) = 1 + max (0, C; — Dt ) = 1 + max (0,16 — 8 ) =9 For p[— 35],: 7) = 1 + max ( 0, C, - ) = 1 + max (0,16 - 8 ) =9 For p[— 25],: 7) = 1 + max ( 0, C/ — £>; ) = 1 + max (0 ,16 — 6 ) =11 For p[— 15],: 7) = 1 + max ( 0, C/ — D; ) = 1 + max (0, 16 - 5 ) =12 Also, the p[— 45] and the p[— 35] are explored further. This process continues until all the explored branches were explored as illustrated in Fig. 1. The optimal solution from the Branch and Bound is 11 and the schedule is (12435). 115 The Modified Due Date (MDD) heuristics for the Problem The Modified Due Date (MDD) Rule: MDD schedules the next job from unscheduled jobs set ‘U’ with the smallest priority index (ITi). The priority index is given by: n f = {max{t£ + pi ,di}} where: tj is the starting time of the next unscheduled job i(ie U) which can either be the completion time of the job in position i-1 or the release date of jobi, p£is the processing time, and di is the due date. If two jobs j and k compete to be scheduled at time t, then, job j will precede job k if II/ h (5) There must be at least a day’s break between the last game of all football group games and the first game of the semi-finals. Ix w ~ x n\ — 1 (6) There must be at least a day’s break between the last semi-final game and the final match \xr — xw| > 1 (7) The soft constraints of the soccer timetabling problem are shown mathematically as follows: There should be days off between the last game of a football group and the first game of the next football group [ X n - x ^ ^ d (8) There should be days off between the last game of all football group games and the first game of the semi-finals \xw - x n\ > d (9) There should be days off between the last semi-final game and the final match | xr - x w\ > d (10) 143 Objective Function The combination of the soft constraints gives the objective function: Let fl(t) represent equation (8). Let a l be the weight assigned to this constraint. Hence, we aim to maximize: a l / l ( t ) Let f2(t) represent equation (9). Let a2 be the negative weight assigned to this constraint. Hence, we aim to maximize: a 2 /2 (t) Let f3(t) represent equation (10). Let a3 be the negative weight assigned to this constraint. Hence, we aim to maximize: a 3 /3 (t) Combining the above three soft constraints, gives the objective function of the model: F(t) = a l / l ( t ) + cc2f2(t )+ a 3 /3 (t) (11) The University soccer timetabling model is given as Maximize F(t) = a l / l ( t ) + a 2 /2 (t) + a 3 /3 (t) Subject to: r Z p->‘ = 1 X =1 I < 1 xeCGa y = l Z Z y zeCTH Z Z Z " . = u >■ = 1 V = 1 7 = 1 144 ^i+(h+ l) Z l > h \xw xn\ > 1 \xr xw | > 1 3.2.3 Method of Solving the Soccer Timetabling Problem A decision-based algorithm is applied to solve the soccer timetabling problem. Figure 1 gives a flowchart representation of the algorithm. Given a pool of unassigned match indices and a specific time slot to assign matches to, the algorithm is given as follows: STEPO Check if there exist unassigned match indices. If yes, proceed to step 1. If no, stop algorithm. STEP 1 Randomly select the maximum number of match indices that can fit into the current time slot. STEP 2 For each unique soccer teams in the match indices selected, do: 2-A Check if the same soccer team appears in multiple match indices selected 2-B If the soccer team appears in more than one of the match indices selected, select only one such match index and discard the other selected match indices the team appears in 2-C Proceed to randomly select another n match indices from the unassigned pool to replace the n discarded index / indices above. This selection will be done such that the soccer teams 145 in the selected index in step a. above are not present in any of the newly selected match index / indices. STEP 3 For each match index in the selected match indices, do: 3-A Check if any of the soccer teams in the match index have had any immediate previous games 3-B If no, proceed to step 4. If yes, proceed to 3-C. 3-C Check if the difference between the current timeslot and the timeslot of the immediate previous game is greater than one. 3-D If yes, proceed to step 4. If no, discard the match index 3-E If this is the last match index amongst selected match indices, proceed to step 0. STEP 4 Insert match index in this timeslot 146 START No Fig. 1: Flowchart for decision-based algorithm 4. Model Application and Discussion of Results This section gives the description of the case study, collection of data, defining and solving the University of Ibadan inter-faculty soccer timetabling problem, presentation and discussion of results. 4.1 Brief description of the case study The interfaculty soccer competition in the University of Ibadan is an annual competition. This competition is held between faculties in the 147 University of Ibadan. The competition has two phases - a single-round robin group stage and a knockout stage. The competition usually consists of 12 teams split into two groups. Each team in a group plays every other team in the same group once. Two teams then qualify from each group based on a point-based system (win - 3 points, Draw - 1 point, Loss - 0 point). The two top two teams which qualify from each group (making four teams in total) then proceed to the semi-final stages. Two teams are knocked out in this stage and then the two teams which qualify then proceed to the final. The winning team at the final wins the competition. The duration of this tournament is usually five weeks. 4.2 Data Collection The data and information about the university of Ibadan inter-faculty soccer competition was gotten from the organizing sports council. The organizing sport council provided the various rules of the competition, as well as information about facilities, officials, groups, teams, fields, and so on. The values of the parameters for the competition obtained are shown in Table 2. Also, the faculty teams that will play in the University of Ibadan inter-faculty competition and their respective groups are shown in Table 3. The predefined teams that will play in soccer matches in the competitions were obtained and match indices were assigned to them as shown in Table 4. Table 2: List of Parameters and their respective values for the University of Ibadan Inter-faculty soccer timetabling problem Name of Parameter Value Number of football fields 2 Timetable Duration 5 weeks (Available days - Mondays to Saturdays) 148 Number of available days 30 Number of football teams 12 Number of football groups 2 Number of football teams per 6 group Number of soccer matches to be 15 played per group Total Number of Soccer matches 30 in the group stage Number of soccer matches in 3 knockout stages Total Number of soccer matches 33 in the inter-faculty competition Table 3: Groupings of teams in the University of Ibadan Inter faculty soccer competition 149 Group A Group B Science Law Social Science Basic Medical Sciences Pharmacy Public Health Agriculture and Forestry Clinical Sciences Technology Education Arts Veterinary Medicine Table 4: List of Soccer matches and their corresponding match indices in the University of Ibadan Inter-faculty soccer competition Match Corresponding Match Indices Science vs Social Science 1 Science vs Pharmacy 2 150 Science vs Agriculture and Forestry 3 Science vs Technology 4 Science vs Arts 5 Social Science vs Pharmacy 6 Social Science vs Agriculture and 7 Forestry Social Science vs Technology 8 Social Science vs Arts 9 Pharmacy vs Agriculture and Forestry 10 Pharmacy vs Technology 11 Pharmacy vs Arts 12 Agriculture and Forestry vs Technology 13 Agriculture and Forestry vs Arts 14 151 Technology vs Arts 15 Law vs Basic Medical Sciences 16 Law vs Public Health 17 Law vs Clinical Sciences 18 Law vs Education 19 Law vs Veterinary Medicine 20 Basic Medical Sciences vs Public Health 21 Basic Medical Sciences vs Clinical 22 Sciences Basic Medical Sciences vs Education 23 Basic Medical Sciences vs Veterinary 24 Medicine Public Health vs Clinical Sciences 25 Public Health vs Education 26 152 Public Health vs Veterinary Medicine 27 Clinical Sciences vs Education 28 Clinical Sciences vs Veterinary 29 Medicine Education vs Veterinary Medicine 30 First semi-final game 31 Second Semi-final game 32 Final game 33 Other rules concerning the tournament were stated thus: • Four teams will be eliminated from each group, leaving two teams from each group to qualify for the knockout phase • Timeslot is defined as the continuous length of time during which the match takes place. For the university soccer timetabling, since matches can only be played early in the morning or in the evening before or after lectures respectively. 2 timeslots are available per day. The number of available timeslot per day is equal to 2 timeslots per day multiply by the number of football pitch available. Timetable must span a maximum of 5 weeks, and the only available timeslots are from Mondays to Saturdays. This means there are 30 available days, available timeslot in 5 weeks is 2 x 2 x 30 = 120 153 4.3 Defining and Solving the University of Ibadan Inter-Faculty Soccer Timetabling Problem Problem parameters are estimated and weights are selected for the objective function and a decision based model is applied to solve the University timetabling problem for inter-faculty soccer competition. Defining the University of Ibadan Inter-Faculty Soccer Timetabling Problem The soccer timetabling problem is defined as the University of Ibadan inter-faculty soccer competition. The problem parameters are listed as follows: Number of football fields (s) - 2 Timetable Duration - 5 weeks Number of available timeslots in days -30 Number of available timeslots (H) - 120 Number of football teams (F) -12 Number of football groups (v) -2 Number of football teams per group (J) - 6 Number of soccer matches to be played per group (K) - 15 Total Number of soccer matches in the inter-faculty competition (U) - 33 The mathematical model for University of Ibadan inter-faculty soccer timetabling is given as Maximize F(t) = 3 ( /I ( t ) ) + 1.5 ( /2 (t)) + 2 ( /3 (t))) Subject to 154 ^ P xyz = l , V y = 1,2. Vz = 1 , 2 ......120 X = 1 5 ^ ^ Pxyz < 1 Vx = 1 ,2 ,...,33 Va = 1,2. xeC G a y = 1 Pxyz < h fo r 1 < x < 30 y zecrH xr z2 z1 2*0 = 33 V = 1 V = 1 7 = 1 z i+ (/i+ l) — Zi > 4 |xw xn| > 1 |xr — xw\ > 1 Solving the University of Ibadan Inter-Faculty Soccer Thnetabling Problem The decision algorithm was used to solve the University of Ibadan Inter­ faculty soccer timetabling problem and the result is shown in Table 5. There is 4-timeslot per day which makes a total of 120 timeslots for the available days for the match which is 30 days. For constraint of space, the result only shows the timeslot for each match and the field at which 155 the match will take place. The results in Table 5 is presented as follows; On Day 1, Match 2 takes place on field 1 at timeslot 1 while match 7 takes place on field 2 at timeslot 4. Table 5: Timetable obtained for the University of Ibadan Inter­ faculty soccer competition Available Available Match Field indices Indices days for Time Slots match 1 1,4 2,7 1,2 2 6 15 1 3 11 1 2 4 14,15 11,14 1,2 5 6 21,24 9,10 1,2 7 26 4 1 156 8 31 6 2 9 33,36 5,13 1,2 10 11 42,43 3,8 1,2 12 45 12 1 13 14 15 58,59 17,28 1,2 16 61 30 1 17 68 16 2 18 69,72 26,29 1,2 19 20 78, 79 24,25 1,2 157 21 81 19 1 22 87 21 2 23 89,92 20,28 1,2 24 25 98,99 18,23 1,2 26 101 27 1 27 28 110,111 31,32 1,2 29 30 117 33 1 4.4 Discussion of Results A feasible timetable obtained for the University of Ibadan inter­ faculty competition with the use of the decision algorithm indicates that an optimal timetable was obtained. The timetable obtained satisfies all hard constraints and all soft constraints of the University soccer timetabling problem. 33 soccer matches were assigned to 33 timeslots 158 out of the available total of 120 timeslots, Matches were played on 22 days out available 30 days. This means that there were eight seven timeslots during which no soccer match held. The field assignment shows that field 1 was used more than field 2. Out of the 33 games to be played in the University of Ibadan inter-faculty soccer competition, 18 are to be played on field 1. The remaining 15 soccer matches were assigned to field 2. The timetable obtained shows that the soccer matches begin on the first timeslot and the last soccer match, which signifies the end of the competition is assigned to the last available timeslot. The results show that the group stage matches is completed by day 26 and necessary breaks are observed in the timetable. Also, there would be a day rest before the semi-final games as well as a day rest before the final game. The results show that the decision algorithm gives a feasible timetable that satisfies all hard and soft constraints. 5 Conclusion and Recommendation This study focuses on the development of the University soccer timetabling problem. The parameters, decision variables, hard constraints and soft constraints were identified for the university soccer timetabling problem. A mathematical model was developed for the university soccer timetabling problem. The model developed was applied to University of Ibadan inter-faculty soccer competition. The competition featured 12 teams split into 2 groups, with 6 teams in each group. The competition featured a single-round robin group stage from which two teams qualified into the knockout stage. The timetable for this competition was obtained with the use of a ♦decision algorithm. The algorithm was developed to adequately cater for the hierarchical weighted soft constraints. The algorithm was applied until an optimal solution was obtained. 33 soccer games were scheduled over 120 available timeslots within 30 available days without violating any hard or soft constraint. 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Bolarinwa Department of Industrial and Production Engineering, University of Ibadan, Nigeria +234703 317 2005 mojimolati@gmail.com Abstract The domination of the energy mix of most countries across the globe by fossil fuel has been having serious effects on the climatic conditions, resulting from constant emission of greenhouse gases, GHG. It has also been found to be detrimental to human health, and as such, not less than 5 million cases of premature deaths due to local air pollution are annually recorded. Therefore, to combat GHG emissions and air pollution, there is an urgent need to adopt clean sources of energy generation, such as the renewables. This chapter discusses the meaning, history and benefits of renewable energy, highlights the common forms and sources, dwells on energy trends in Nigeria, reflects on hydropower plants in relation to technology, material selection and efficiency, as well as draws conclusions from areas covered. Renewable energy - What does it mean? Renewable energy, also called clean energy, is that source of energy that is being constantly replenished, originates from natural sources or processes and does not bring any harm to nature (Shinn, 2018; Project Solar, 2018 and Quaschning, 2019). As defined in the national renewable energy and energy efficiency policy (NREEEP) of Nigeria, renewable energy is that energy obtained from energy sources whose usage will not 171 lead to the depletion of the earth’s resources (Kehinde et.al., 2018). Examples are solar, hydro, wind, biomass energy and geothermal power. Another typical example is the bioenergy, which include biofuels, biopower and bioproducts (Bolarinwa, 2018). However, biofuel usage has been gaining popularity by the day, as biogas, a typical biofuel, is being increasingly used in both developed and developing countries. A major advantage of the renewable energy types is that they cannot undergo depletion (Shinn, 2018 and Project Solar, 2018). As the world continues to move away from fossil fuel (oil, gas, coal and so on), into the clean energy era, consumption of renewable energy types increasingly gain global recognition (Bolarinwa, 2018). Although entirely new to many parts of the world in advanced forms, humans have been using renewable energy in different forms for heating (sunlight), as means of transportation (wind for sailing) and grinding (windmills) to mention a few (Shinn, 2018). Energy is of paramount importance, as it continuously plays key roles in the technological, industrial, economic and social advancement of any nation (Bolarinwa, 2018). Historically, adoption of renewable energy started in Europe more than two thousand years ago in the form of water wheels, which forms the principles guiding the hydropower (Project Solar, 2018). Although its use dated back to around 635 AD in the Middle East and Central Asia, its perfection took place in Netherlands. Table 1 shows the historical development of renewable energy across time. Table 1: Historical development of renewable energy (Source: Richie, 2017; Project Solar, 2018; Nunez, 2019; OECD/FAO, 2019; Folk, 2020) Year Development that took place in relation to renewable energy. 1590 Windmills were the order of the day in Netherlands. 1839 Discovery of photoelectric effect by Edmond Becquerel. 1860 A famous French inventor, Augustin Mouchot perfectly developed the first solar energy system in the world. 172 1876 Kings College, London’s professor of natural philosophy, William Grylls Adams used selenium to trap sunrays for electricity generation. 1882 The world’s first hydroelectric power plant was in the United States, situated along the Fox River in Appleton, Wisconsin was commissioned. 1887 Wind turbines were built in Europe 1888 Charles F. Brush developed the first windmill for electricity generation. A total of 72 electricity generating wind turbines were available back then in Denmark. 1921 Perfection of photoelectric effect by the famous physicist, Albert Einstein. 1927 Wind turbines were commercialised in the United States to aid farming. 1930 Electricity generating wind turbines had widely spread across the United States. 1935 United States’s largest hydroelectricity system, Hoover Dam was built in Colorado for water supply to South California, Arizona and later to Connecticut. 1958 The first United States’s solar-powered satellite (Vanguard 1) was launched. 1978 The whole of Tohono Oodam reservation in Arizona was solar-electrified. 1996 Sodium nitrate and potassium nitrate were combined to enhance storage of solar energy for a longer time, especially after sunset. 2013 The world’s largest solar plant (Ivanpah) was built in the Mojave Desert of South California on about 4,000 acres of land (with construction cost of about 2.2 billion cellars). 2016 About 341,320 electricity generating wind turbines were already functioning across the globe, creating up to 1.55 million jobs across the globe. 2019 7%, 2% and 1% of the World’s energy; together with 16%, 5% and 2% of the World’s electricity supply were 173 respectively coming from hydropower, wind and solar energy. 2019 77% of the total biodiesel production, and 60% of the bioethanol production were already coming from vegetable oils and crops respectively. Forms and sources of renewable energy Renewable energy can come in different forms, depending on the primary source of the energy in question. Solar energy is obtained by arresting the radiant energy from sunlight and transforming it into heat, electricity, or hot water (Just Energy, 2020). The use of photovoltaic (PV) systems help to convert direct sunlight into electricity through the use of solar cells (Just Energy, 2020). This form of energy has continued to gain global attention, that is, it is the fastest growing and most widely acceptable nowadays, due to its efficiency and convenience (Richie, 2019; Tesla, 2020). Wind power is created when sunlight hits the earth's surface, causing a difference in temperature across different regions of the earth surface and resulting to movement of air molecules in the atmosphere (Nelson & Starcher, 2018). It is naturally harnessed using wind turbines, but requires a large region of area fields (Nelson & Starcher, 2018). In simple terms, mechanical energy is created with the wind going into the wind turbine and this energy is finally transformed to electricity (Tesla, 2020). Hydroelectric power is the form of energy that can be harnessed using the kinetic energy of water to turn a turbine, which then generates electricity from the mechanical movement of the turbine blades, usually aided by generator in most cases (Grigsby, 2018; Tesla 2020). Although about a quarter of World’s total electricity generation comes from renewables, hydropower is the biggest source of renewable energy, accounting for more than 60% of renewable energy generation (Ritchie, 2017). Hydropower energy is not only continuous, but can be predicted for proper management (Tesla, 2020). 174 Geothermal energy comes from heat trapped underneath the earth’s crust and possibly from radioactive decay (Just Energy, 2020). This heat can cause volcanic eruptions and geysers when released at once naturally. It can however be arrested and used to generate geothermal energy, using the steam coming from the heated water pumping below the surface and rising to the top to operate a turbine (Just Energy, 2020; Tesla, 2020). Other forms of renewable energy include biomass, hydrogen, fuel cells, hydrogen fusion, and ocean tides (Johansson et. al. 1993). The use of biomass, as renewable energy is not only common, but ancient (Ogunsola, 2007: Tesla, 2020). A typical example is the burning of wood. It involves using both organic and natural materials, which are later transformed into some other utilisable forms. The technologies adopted today are such that tend not generate CO2 gas. Renewable energies supply up to 26% of the entire electricity presently available worldwide (Folk, 2020). This has been estimated by IEA to increase to about 30% by the year 2024. Figure 1 shows some common forms of renewable energy. Fig. 1: Common forms of renewable energy (Source: Pazhamkavil, 2014) 175 Benefits of renewable energy The major benefit of renewable energy is that since it does not undergo depletion, the problem of emission of greenhouse gases, hence global warming is not there (Bolarinwa, 2018; Tesla, 2020). This makes both the atmosphere and environment to be free from pollution. It also plays vital roles towards the survival of mankind. For instance, it is equally useful for cooking, heating of water and space, electrification, farming, industry, food processing and storage, education, mineral'extraction and processing, water damming to mention a few (Asokoroogaji, 2011; Project Solar, 2018). Biomass helps to minimise landfills and produces no greenhouse gases (GHG). In more specific terms, benefits of renewable energy are numerous and include: (1) Improved public health and environmental conditions. (2) Constant availability and limitless supply. (3) Reduction of energy costs. (4) Creation of more employment opportunities. (5) Possibly embarked upon on both small and large scales to cater for both domestic and industrial energy consumptions. Nigeria and energy trends While attainment of clean energy is one of the 17 sustainable development goals of the United Nations, of which Nigeria is a member, energy demand in Nigeria is still higher than the present supplies (Kehinde et. al„ 2018). Setbacks keep recurring in her energy sector (Nwagbo, 2017; EIA, 2020). In 2017, energy consumption in Nigeria was estimated to 1.5 quadrillion British thermal units, BTU (EIA, 2020). This is mostly derived from natural gas, petroleum and other liquids (97%). The remaining quota (3%) came from renewables, coal, biomass and waste. While Nigeria’s electricity generation capacity was about 12,664 MW in 2017; 10,522 MW (83%) came from fossil fuels, 2,110 MW (about 16%) was from hydroelectricity. Only 32 MW (1%) came from 176 solar, wind, biomass and waste (EIA, 2020). As a result of this under­ capacity electricity generation, up till the end of 2018, just about 60% of Nigerians had access to electricity supply. In 2018, Nigeria was the highest producer of oil and natural gas in Africa, and was the fifth-largest exporter of liquified natural gas worldwide, coming after Qatar, Australia, Malaysia and United States (EIA, 2020). Her exportation of about 982 Bcf of LNG accounted for about 6.5% of the global LNG trade. While India was the largest importer of Nigerian crude oil, Spain emerged as the largest importer of her LNG, followed by India and France (EIA, 2020). The 2018 estimate of EIA indicated that while crude- oil is mainly used for backup power generation in Nigeria, most of the electricity generation coming from fossil fuel is from natural gas (EIA, 2020). These 2 products have remained the country’s main source of income. IMF estimated that alone in 2018, Nigeria realised about $55billion from the sales of oil and gas. Unfortunately, the non-oil revenue constitutes just about 3.4% of gross domestic product (GDP), about the lowest in the world (EIA, 2020). Towards the end of 2019, while Nigeria’s proved crude oil reserves was estimated to 37 billion barrels, her proved natural gas was estimated to 200.4 trillion cubic feet (Tcf), and marketed natural gas of about 1.6 Tcf (EIA, 2020). The country has since increased her LNG by about 365 billion cubic feet (Bcf). On the other hand, Nigeria ranked the 7th largest natural gas flaring nation in 2018, flaring up to 26.1 Bcf (EIA, 2020). Renewable energy from hydropower, which is the bedrock for electricity generation into the Nigeria national grid, has been in existence since around the middle of the twentieth century (IIED, 2012). Presently in Nigeria, there are three major hydropower plants all together generating about 1.9 GW hydropower capacity (Ufondu et. al., 2019). These are located at Kainji, Jebba and Shiroro. Whereas, the extent of the industrial growth of a nation largely depends on available energy and its utilisation. Prospects exist for renewable energy in Nigeria due to its ability to provide energy in the remote areas (BED, 2012). For instance, the technical potential of solar energy in Nigeria is estimated at 1.50 x 108 joule of useful energy annually on a 5% device conversion efficiency, which almost equals 258.62 million barrels of oil on annual basis (Nwagbo, 2017). Nigeria 177 also has the capability to harness wind for electricity generation. While a wind data survey was conducted between 1979 and 1988, as at 2017, about 30 wind stations have been developed (Nwagbo, 2017). In the case of hydroelectricity, recent studies by experts show that only 24% of large and 4% of small possible hydropower generation in Nigeria have been embarked upon. Although renewable energy is undoubtedly available in Nigeria, it is yet to take its full course! Government policies are regularly put in place to coordinate the activities of this sector. For instance, the Nigerian government, in 2003 introduced renewable into the national energy grid. This came up again in the 2005/2006 renewable energy master plan (REMP), whose successful implementation means adequate wind, solar PV, solar thermal and hydroelectricity sources by 2025 in providing an equivalent of the capacity available in Nigeria today (Nwagbo, 2017; Ufondu et. al., 2019). NREEEP to actualise the objectives of REMP and REAP (renewable energy activation plan). The government also came up with the national biofuel policy in 2007 and incentive for integrating the agricultural sector in order to improve the quality of automotive fossil-based fuels in Nigeria. Other governmental efforts put in place to develop the country’s energy sector include the rural electrification strategy and implementation plan (RESIP) and the building energy efficiency code of 2017 to control the cost and availability of energy at domestic and industrial levels, as well as minimising wastage (Ufondu et. al., 2019). Nigeria’s energy problems are created by very poor maintenance of her power sector, especially the electricity facilities; bad electricity transmission and distribution network; as well as shortages in natural gas supply (ELA, 2020). Table 2 shows some of Nigeria’s energy resources (Akorede et. al., 2017). Table 2: Energy Resources in Nigeria (Source: Akorede et. al., 2017) Resource Reserves Production Utilisation (natural units) level (natural (natural units) units) Crude oil 36.22 billion 2.06 million 445,000 bpd barrels bpd 178 Natural gas 187 trillion SCF 7.1 billion 3.4 billion SCF/day SCF/day Coal and 2.734 billion Insignificant Insignificant lignite tonnes Tar sands 31 billion 0 0 barrels of oil equivalent Large 11,250 MW 1,938 MW 167.4 million hydropower (167.4 million MWh/day MWh/day) Small 3,500 MW 30 MW (2.6 2.6 million hydropower million MWh/day MWh/day) Solar radiation 3.5 - 7.0 excess of 240 excess of 0.01 kWh/m2/day kWp of solar million PV or 0.01 MWh/day solar million PV MWh/day Wind 2 - 9 m/s at 10 " m height Biomass 11 million 0.12 million 0.12 million (Fuel wood) hectres of forest tonnes/day tonnes/day and woodland Biomass 245 million 0.781 million not available (Animal waste) assorted tonnes of animals in 2001 waste/day in 2001 Energy crops 72 million excess of 0.256 not available and agric. hectares of million tonnes residues agric. land and of assorted all waste lands crops residues/ day in 1996 * SCF - standard cubic feet * bpd - barrel per day 179 Hydropower plants and available technology Hydropower, produced from water’s kinetic energy is one of the most reliable and efficient sources of renewable energy. (Elbatran et. al., 2015). The amount of electricity possibly generated by one hydropower plant depends on the head and flow rate of the river being used, in addition to turbine efficiency and depth (Jawahar, 2017). The existence of hydropower can be traced back to the era during which it was used to grind millet and grain (Lewis et. al. 2014). The technology involved determines the resulting hydropower plant (Yaakob et. al., 2015). Possibly available technology can be: (1) Run of River (RoR) (2) Pumped storage (3) Dammed reservoir. (1) Run of River: This produces electricity by means of the water flowing from the natural range of the river topography, and as well utilises other components within the area. (Egre & Milewski, 2002). (2) Pumped storage: This pumps water during off-peak hours when electricity is in excess, into an upper storage basin (Hadjipaschalis et. al., 2009). Afterwards, the water flow is reversed, and as such, the water falling through a height creates enough kinetic energy to turn the turbines at the base and generate electricity during peak load. (Mahlia et. al., 2014). (3) Dammed reservoir: This utilises constructed dam(s) to generate electricity by creating a large mass of standing water known as a reservoir, once this body of water is released through the dam gates, electricity is generated by converting resulting kinetic energy and mechanical energy from the flowing water using turbine and generators. (Cemea, 1997). In terms of capacity, the quantity of energy generated by the plant determines the size of the hydropower plant in question (Sopian and Razak, 2009). Based on this, hydropower plants can be categorized as: 180 1. Large hydropower plant: Capacity greater than 10 MW. 2. Small hydropower plant: Capacity ranging between 1 and 10 MW. 3. Mini hydropower plant: Capacity of 100 KW to 1 MW. 4. Micro hydropower plant: Capacity of 5 Kilowatt to 100 KW. 5. Pico hydropower plant: Capacity less than 5 KW. The Pico hydro energy source is simple and economical to set up (does not require a dam) and with high efficiency rate (Basir and Othman, 2013). It is a form of clean energy source that does not rely on non­ renewable energy sources, and most times use the run of river (ROR) technology. It can exhibit up to a maximum of 5 KW output of electricity output (Zainuddin et. al., 2007; Basir and Othman, 2013). This energy source is useful for indoor and streets lightning, powering of TV and radio sets, telephones, refrigerators, farming purposes and poultry rearing, charging of mobile phones and so on. It can be adapted in communities wherein the energy consumption is not much, especially in villages and remote areas to which it is impossible or expensive to extend the national grid (Basir and Othman, 2013). The Pico hydropower system of electrification has been widely adopted in Malaysia (Basir and Othman, 2013), Thailand (Chuenchooklin, 2006) and Rwanda (Kabeja, 2018) in recent times. It is known as a versatile source of power (Chuenchooklin, 2006). Figure 2 shows the setup of a typical Pico hydropower plant. Fig. 2: The Pico hydropower plant (Source: Jawahar and Michael, 2017) 181 Components o f the hydropower plant The hydropower plant consists of the following components (Anupoju, 2020): 1) Forebay: Basin area of the hydropower plant which temporarily stores water before it is transported to the intake chamber. 2) Intake structure: Directs the water coming from the forebay to the penstock. 3) Penstock: Laid pipes, usually large, for sending water to the turbines. 4) Surge chamber: An open top cylindrical tank for controlling pressure in the penstock. 5) Turbines: Converts the resulting kinetic energy to mechanical energy. 6) Powerhouse: The building that houses the hydraulics and electrical parts for protection. 7) Draft tube: Particularly used with reaction turbines to connect the turbine outlet to tailrace to enable water discharge with safe velocity. 8) Tailrace: Channels the water from turbines to the stream to avoid plant damage, in the form of lowered efficiency, cavitation, damaged turbine blades, due to silting or scouring resulting from unguided flow of water from the powerhouse. 9) Generator: Converts generated mechanical energy to electrical energy. The Turbine as a critical component Without the turbine, generation of electricity would not have been possible. The reason is that it converts available mechanical energy to electrical energy by coupling to the generator, the shaft of turbine. It operates in such a manner that high pressure is generated, which in turn rotates the shaft and makes the generator to produce electrical energy (Anupoju, 2020). Turbine types can be: 182 1) Impulse turbine: Otherwise known as the velocity turbine. Example is the Pelton wheel (Figure 3). The impulse turbine operates by a principle based on the Newtons second law of motion, in which a water jet coming from a nozzle standing-still touches a properly designed blade which subsequently generates a turning force that spins the turbine, thus removing the kinetic energy of water touching the blade of the turbine. The blade movement then converts pressure into kinetic energy. The discharge the water pressure at atmospheric pressure (Benzon et. ai, 2016). The performance of impulse turbine is at its best when water head is high but water-flow is low. (Norman, 2003). 2) Reaction turbine: Otherwise known as the pressure turbine. Example is the Francis turbine. A reaction turbine builds torque as a result of the interaction between pressure and the weight of water. The principle of operation here is guided by Newton’s third law of motion. (Paish, 2002). Reaction turbines become useful at sites with low head but high flow of water, unlike the impulse turbines. (Norman, 2003). Pelton Fig. 3: The Pelton turbine (Source: Basil and Keroh, 2013) 183 Hydropower plant and material selection Materials can be selected from a wide category of materials, such as metals, ceramics, polymers and composites. Selected materials must be able to serve the purpose for which they have been selected, and leave behind no limitations (Saidi et. al., 2019). For example, in designing the turbine, selected material must be able to ascertain resilience and possess a high load bearing capacity. Where necessary, thick aluminium blades are utilised to resist wear and tear. Moreover, in order to reduce maintenance cost acquired from periodic painting, frames may be made with galvanised steel to avoid corrosion, at the expense of weight. In a nut shell, material selection is very crucial in the manufacture of hydropower plants, in order to ascertain good quality, durability, sights appeal, adequate in-built properties (physical and mechanical) and reasonable production cost. The selection is guided by number of factors, such as available technology, cost, available materials, product safety, expected functions and so on (Saidi et. al., 2019). It is best done at the early stage of product development, especially when the expected functions of the system are being considered. Hydropower plant and efficiency Efficiency of the hydropower plant can be affected by the efficiency of the generator, penstock, design of the tailrace, as well as efficiency of the turbine, which itself is dependent on the nature of the water source available, that is, on the head and flow rater of the river in question (Basir and Othman, 2013; Anupoju, 2020). For instance, to maximise the output, a step-up transformer may be introduced in order to raise the output voltage. Also, the blades of the turbine can be provided with metal enclosure to increase efficiency. Where necessary, well lubricated ball bearings are to be used to overcome friction. Nigeria and renewable energy Despite the fact that renewable energy from hydropower has been in existence since around the middle of the twentieth century in Nigeria, serious explorations in different dimensions did not commence until 184 around the end of the same century, particularly in the area of photovoltaic (PV) panel solar power (IIED, 2012). Although electricity generations from Nigeria’s gas power stations would have overtaken that of her hydropower plants in terms of quantity, the gas stations continue to encounter problems due to unstable gas supplies and poor state of the national grid (IIED, 2012). The history of renewable energy in Nigeria is somehow short, with the public’s opinion of seeing solar energy and wind power as the only available sources of alternative energy (IIED, 2012). Some of the achievements, successes and limitations of associated with renewable energy in Nigeria have been identified. Achievements and successes of renewable energy in Nigeria Water pumping: The use of renewable energy to power boreholes for the provision of clean and safe drinking water. This has come a long way in overcoming the problem of unstable electricity from the grid with which to operate boreholes, especially in towns and villages, as well as fueling generators where present. For example, the water borehole drilling projects of the Niger Delta Wetlands Centre (NDWC), using solar power since the mid-1990s (IIED, 2012). Figure 4 shows the basic components of a typical DC solar water-pumping system. Sunmodule m Control unit m Solar water pump m Water reservoir 185 Fig. 4: Basic components of a DC solar water-puraping system (Source: IIED, 2012) Lighting projects: Renewable energy has been in use for a while now in Nigeria for powering street lights, security lights around banks, schools, campuses, organisations, laboratories, hospitals and research institutes. This has helped to reduce the use of generators, hence noise and air pollution, as well as fueling and maintenance costs. Hospitals and medical stores: Renewable energy has been useful in powering the theatre for surgical operations as well as refrigerating certain medicines and vaccines that require being stored well below room temperature in Nigeria. An example of such vaccine is the polio vaccine (IIED, 2012). Household usage: Renewable energy is commonly used as an alternative to the national grid supply in some urban homes in Nigeria, and as source of electricity supply in rural areas not having access to the existing national grid to light house bulbs and power TV sets, radios, fans, etc. Bank and office usage: Renewable energy is also used in Nigeria as an alternative to both national grid and generators for electricity supply to banks and offices to power computers, type-writers, printers, projectors, telephones, security doors and safes, fans, etc. Information and communication technology: The use of renewable energy in Nigeria has been aiding information and communication networks by improving access to the internet. Without renewable energy as a stable option of electricity supply, eased access to the internet using band-widths, modems, WIFI, etc. would not have been possible. Surveillance and security checks: Renewable energy has been used to power CCTV in some homes, offices, streets, banks, religious and other institutions in Nigeria for surveillance and security checks. Job opportunities: Renewable energy installations continue to create jobs for the willing unemployed in Nigeria, especially those with skills along 186 that area and others that have been able to acquire necessary skills through training by experts. Some limitations associated to renewable energy in Nigeria Set-up cost: The initial set-up cost is usually high, that is, it is capital- intensive and as such, not many people can afford it in Nigeria. Maintenance cost: The maintenance cost is also on the high side, especially with solar systems in which batteries need to be replaced periodically. Awareness: Renewable energy is still relatively new to many Nigerians, as a result of this, it is not wide-spreading as expected. Destruction o f aquatic lives: Aquatic lives are usually endangered or destroyed in places where the source of renewable energy is by means of river or dam. Solution development to renewable energy problems in Nigeria 1) The government must pay special attention towards strengthening the growth of renewable energy in Nigeria by integrating existing projects and widening research scopes in the area of renewable energy (IIED, 2012). 2) Government can also release funds for the pursuit of major pilot projects, and incentives to researchers to boost their morale. 3) The general public need to be well sensitized by the government to increase awareness so that consumers can show better interest in digressing to renewable energy and investing therein. 4) Both policymakers and renewable energy experts need to work together to come up with best practices of renewable energy that will function effectively in specific areas, in particular the rural areas to cater for the necessary amenities, such as water, hospitals and schools (IIED, 2012). 187 5) Renewable energy education may as well be incorporated into schools curricular in order to encourage wide participation of the public towards developing renewable energy projects (IIED, 2012). Conclusion While availability of energy remains crucial towards the development of a nation’s economic and industrial growth, means of overcoming the problems associated with fossil fuel consumption for energy generation have been traced to using renewable energy in its place. With examples including solar, hydroelectric power, wind, biomass energy and geothermal power, renewable energy is a safe source of energy because it is clean (neither harms nature nor undergo depletion) and also readily available. The consumption of renewable energy continues to increase as the world gradually digresses from the use of fossil fuels. Nigeria, although with 3 major hydropower plants still suffers from energy shortage due to under-capacity production of electricity and improper maintenance of available electricity facilities; poor electricity transmission and distribution network; as well as shortage of natural gas supply, as a result of gas flaring. Hydropower, as a renewable energy source is very reliable and efficient. The smallest available capacity, which is the Pico hydropower plant can be established on a small scale, especially in remote areas as it is simple to construct, economical, yet a very clean source of energy. To ensure high quality, durable and efficient hydropower plants, materials must be carefully selected, bearing in mind product safety, available technology, cost and expected functions at the early stage of the design. Aside renewable energy from hydropower, other notable projects did not kick until towards the end of the twentieth century. 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International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering. 3(11). World Academy of Science, Engineering and Technology. Retrieved 193 from, https://www.researchgate.net/publication/280688181- Design-and-Development-of-pico-hydro-generation-system-for- energy-storage-using-consuming-water-distributed-to- houses/citation/download 194 CHAPTER 8 Application of Deep Learning in Disease Prediction S. C. Nwaneri1 * and C. O. Anyaeche2 '• Department of Biomedical Engineering, Faculty of Engineering, University of Lagos, Akoka, Lagos State, Nigeria z Department of Industrial & Production Engineering, University of Ibadan, Oyo State, Nigeria ♦Corresponding Author E-mail addresses: 1snwaneri@unilag.edu.ng, 2osita.anyaeche@ui.edu.ng 1. Overview of Deep Learning 1.1 Definition of Deep Learning Traditional computers are limited by their inability to reason like humans. With advancements in the field of Artificial Intelligences (AI). modem computers can be programmed to reason like humans with the ability to understand patterns and take decisions based on available information. An essential component of AI is machine learning (ML), generally defined as a field of AI that finds patterns from empirical data using algorithms (Wittek, 2014). Deep Learning (DL) is a very important branch of ML composed of artificial neural networks (ANNs). In ANNs, learning could be deep or shallow. DL is a term that refers to a class of ML algorithms mostly ANNs that makes use of multiple layers in the extraction and transformation of higher level features from the raw input (Deng and Yu, 2012). DL involves learning with deep architectures. Deep learning originated based on the need to overcome the limitations of shallow architectures. Shallow architectures are not fully able to handle complex real-life problems due to their limited modelling and representation power. The substantial increase in the amount of data available, as well as improved computational power have necessitated the use of DL in recent times as traditional ML methods are incapable of handling big data efficiently (Aggarwal, 2018). The performance of DL 195 networks is further aided by graphics processing units (GPUs) in modem computers. DL proves very useful when simpler networks are unable to give the desired level of accuracy. Interestingly, DL can be applied in several areas of human life such as in: speech and language processing, programming of driverless cars, customer relationship management, detection of financial fraud, healthcare and bioinformatics. For instance, in driverless cars, a huge amount of data can be fed into DL system which could be trained to function autonomously having learnt from experience. 1.2 Classical Deep Learning Neural Networks Classical DL networks are made up of several features similar to conventional multilayer ANNs. The distinguishing features include the number of layers, GPUs, and the type of activation functions that enhance their performance. Common examples of DL networks are briefly described. i. AlexNet - A Deep Convolutional Neural Network (CNN) model that was developed to classify about 1.2 million high resolution images in the ImageNet Large Scale Visuai Recognition Challenge (LSVRC) 2010 competition into the 1000 different classes. It was developed with the ReLU activation functions and consists 60 million parameters, 650,000 neurons in 8 layers (Krizhevsky et al., 2012). i. GoogleNet -This is a Deep CNN developed through a collaborative research partnership between Google and some universities developed for image classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The network is 22 layers deep and was developed using ReLU activation function. In addition, it performs dimension reduction lx l convolution with 128 filters (Szegedy et al., 2015). 1.3 Activation Functions for Deep Learning Activation functions enhance the ability of ANNs to handle complex problems by adding non-linearity to the network. The power of multilayer ANNs is increased by activation functions. Conventional 196 activation functions are generally used in the initial development of ANNs. A well-known example is the Sigmoid activation function. However, their performance is limited by the vanishing gradient problem (VGP). The VGP is responsible for the difficulty in training ANNs with many layers, as it can cause the gradient of the loss function to be too smarll wfor t=raining.The Sigmoi di ta?cti vation function is calculated thus: (Wang et al„ 20(2i0d): The derivative of the activation can be written as: dy _ exp(-x) dx (l+ exp(-x)) (1.2) Tanh activation function is an improved version of Sigmoid activation function and is computed as: / ( * ) = (13) The gradient of Tanh activation function is computed as: dy _ 4.exp(2x) dx (exp(2x)+l)2 ' ' ' However, in DL and most multi-layered neural networks Rectified Linear Activation function (ReLU) and Hard tanh activation functions are mostly preferred. 1.3.1 Rectified Linear Activation Function This refers to a piecewise linear function commonly used in DL to generate an output that is exactly the value of the input if it is positive, otherwise, it will output zero. ReLU is mostly preferred in networks with many layers due to its ability to overcome the VGP and given as (Wang etal., 2020): (1.5) 1.3.2 Leaky RELU The Leaky RELU activation function is designed to return the same value if the input is a positive number, but it gives a negative value scaled by 197 0.01, if the input value is negative. It was initially developed to address the dying neuron problem of RELU (Iuhaniwal, 2019). 1.3.3 Hard Sigmoid The Hard-Sigmoid function can be approximated to generate improved outputs than the Sigmoid. It is defined mathematically as (Nwankpa et aL. 2018): f(x) = max ( 1.6) 1.3.4 Hard Tanh Activation Function Hard Tanh is a variant of Tanh Function used in DL applications. It is computationally cheaper and more efficient than Tanh Function with a range of between -1 and +1 (Ingole, 2020). 1.4 Backpropagation Algorithm Backpropagation algorithm is often used in training multilayer neural networks to minimise the errors between desired and actual outputs by adjusting its weights and biases. For this to be achieved, it computes the partial derivative of the cost function using the chain rule by a combination of the forward and backward pass approaches (Aggarwal, 2018). The forward pass through the network computes the overall output across the various layers of the network which is then compared with the desired output. The derivative of the cost function is then computed. The Backward pass follows immediately thereafter with the application of the chain rule to leam the gradient of the cost function in the backward direction beginning from the output node (Goodfellow and Courville, 2016). Consequently, the weights are adjusted. Consider a multilayer feedforward neural network with an input vector x, an activation function, N layers, hN~x hidden layers, Upweights from node j in layer N-l to node k in layer N, The output of the first hidden layer is calculated as: h(1) = wx + b (1.7) The cost function, C is computed as: c = £ i r = i ( y - y ) 2 ( 1-8) 198 The cost function is minimised using the Gradient descent algorithm. J£ _ = ££ J L n 9) aw" as ‘ awN K ’ The gradient in the penultimate layer is calculated as (Rawat and Wang, 2017): ac _ ac as an"-1 aw"-1 ~ as ' ah"-1 ' aw"-1 ( 1.10) The gradient in the layer before the penultimate layer is calculated as: ac _ ac as an"-2 aw"-2 ~ as ( 1.11) ' an"-2 " aw"-2 The gradient in the first layer is computed as: ac _ac as_ atf_ aw2 ~ as ' an2 ' aw2 ( 1. 12) 1.5 Deep Learning Optimisation Algorithms DL networks are trained to minimise the loss function using various optimisation algorithms. The most common are Gradient descent, Stochastic gradient descent (SGD), Newton’s method, Batch stochastic gradient descent with momentum, Adagrad, Adaptive moment estimation (Adam), Adadelta and Root Mean Squared Propagation (RMSprop) (Sun and Scanlon, 2019). 1.5.1 Stochastic Gradient Descent Stochastic Gradient Descent is an optimisation technique, that calculates the degree of change of a variable in response to the changes of another variable using a few randomly selected samples. In the conventional Gradient descent algorithm, the parameter 6, of the loss function,/(0) is updated as (Sun et al., 2018): e = e - ccV gE um (1.13) In equation (1.13), the expectation, E is obtained by estimating the cost and gradient on the entire training data. SGD eliminates the expectation in the update and calculating the gradient of the parameters using only a single or a few training examples as indicated in equation (1.14) 6 = 0 - aVe; ( 0 ; x « y « ) (1.14) 199 1.5.2 Adaptive Moment Estimation (Adam) The Adam optimisation algorithm is an adaptive moment estimation algorithm that combines the benefits of Adagrad and adaptive learning rates. Adaptive learning rates are considered to be modifications to the learning rate during the training phase by reducing it to a pre-defined value. Root Mean Squared Propagation, was designed to reduce the learning rate at a slower rate in relation to AdaGrad. The Adam optimisation algorithm developed by Kingma and Ba (2015) is shown in Figure 1. Consider a stochastic scalar differentiable objective function f(0) with each function f1(0 ) ,... , ,fx(0) achieved at specific timesteps 1, ........... T. The main aim is to minimise the expected value of the objective function, E[f(0)]. The gradient at timestep, g t is given by gt = V 0 f t(0) (1.15) Let mt represent exponential moving averages of the gradient, and vt the squared gradient, where the hyper-parameters p2 £ [0.1) control the exponential decay rates of these moving averages (Kingma and Ba, 2015). 200 The algorithm is summarised as: Set initial parameter vector v0 Initialise 1st moment vector, m0 «- 0 Initialise 2nd moment vector, v0 «- 0 Initialise timestep, t «- 0 While 9t not converged do t <— t + 1 Compute gradient, g t <- Veft(&t-i) Update biased first moment estimate, mt *- ■ m t_1 + (1 — /?x) ■ g t Update biased second moment estimate, v t «- /?2 • vt_i + (1 — /?2) ' 9t Calculate biased corrected first moment estimate, fht <-171 Calculate biased-corrected second moment estimate, vt <- Update parameters, 9t *- 9t^1 — a • end while return 9t (Resulting parameters) Fig. 1. Adam Optimisation Algorithm (Kingma and Ba, 2015) 2. Deep Learning Types and Architectures 2.1 Classes of Deep Learning Networks The three major classes of DL networks are: i. Deep networks for supervised learning ii. Deep networks for unsupervised learning iii. Hybrid deep networks 2.1.1 Deep Networks for Supervised Learning Supervised learning is a learning technique that provides a target or set of examples for the network to learn from. It is also known as learning from examples or learning from the teacher. This is achieved by labelling each input with a desired output value, thereby providing a set of target values of output (Masolo, 2017). Deep networks for supervised learning are also 201 known as discriminative deep networks as demonstrated by CNNs (Deng and Yu, 2012). 2.1.2 Deep Networks for Unsupervised Learning In unsupervised deep learning, the deep network is only provided with a set of inputs with no target values. Learning is without the support of a teacher or examples. There is usually no feedback from the environment with regard to what should be the desired output and whether it is correct or incorrect. They are also referred to as generative networks because they have the ability to generate samples by sampling from the network. Common examples are autoencoders, deep belief networks and generative adversarial networks (Hinton et al., 2012; Patterson and Gibson, 2020). 2.1.3 Hybrid Deep Networks Hybrid deep networks have a combination of discriminant and generative abilities associated with both supervised and unsupervised learning. For example, a speech recognition is generative in nature, nevertheless it may have parameters that are discriminative in translating speech to text (Deng and Yu, 2012). 2.2 Deep Feed-Forward Networks In Feedforward Neural Networks (FFNs), successive layers feed into one another in the forward direction from input to output (Aggarwal, 2018). This is based on the assumption that all nodes in one layer are connected to those of the next layer. FFNs are acyclic graphs. Fig. 2 shows an FFN with 4 inputs, 4 hidden layers and an output layer. 202 Input Layer Output Hidden Hidden Hidden LayerHidden Layer Layer LayerLayer Fig. 2. Feedforward Neural Network 2.3 Deep Convolutional Neural Networks Convolutional Neural Networks (CNNs) transform input data by p ilution operations in a minimum of one layer of the neiworK. convolution involves the application of a matrix to the input image to generate modified filtered data. Deep CNNs have several layers, with each layer able to compute convolutional transforms, after that non- linearities and pooling operators (Wiatowski and Bolcske, 2017). A typical CNN consists basically of convolution, pooling and full- connection (FC) layers (Wang et al., 2020). The convolution layer consists of neurons organised as feature maps that are trained to extract features from the input data. Each neuron in a feature map is connected to other surrounding neurons in the previous layer known as a filter bank. All neurons within a feature map have approximately equal weights. The pooling layer decreases the spatial resolution of the feature maps (Rawat and Wang, 2017). High-level reasoning and the interpretation of feature representations are the main functions of the full-connection layer (Hinton et al., 2012). CNNs are mostly applied in image classification and considered to work with grid-structured inputs (Aggarwal, 2018). A 203 good activation function can efficiently map data in dimensions (Dubey and Jain, 2019). Figure 3 depicts a typical CNN architecture of an image classification problem. As the input image is fed into the network, the features are extracted at the convolution layer. The neurons at this layer form a feature map. The jth output Yj of the feature map is given by: Y, = f(Wj . x) (2. 1) • • t - Output •M • 9 Output Pooling M A. - Output 1 • I Output | Fig. 3. Convolutional Neural Network Architecture (Rawat and Wang, 2017) Output T heu j^ l stage after convolution is pooling which aims to decrease the spatial resolution of the feature map (LeCun et al.} 2015). The output of the kth feature of the map is given by: Ykij = max xkpq (2.2) Where xkpq represents the element at location (p.q) After the pooling operations, the fully connected layer performs the function of interpreting the features as well as high level reasoning (Hinton et ah, 2012). The Softmax operator is generally used for classification problems (Krizhevsky et al., 2012). 2.4 Recurrent Neural Networks Recurrent Neural Networks (RNNs) are considered to accept a series of input with no fixed limit on size (Venkatachalam, 2019). RNNs are 204 described as “the deepest of all ANNs due to their computing power and ability to process sequential information” (Siegelmann and Sontag, 1991; Schmidhuber, 1990a). RNNs use the inputs of the previous layer and previous information observed by the individual neurons because they also have the ability of memorising previous inputs (Wang and Huang, 2019). The performance of RNNs in time series data is known to be better than other neural network architectures like CNNs. RNNs are therefore used in the classification of biological sequences Fig. 4 is a typical architecture of an RNN that shows the input, hidden and output layers of the network. Inputs are fed into the network at specific timestamps. The output yW of an RNN given input x c at time is computed as (Torti et cil, 2019): y0) = wg(W x( ^. +) Uh^-1) + b) + c2 2 Where g is a nonlinear function while W, U, w, b and c represent network parameters, h ^ is the hidden state which is computed as: h(t) = g(Wx(t) + Uh(t-1) + b) + c (2.3) Fig, 4. Recurrent Neural Network 205 2.5 Deep Learning Implementation Deep Learning data computations can be performed with a variety of open-source and propriety software available for deep learning application. We shall focus on the use of Python software, a simple open- source programming software. Implementation of DL in Python is achieved with the following important libraries Numpy, Pandas, Keras, Scikit-lean, matplotlib. The file containing the datasets should be in csv format. The file is loaded using pandas followed by data normalisation (Zhang, 2019). The Keras library runs on Tensorflow or Theano and is used to develop the models including defining the layers. Keras is a DL application programming interface (API) designed to enhance the speed of computation. The main data structures of Keras are layers and models. i. Data Collection DL networks are usually implemented with large datasets and loaded into the software. ii. Data Pre-processing a. Missing Values Various techniques are used to handle missing data. b. Covariance Matrix Covariance matrix is computed to determine variables that are highly correlated. The covariance of two random variables X and Y having values (xi, yi) with probability py is defined as: COVCX, Y) = - Hx) (yj - M r ) (2.4) c. Data Normalisation Data normalisation is performed to ensure that all the features are measured on the same scale.: iii. Feature extraction Important features of the data are extracted leading to considerable reduction in the size of data to a controllable size and improved accuracy. Common feature selection techniques include correlation matrix, F-test, feature importance and variance thresholding. 206 iv. Splitting the dataset The dataset is split into training and testing datasets. This is achieved with the train_test_split package imported from scikitileam. iv. Building the model: This process involves creating the type of deep neural network, its network architecture and the activation functions to be used at the output of each layer of the network. Optimization technique to reduce cost function (error between the target output and the local output from each layer). Network structure is specified by importing dense from keras.layer (from keras.layers import Dense). v. Evaluating the model The performance of DNNs can be determined by the following evaluation metrics including, accuracy, sensitivity, specificity, positive predictive value, negative predictive values. a. Accuracy is defined as the proportion of the total number of predictions that were correct. . TP+TN ACCUraCy = TP+TN+FP+FN (2.5) b. Sensitivity is defined as proportion of positive class correctly classified. Sensitivity = TP TP+FN (2 .6) c. Specificity is defined as the ratio of true negatives, righdy predicted as a negative class or true negative. Specificity - —TN— (2.7) d. Positive predictive value or precision is defined as the ratio of true positives to the sum of true positive and false positives. Precision = TP (2 .8) Where TP = True positive value 207 TN = True negative value FP = False positive value FN = False negative value 3. Predictive Analytics in healthcare In recent times, concerted efforts have been made to improve medical diagnosis through use of predictive analytics. This is borne out of the need to improve diagnostic accuracy and speed. 3.1 Overview of Predictive analytics Predictive analytics are generally used to develop effective methods that can accurately predict future observations from historical data while also trying to understand the relationship between the features and response for scientific purposes (Bickel and Roy, 2008). The various applications of predictive analytics include forecasting of disease outbreaks and epidemics, disease diagnosis and therapy. The application of predictive analytics in big data has the potential not only to improve profits but also to minimise wastes in healthcare operations management. Deep learning as well as other machine learning algorithms are very useful tools in predictive analytics for disease classification. For instance, Nwaneri et al., (2014) developed an ANN based model for the prediction of breast cancer. 3.2 Limitations of Predictive Analytics in Healthcare Notwithstanding the several benefits associated with the use of predictive analytics in healthcare, it has the following limitations: i. Data collection is often characterised by some challenges such as incomplete, inconsistent and heterogenous data. ii. Data access is limited by privacy issues iii. Predictive analytics of high dimensional data (data with too many attributes in relation to the number of observations) are usually susceptible to the “curse of dimensionality” problem (Dinov, 2016). iv. Since large datasets is a major requirement for deep learning, the use of deep learning in healthcare is usually 208 limited by the availability of large amount of data from patients. v. Deep neural networks are difficult to train as they are susceptible to overfitting. 3.3 Selected Deep Learning Applications in Disease Prediction 3.3.1 Application of Deep Learning in Diabetes Prediction Diabetes mellitus (DM) is defined as “a chronic, metabolic disease characterized by elevated levels of blood glucose” (WHO, 2020). Therefore, early diagnosis and prediction of DM in persons with certain risk factors is necessary. Deep Learning algorithms can be used to develop predictive models for DM prediction based on certain risk factors of patients. In a typical DL model, the input nodes consist of risk factors such as age, weight, hypertension, family history of DM, waist circumference, consumption of sweet foods etc. The network is trained to help the network classify data as diabetic or non-diabetic. Various computations are done in the hidden layers with the results forwarded to the output layer which indicates if the person is diabetic or not. 3.3.2 Application of Deep Learning in Breast Cancer Classification Breast cancer is a malignant tumour that affects mostly women. It accounts for 10.4% of all cancer incidences among women and is the fifth most common cause of cancer death globally (Sharma et al., 2010). Early diagnosis of the disease is known to improve the chances of survival from the disease (Murtaza, 2019). Mammography is an imaging technique used in diagnosing breast cancer. However, diagnosis of mammographic breast images is subjective and difficult to interpret and requires a lot of skill and experience. Therefore, DL can be used in the prediction of the status of breast image to determine if it is benign or malignant. This is implemented by first digitizing breast images of fine needle aspirates of the breast mass of patients. Features of interest in the images are considered and their values computed. The features commonly used include uniformity of cell size, uniformity of cell shape, marginal adhesion, single epithelial cell size, bare nuclei, brand chromatin, and 209 normal nucleoli (Dhanya 2020). The data are usually pre-processed. The features values are usually icrl as inputs to the DL model. Activation functions are used in the computation of the output of the various layers of the model. The model trains the input data and generates the output which may be classified as a benign or malignant tumour. The models are evaluated in terms of the accuracy, specificity, sensitivity and positive predictive value (PPV). 3.3.3 Application of Deep Learning in Chronic Kidney Disease Prediction Chronic Kidney Disease (CKD) refers to kidney damage or glomerular filtration rate (GFR) < 60 mL/min/1.73 m2for three (3) months or more (Inker et al., 2014). It is associated with high rates of mortality and morbidity. Some of the risk factors of CKD include: high blood pressure, old age, heart and blood vessel disease, smoking, diabetes, obesity, abnormal urinary structure and history of family of kidney disease. Early diagnosis and detection of CKD helps patients to know their health status and commence early treatment in order to improve chances of survival and quality of life of CKD patients. Deep Learning algorithms can be used for early prediction of CKD. Chen et al, (2020) developed an Adaptive hybridised deep CNN for early detection of CKD. 3.4 Data Computations and Results Example 1: What is the output of a rectified linear unit of Deep Convolutional Neural Network if the input is: (a) -550 (b) 500 Solution: RELU(*) = { ° ^ < ° Therefore, based on the above equation, the output is determined by the input. If the input is less than 0, the output is equal to zero. However, if the input is greater than or equal to zero, the output is equal to the input. Therefore, (a) 0 (b) 500 210 Example 2: Consider a 4 by 4 matrix representing the patients and attributes in a dataset for the prediction of diabetes. Calculate the covariance between the 2nd (Age) and the 4lh Column (Glucose). Solution: The covariance of two random variables X and Y having values (xi, yi) with probability pij is defined as: N COV(X, Y) = - ^ ( * t - fix) (yj - nY) i=l 3 28 10 90 5 39 12 88 8 45 8 120 6 65 6 130 Let 2nd column = X, 4th column =Y 28 90 y _ 39 v _ 88 45 K 120 65 130 E[X] = 44.25 E[(2Y8] = 107COV(X.Y) - 44.25)(90 - 107) + (39 - 44.25)(88 - 107) + 42(1425. 8-6 44.25)(120 - 107) + (65 - 44.25)(130 - 107)= Question 3: Compute the image X by convolving the image I of size 6x6 with a 2 x 2 filter. 1 8 4 7 8 2 9 1 21 10 3 7 1 = 2 1 2 8 17 9 18 5 10 5 5 3 5 12 5 9 22 7 1 6 7 11 6 5 211 F = 1 0 1 1 Solution ( l x l + 8 x 0 + 9 x l + l x l ) = l l ( 8 x 1 + 4 x 0 + 1 x 1 + 2 1 x 1 ) = 30 (4 x 1 + 7 x 0 + 21 x 1 + 10 x 1) = 35 ( 7 x l + 8 x 0 + 1 0 x l + 3 x l ) = 20 (8 x 1 + 2 x 0 + 3 x 1 + 7 x 1) = 18 ( 9 x l + l x 0 + 2 x l + l x l ) = 12 . ( 1 x 1 + 2 1 x 0 + 1 x 1 + 2 x 1 ) = 4 (21 x 1 + 10 x 0 + 2 x 1 + 8 x 1) = 31 (10 x 1 + 3 x 0 + 8 x 1 + 17 x 1) = 35 ( 3 x l + 7 x 0 + 1 7 x l + 9 x l ) = 29 ( 2 x l + l x 0 + 1 8 x l + 5 x l ) = 25 ( l x l + 2 x 0 + 5 x l + 1 0 x l ) = 16 (2 x 1 + 8 x 0 + 10 x 1 + 5 x 1) =17 ( 8 x l + 1 7 x 0 + 5 x l + 5 x l ) = 18 (17 x l + 9 x 0 + 5 x l + 3 x l ) = 25 (18 x 1 + 5 x 0 + 5 x 1 + 12 x 1) = 35 (5 x 1 + 10 x 0 + 12 x 1 + 5 x 1) = 22 (10 x l + 5 x 0 + 5 x l + 9 x l ) = 24 ( 5 x l + 5 x 0 + 9 x l + 2 2 x l ) = 36 (5 x 1 + 3 x 0 + 22 x 1 + 7 x 1) = 34 ( 5 x l + 1 2 x 0 + l x l + 6 x l ) = 12 (12 x l + 5 x 0 + 6 x l + 7 x l ) = 25 ( 5 x l + 9 x 0 + 7 x l + l l x l ) = 23 (9 x 1 + 22 x 0 + 11 x 1 + 6 x 1) = 26 (22 x l + 7 x 0 + 6 x l + 5 x l ) = 33 After convolution the image is transformed to: 212 11 30 35 20 18 12 4 31 35 29 25 16 17 18 25 35 22 24 36 34 12 25 23 26 33 Example 4: A deep CNN was recently developed for breast cancer screening. The model was tested on a large dataset comprising 10,000 digitised breast images of women who participated in a recent screening conducted in 3 tertiary hospitals in Southwest, Nigeria. Of the 10,000 breast images, 9100 were benign while 900 were confirmed to be malignant from confirmed biopsy procedures. The model correctly classified 8,950 breast images as benign, and 780 as malignant. It wrongly classified 120 images as benign and 150 as malignant. Calculate: i. The accuracy ii. Sensitivity iii. Specificity iv. Precision Solution Total number of breast images =10,000 Total number of positive cases = 9100 Total number of negative cases = 900 True positive cases = 780 False positive cases = 150 True negative cases = 8,950 False negative cases = 120 A. ccuracy = -----T-P--+-T--N----- 780+8950 J TP+TN+FP+FN 10000 0.973 ii. Sensitivity = TP _ 780 0.867 TP+FN — 780+120 ' iii. Specificity = TN _ 8950 = 0.984 TN+FP _ 8950+150 iv. Precision = TP _ 780 0.839 TP+FP _ 780+150 ~ 213 Example 5: In a recent study, a deep learning model was used to predict CKD. The model was tested on a large dataset comprising 20,000 adults who participated in a nationwide screening conducted across the 6 geographical zones of Nigeria. Of the 200,000 subjects, 170,000 tested negative while 30,000 subjects were diagnosed with CKD. The model correctly classified 165,000 negative cases and 28000 positive cases. It misclassified 5000 samples as positive and 2000 as negative. Solution Total number of datasets =200,000 Total number of positive cases = 30,000 Total number of negative cases = 170,000 True positive cases = 28,000 False positive cases = 5,000 True negative cases = 165,000 False negative cases = 2,000 Accuracy = TP+TN 28,000+165,000 TP+TN+FP+FN 200000 = 0.965 ii. Sensitivity = TP 28,000 = 0.933 TP+FN 28,000+2000 iii. Specificity = TN 165,000 = 0.971 TN+FP 165,000+5000 Precision = TP 28,000IV. = 0.848 TP+FP 28,000+5,000 214 4. 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(2019) Deep Learning in Wisconsin Breast Cancer Diagnosis. Retrieved October 5, 2020, from https://towardsdatascience.com/deep- leaniing-in-winonsin-breast-cancer-diagnosis-6babl3838abd. 219 CHAPTER 9 New Normal: Ergonomic Awareness For Telecommuters In Nigeria xEzekiel Olatunji* and 2Ebenezer Olowolaju 'Risk Consultant, Deloitte Nigeria. olatunjiezekielolaoluwa@gmail.com 2Business Process Analyst, Manqala Ltd. ebenezer.olowolaju@gmail.com Abstract The challenges faced by the ever-growing nature of work cannot be overemphasized, the complexities and uncertainties faced by organizations are not confined to the societal, economic and national borders. The emergence of COVID-19 was an eye-opener that the future of work is here. The definition of work is gradually shifting from being at an employer’s location as it has been for decades. Many organizations and individuals are unprepared and some unaware of the ergonomic importance of telecommuting at this time. An ergonomic awareness for telecommuters in the world and specifically in Nigeria will cause a shift in the design of our homes and our work environments to fit the job to telecommuters. This does not have to come at a high cost. This is why this study highlights trends in the new normal office by studying six predominant components of workstations (chair, work surface, type of workstation and computer system-screen, keyboard, mouse/touchpad) in the work environment of telecommuters in Nigeria. The significance of this study can be adopted by well-adjusted telecommuters and potential ones. Organizations can leverage on this awareness to better improve the overall health of employees working in the new normal office. This should drive modification in budget 220 allocations to make provision for the ergonomics training and implementation of an ergonomic workplace for telecommuters. 1.0 Introduction The Industrial Revolution came with leaving home and labouring in an outdoor work environment as its definition of work. Work in the 1990s was restricted to being in the four comers of a building, offices were mostly cubicles and c-suites. This work outside the home model with its 9-5 in-office work-hours is what many employers of labour still employ today, though it is increasingly becoming outdated. The history of telecommuting dates back as far as the 1970s when Jack Niles published a book called “The Telecommunications Transportation Trade-off- Options for Tomorrow” (Nilles et al, 1973) when there was a problem with the transportation of employees from one location to the other due to the scarcity of non-renewable energy sources. Furthermore, the book recommended that either the jobs of employees be set up such that they can be done from each individual’s location or a sufficiently sophisticated information-storage system and telecommunications be set up to allow for information transfer to be as effective as though employees were centrally located. Today, telecommuters have increased in number due to the available technological capabilities. In recent years, online start-ups like Freelancer (founded 2009), Fiverr (founded 2010) and Up work (founded 2015) have enhanced telecommuting. In Wuhan, China, coronavirus disease (COVID-19) emerged in December 2019 with various symptoms like cough, pneumonia, shortness of breath, fever and in some cases death. The World Health Organization by April 30,2020, recorded over 3 million cases of the virus and 217,769 confirmed deaths (WHO, 2020a). With the high transmission rates in 214 countries, areas and territories, it was declared to be a Public Health Emergency of International concern (WHO, 2020b) This led to the declaration of a state of emergency or lockdowns by the governments of many nations (Kap2l2a1n, Frias, & McFall-Johnsen) The temporary lockdown led to an unexpected working from home therefore leading to an increase in the number of telecommuters globally. The normal remote working may not apply because of the various work environments that employees are forced to work from, unprepared (Donnely & Proctor-Thompson, 2015). Some employees are working from kitchen tables, beds while other family members disturb them. With childcare and schools closed, parents juggle between work and childcare. While numerous researchers have studied remote work, few have considered it in the light of the challenges that came with COVID- 19 without preparation. This “new normal” has changed the predominant work environment of employees to those that might not fit them ergonomically. 1.1 Background Organizations are constantly faced with growing confusion and uncertainties, as the kind of problems faced is not typically confined to economic, national or societal borders (Eisenhardt, Graebner, & Sonenshein, 2016) (Ferraro, Etzion , & Gehman, 2015). These challenges are diverse and range from several issues like climate change, political instability to severe economic downturns (George, Howard-Grenville, Joshi , & Tihanyi, 2016) The physical working environment can make a person misfit or fit their workplace. This working environment is known as an ergonomic workplace. Research on ergonomic workplaces for employees has to be done to help prevent nerve injuries (Cooper & Dewe, 2004). In addition, the elements in a working environment have to be proper, this will reduce their stress level while getting the job done (McCoy & Evans, 2005) In Quebec Canada, 7% of employees that were absent from work for six months incurred 70% of the total cost for occupational back pain (Abenhaim & Suissa, 1987). This is just one of the various occupational health problems that have continually affected the workforce. Low back pain has specifically attracted the attention of many industrialized 222 countries and governments due to the unreasonable costs it poses on compensation and health care systems (Crook, et al, 2002). Brill, (1992) stated that the improvement of workplaces to make them ergonomically compatible can increase the productivity of employees from five to ten per cent. Working environments are those systems, processes, structures, work location, conditions or tools in the workplace that impact the productivity of each employee (Opperman, 2002). More attention should be given to identifying and dealing with the ever- changing nature of work environments (Noble, 2009) especially now with the presence of COVID-19 that has disrupted our workspaces. The pandemic is having a dramatic effect on livelihood, well-being and jobs of workers across the globe. Towards this end, this study focuses on enlightening telecommuters and employers about the impact of COVID-19 pandemic on the need for ergonomic consideration in their design and choice of workstations. This awareness can help improve the overall health of well-adjusted telecommuters or those that became one as a result of the pandemic. Organizations can also leverage on this study to make an organizational schedule that suits their industry. 1.2 Study objectives 1. To assess the impact of the Covid-19 pandemic on the type and availability of ergonomically compatible workstations of Nigerian telecommuters in their various work environments. 2. To create ergonomic awareness to telecommuters concerning musculoskeletal disorders resulting from various work environments. 223 1.3 Limitations of the study 1. Due to social distancing and the national lockdown, participants of the survey were not examined in their workplaces physically to know how their working environments are. 2. As at the time the survey was sent, many telecommuters in Nigeria were already returning to work while some kept a flexible schedule as organized by their employers. 3. Due to the time frame of the study and cultural factors, telecommuters that met the inclusion criteria could not be reached in some geopolitical zones (North East, North West and South-South). Section 2.1 gives the full details. 2.0 Methods 2.1 Study participants The survey went out to 1000 telecommuters across Nigeria. Some geopolitical zones in Nigeria were represented. However, 3 (North East, North West, and South-South) out of 6 were not present. The North East and North West region lacked telecommuters that met the inclusion and exclusion criteria due to cultural reasons and duration of the study. The South-South region had many manufacturing and production (example Oil and Gas Industry) companies that continued the business under COVID-19 guidelines as essential services firms during the lockdown. This limited the survey to telecommuters that had well-adjusted before the pandemic who did not meet the inclusion criteria. However, after cleaning the responses, the survey got fifty (N=50) responses suitable for use. 224 2.2 Study Design An online survey research method (Google Forms) was used for the study for easy understanding and accessibility, considering the fact the target participants are telecommuters (that use a computer system, see section 2.2.1 for inclusion and exclusion criteria). The survey was to telecommuters online. The duration of the study was for 7 weeks from pre to post-survey (21, August to 15, October 2020). The survey was filled anonymously and no contact information was taken. For clarity sake, questions were asked in a way that differentiates between before and after the switch to telecommuting, especially during the national lockdown in Nigeria. ESEBBES Fig. 1: Ergonomic Workstation, Source: https://www.cmd- ltd.com/advice-centre/ergonomics/office-ergonomics/#officeergl2 The survey also included traditional demographic variables like age, gender, education and profession. It goes further to ask how many people (including adults and children) the respondents live with and to ask if any of them has tested positive for COVID-19. To enable participants to 225 respond to questions with proper understanding, two pictures of both a standing and sitting workstations (Figure 1) were included in the survey and referred to throughout the survey. Examples of such questions are: While you work from home, 1. Is your arm at 90° to your body as seen in Figure 1? 2. Are your feet rightly placed to the ground as seen in Figure 1? 3. Does your chair have lumbar (lower back) support as seen in Figure 1? 4. Is your hand in a natural position when you are using the mouse as seen in Figure 1? 5. Is your head at 90° to your body while working as seen in Figure 1? 6. Is your screen at your eye level as seen in Figure 1? Also, questions around musculoskeletal disorders like back pain, eye strain, neck pain and shoulder pain were framed to ascertain any trend that might have surfaced after the shift in the work environment. Lastly, questions that border around locations employees worked from during the lockdown, their preference going forward, their work postures and how they have been making themselves comfortable while working from other locations asides the employer's location. 2.2.1 Inclusion and exclusion criteria To get quality data, inclusion criteria had to be set up for participants. Respondents who did not meet these criteria either skipped to the end of the survey, or did not respond at all as it was made clear from the first section of the survey. Section 3.1 gives the provision made available to exclude responses that did not meet the criteria. For Telecommuters, the inclusion criteria are: 226 1. Country: The telecommuter must be a Nigerian. 2. Location of work: The telecommuters must have changed the location of work during the national lockdown in Nigeria or worked from another location asides the employer's location. 3. The equipment used for job tasks: The telecommuter must have a computer system to fulfil daily tasks and responsibilities assigned by the employer. 2.2.2 Factors considered in the survey A workstation is defined as an area with equipment for the performance of a specialized task, usually by a single individual. Three types of workstation was considered for this study: 1. Sitting Workstation 2. Standing workstation 3. Combination of both sitting and standing Factors were categorized into various components in the workstation, which were then subjected to reviews by corresponding authors. Table 1 summarizes the category of factors considered for each component in the workstation. 227 Table 1: Summary of the category of factors considered for each component in the workstation s / Chair Work Input Input Screen/Monito N surface devices devices r (keyboard) (mouse) 1 Dinin Desk Laptop Laptop Laptop screen g chair keyboard touchpad 2 Couch Centre External External External table keyboard mouse monitor/screen 3 Office Dining Combinatio Combinatio Combination of chair Table n of both n of laptop both laptop laptop and touchpad screen and external and external external keyboard mouse monitor 4 Bed Ironin g board 5 Others Furthermore, ergonomic considerations of various work environments revealed the following characteristics that were used in the survey as seen in Table 2. For the type of workstations, the following factors were considered in the survey. 1. Type of work station 228 2. Lighting of work station and 3. Glare at work station Table 2: Summary of characteristics evaluated for each component in the workstation s/ Chair Work Input devices Input Screen/Monito N surface (keyboard) devices r (mouse ) 1 Type of Type of Type of Type of Type of screen chair work keyboard mouse surface 2 Elbow Material Keyboard fit Mouse Body leaning placed on work without fit towards the the side surface is readjustment screen while made up s working of 3 Armrest Shape of Keyboard Pressur Head at 90° to present or work setup for the e points the body while absent surface dominant or drags working hand while using the mouse 229 4 Armrest Space Knowledge Natural Screen at eye adjustabl under the and use of position level e work hotkeys of the surface hand to while change using leg the positions mouse 5 Lumbar Space Use of Use of (lower between mouse secondary back) the top of outside screen and its support the thigh the base position present or and of absent undersid support e of the forearm 6 Feet Turning of rightly neck to access placed to secondary the screen ground 7 Arm at Optimize 90° to the screen body brightness to reduce glare 230 8 Hard or comfy surface to sit on 3.0 Results and Discussion 3.1 Data Cleaning The data collected was cleaned as follows: 1. Responses that do not meet the inclusion criteria were deleted 2. Timestamp fields were deleted to enhance confidentiality 3. All free-text responses were moved to a separate sheet 4. Exported all responses into a single excel file 231 3.2 Summary of survey responses Table 3: Profile of telecommuters (n=50) Ag % Male/Femal % Educationa % Income % e e 1 Attainment 20- 82 Male 62 Secondary 6% Under 28 30 % % school or 50,000 % less 30- 14 Female 38 University 78 50,001- 42 40 % % graduate % 100,000 % 40- 4% Post 16 100,001 26 50 graduate % - % 300,000 300,001 4% 500,000 Table 4: Profession of Telecommuters (n=50) 232 Cons IT Dat Educatio Gra Custom Medic Grap ultan Personnel a nalist duat er Care al hie t /Software Ana (Teacher e Repres Profes desig Engineer lyst /Lecturer Trai entativ sional ner, and ) nee e, s Agric Fina Entrepr ultura ncia eneur 1 1 and Econ Ana Student omist lyst Write r, Trade r, Baker and Minin g Engin eer 30% 8% 6% 10% 10% 4% 6% 2% each each each Table 5: Locations telecommuters worked from (n=50) Location % Home 88% 233 Telework Centre 2% Office 2% Hospital (Employer) 2% Client’s location 6% Table 6: Musculoskeletal disorders telecommuters experienced before and after the switch (n=50) S /N M u s c u lo s k e le ta l d is o rd e rs B e fo re th e lo c k d o w n D u r in g /a f te r th e lo c k d o w n Y e s N o Y e s N o 1 B a c k p a in 5 0 % 5 0 % 2 4 % 7 6 % 2 E y e s tra in 4 4 % 5 6 % 3 8 % 6 2 % 3 N e c k p a in 2 2 % 7 8 % 2 2 % 7 8 % 4 S h o u ld e r p a in 4 0 % 6 0 % 54% 46% 234 According to the study, the summary of the survey responses for each component in the workstation (Section 2.2.2) is summarised below 1. Type of Workstation a. Standing workstation 2 b. Sitting workstation 36 c. Combination of standing and sitting workstation 12 2. Workspace appropriately lighted 32 3. Glare in workstation 34 Table 7: Summary of survey responses of each component in the workstation (n=50) s/ Chair Work Input Input Screen/Monit N surface devices devices or (keyboard) (mouse) 1 Dining Desk-25 Laptop Laptop Laptop chair-15 keyboard- touchpad- screen-46 43 31 2 Couch-6 Centre External External Combination table-7 keyboard-2 mouse-13 of both laptop screen and external monitor-4 235 3 Office Dining Combinati Combinati Move close chair-17 table-10 on of on of to screen to laptop and laptop see-18 external touchpad keyboard-5 and external mouse-6 4 Bed-10 Ironing Keyboard Mouse fit Head at 900 board-2 fit the hand- to the body- worksurfac 41 21 e-42 5 Plastic Stool-1 Keyboard Mouse Screen at eye chair-1 setup for drag level-27 dominant present-15 hand-36 6 Dental Pillow-1 Knowledg Hand in Secondary chair-1 e of natural screen hotkeys-26 position- present-47 34 7 Elbow Floor-1 Use Reach Glare placed hotkeys-17 outside present-33 on side- base of 23 support to use mouse- 7 236 8 Elbow Kid's not table-1 placed on side of body- 27 9 Armrest Bed-1 present- 19 10 Armrest No work absent- surface-1 31 11 Adjustab Wooden le work armrest surface- present-3 43 12 Adjustab Glass le work armrest surface-5 absent- 47 13 Lumbar Metal support work present- surface-2 20 237 14 Lumbar Wooden support surface absent- tapered 30 with leather-9 15 Feet Rectangul rightly ar work placed surface- on the 42 ground- 29 16 Arm at Circular 90% to work the body- surface-4 20 17 Hard L-shaped chair work surface- surface-2 21 18 Curved work surface-1 238 19 Space undemeat h to change leg posture- 36 20 Space between the top of the thigh and underside of arm-37 3.3 Ergonomic Fixes by Telecommuters in Nigeria The survey revealed some ergonomic and economic fixes that telecommuters apply to their work stations to make them more comfortable and effective in delivering their tasks. Some of these fixes can also be applied by well-adjusted and new telecommuters. Table 8 shows the summary of these ergonomic fixes 1. Placing laptop on book or centre table: This raises the screen of the laptop to improve the eye level of the telecommuter. This was done by only 12% of telecommuters in the study, 10% placed their laptops on books to raise the height while 2% placed it on the centre table to match their eye level. 2. Use of speaker: Some of the telecommuters (4%) bought speakers to play background music as they work. This can be used to ease work stress especially while doing repetitive tasks. 239 3. Use of pillow/blanket: Majority of the telecommuters (26%) use pillow or blanket as a support for their lower back as many of their chairs lack lumbar support. 4. Did nothing: 22% of the telecommuters did nothing to improve their workstation, they simply worked with the pre-existing work condition in their workspaces. 5. Break: 4% of the telecommuters took intermittent breaks to relax. 6. Exercise: 54% of telecommuters started workouts during the lockdown, 38% performed it daily, 28% 2-3 times a week and 34% once a week. Only 10% of the telecommuters performed minor exercises at intervals during work hours like stretching and moving their legs. 7. Posture adjustment: Only 4% of telecommuters adjust their work postures during work hours to make themselves more comfortable. Some stand, while others walk out for a few minutes, out of which 36% change their work posture less than 5 times daily, 48% between 6 to 10 times daily, 16% over 10 times daily. 8. Footrest created from book: Some workers (2%) placed their feet on a pile of books to improve their comfort because their feet were not flat to the ground as they should be. 9. Leaning chair towards a pillar for stability: 2% leaned their chairs towards a pillar to give it stability and another 2% got comfortable chairs and table to work with. 10. Business casual dress: Some (2%) telecommuters wore long sleeves shirts to have a feel of being at work. This helped them to be more efficient and start the day with the right motivation. 240 Also, 2% take chilled drinks while they work, 2% adjust their screen brightness, 2% use glasses to reduce glare and 2% set up a mock workspace after working uncomfortably from their bed for some days. Table 8: Ergonomic fixes by telecommuters in Nigeria (n=50) S/N Ergonomic fixes by % telecommuters 1 Nothing 22% 2 Placing the laptop on a book 12% or centre table 3 Use of speaker 4% 4 Use of pillow/blanket 26% 5 Break 4% 6 Stretching/exercise 10% 7 Posture adjustment 4% 8 Footrest created from book 2% 9 Lean my chair towards pillar 4% for comfort 241 10 Take a drink 2% 11 Reduce screen brightness 2% 12 Business casual dress 2% 13 Use glasses 2% 14 Set up Mock workplace 2% 3.4 Significance of the Study to Employers/Human Resource Department in the New Normal According to this study, from table 6, only shoulder pain increased by 14% mostly as a result of raised arms during work hours. The raised arm is as a result of work surfaces (desk, 50%, dining table 20%, centre table 14%, Ironing board 4%, kid’s table 2%, stool 2%, bed, 2%, pillow 2%, floor, 2%) that are too high/low and chairs without adjustable armrest. Most telecommuters (62%) worked with chairs without armrest. 94% out of 38% had armrests that cannot be adjusted. It is recommended that employers and HR experts provide ergonomic chairs and tables (as seen in Figure 1) to their workers at any location. This will reduce the cost of health care schemes for the firm. Furthermore, only 28% received ergonomic tips/training from their employer before the COVID-19 pandemic while 32% received ergonomic tip/training to navigate the ergonomic challenges they faced during the national lockdown. However, there was no test conducted to check the comprehension level of employees and only laptops were provided as the ergonomic tool for the period. From the study, there were no provisions made in the budget of most firms for the ergonomic 242 concerns of their workforce as the global economy experienced a downturn as a result of COVID-19. In Nigeria, decision-makers of firms and employers should make provision for the ergonomic concerns of their telecommuters in the financial budget. Finally, the study showed that 64% of employees will prefer working from another location asides employer’s location while 86% of telecommuters prefer a flexible arrangement of switching between telework station and employer’s location. This calls for modification of organizational framework and employee schedule to accommodate these differences. Millennial are more interested in achieving their personal goals alongside the goals of the organization. This kind of environment is what telework supports and the New Normal has shown the global world that it is possible. 4.0 Further Research For researchers in Nigeria, this paper highlights a new area of interest that intersects disaster management, economic downturns and its impact on specific professions in Nigeria. There is no scarcity of data as regarding the impact of COVID-19 globally and how various countries reacted. These data can be merged with other datasets to investigate the impact of pandemics on various cultures, texts and professions. With adequate time, these impacts can be modelled for specific professions in Africa, unlike this study that dealt with telecommuters generally. Specifically for ergonomic researchers, the limitation of social distancing can be addressed because participants can be observed in their workspaces by a physical observation from an experienced ergonomist. Studies have been done to access the working environment of telecommuters by snapping their pictures while they work in their workspaces. This makes the participant more conscious and not their natural selves in their workstations having a camera taking snapshots beside and behind them. Besides, it can lead to a breach of confidentiality agreements. More specifically, this research can be modified to discover 243 the works of the future and how far telecommuters have adapted to it in various study locations. 5.0 Conclusion The pandemic has created various challenges for families, organizations and nations of the world. Business closures, travel restrictions, absence of child care, educational and fitness facilities are some of the unique conditions COVID-19 brought. Working from home at this time (New Normal Office) is different from the usual remote working. This paper represents the first study in Nigeria that focuses on the ergonomic concerns raised in this time for telecommuters. It goes on to further enlighten telecommuters and employers about the trends in the New Normal offices in Nigeria, the ergonomic and economic fixes that can be used to reduce musculoskeletal disorders and the areas employers and HR experts can focus on. References Abenhaim, L., & Suissa, S. (1987). 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Tackling grand challenges pragmatically: Robust action revisited. Organization Studies, 36(3), 363-390. George, G., Howard-Grenville, J., Joshi, A., & Tihanyi, L. (2016). Understanding and tackling societal grand challenges through management research. Academy of Management Journal (59), 1880-1895. Kaplan, J., Frias, L., & McFall-Johnsen, M. (n.d.). A third of the global population is on coronavirus lockdown, here's our constantly updated list of countries and restrictions. Retrieved from https://www.businessinsider.com/countries-on-lockdown- coronavirus-italy-2020-3?IR=T McCoy, J. M., & Evans, G. (2005). Physical work environment. (I. J. Barling, E. K. Kelloway, & M. Frone, Eds.) Thousand Oaks, CA: Sage Publications. Nilles, J. M., Roy Carlson, Jr, F., Gray, P., & Hanneman, G. J. (1973). The Telecommunications-Transportation Trade-off, Options for Tomorrow. Noble, A. (2009). Building health promotional work setting: identifying the relationship work characteristics and occupational stress. Promotional International journal, 18(4), 351-359. 245 Opperman, C S. (2002) Tropical business issues. Partner Water House Coopers, International Business Review. WHO. (2020a). Coronavirus disease 2019 (COVID-19): Situational Report. Retrieved from https://www.who.int/docs/default-source/coronaviruse/situation- reports/20200430-sitrep-101 -covid-19.pdf?sfvrsn=2ba4e093_2 WHO. (2020b). Statement on the second meeting of the international health regulations (2005) emergency committee regarding the outbreak of novel coronavirus (2019-ncov). Retrieved from https://www.who.int/news/item/30-01-2020- statement-on-the-second-meeting-of-the-intemational-health- regulations-(2005)-emergency-committee-regarding-the- outbreak-of-novel-coronavirus-(2019-ncov) 246 CHAPTER 10 Model-Based Systems Engineering: Relevance and Applications in Contemporary Systems Design ^benezer Olowolaju* and 2Ezekiel Olatunji 'Manqala Ltd. ebenezer.olowolaju@gmail.com 2Deloitte Nigeria, olatunjiezekielolaoluwa@gmail.com Abstract With the increasing complexity of systems, models are now the primary means by which engineers communicate, especially during the design phase. The relevance of models is explored, as well as the application areas of modelling by systems engineers. Model-Based Systems Engineering (MBSE) has proven to generally promote safety, help in compressing time, reduce costs and complexity, as well as leveraging the capabilities of digital transformation. In contemporary times, MBSE is being applied in design, prototyping and lifecycle management of systems, processes and engineered products, in simulating complex and dynamic systems, in optimizing systems design, as well as in data-driven decision-making algorithms. Just like Engineering in general, MBSE continues to grow in definition, scope, acceptance and application. 1.0 Introduction Complex systems are characterized by the inability to humanly overview and also keep an understanding of all the details at the same time (Ogren, 2000). Models are widely used among engineers for communication at different stages of the systems they deal with. Being abstractions of reality, models could be mathematical, iconic, graphical or analogue (Sargent, 2015). The relevance and application of models in systems engineering are discussed in this work. 247 1.1 Background information Over the years, technological advancements have resulted in more complex systems and subsystems, which has seen the term system of systems more commonly adopted. With these complex systems comes the challenge of designing, analyzing, synthesizing, predicting, optimizing and controlling (Gamaey and Gani, 2010). This has made engineers resolve to use models as the primary means of communication throughout the lifecycle of these systems. In addition to having a common language of communication, models have been proven to be highly relevant in many other areas including analysis, synthesis, integration and prediction of systems. 1.2 Objectives The objectives of this essay are to: I. Review the relevance of model-based systems engineering in today’s world. II. Highlight the applications of model-based systems engineering in contemporary systems design. 2.0 Relevance of model-based systems engineering Model-based systems engineering has witnessed increasing application in recent times. This is as a result of the fact that modelling has proven to be generally safe, time-efficient, cost-efficient, simple and digitally compliant in its application. The attributes of model-based systems engineering which makes it relevant are discussed below. 2.1 Safety dimension With increasing costs of incidents ranging from direct costs which may include lost hours, sanctions, compensations and loss of human and material resources, to indirect costs which may be loss of morale, employee turnover and loss of public trust, system designers have resolved to use models as they are generally safer than physical interaction especially when testing out new scenarios of complex and potentially hazardous systems. 248 Application of models in structural analysis, integrity tests, mechanized combats, radioactive power plants and biomedical research has helped to prevent incidents that could have resulted in fatalities. Furthermore, models are useful in defining ergonomic parameters (Ismaila and Charles-Owaba, 2010), as well as in evaluating the safety performance of products, processes and systems (Charles-Owaba and Adebiyi, 2006) and (Adebiyi et al., 2007). 2.2 Time dimension Modelling generally helps in compressing the time required to study the Dehaviour of a system. More importantly, modelling can be applied in predicting future events or trends based on past observation by extrapolation. With the right data, tools and modelling approaches, reliable conclusions about system behaviour can be drawn in good time. Advances in digital technology even made it possible for models to be applied in guiding real-time decision making in areas such as recommender systems, precision manufacturing, automatic guided vehicles and other smart objects. 2.3 Cost dimension Given that organizations are facing increasing pressure to cut down costs (Novak et al., 2017), modelling has grown in application among engineers and other professionals. It is cost-effective to use models and prototypes during preliminary testing and analysis of systems and engineered products such as aircraft and ships, rather than subject expensive materials to destructive testing. Computer-aided design helps in making functional models which are then subjected to different types of stress. 2.4 Complexity dimension Models help to reduce the complexity of systems such as power plants, refineries, submarines, ships and aircraft. The Boeing 747, for instance, is made up of 6 million distinct parts. One impressive use of model-based systems engineering is in the design and operation of the international space station by NASA, in conjunction with Boeing researchers and experts from Massachusetts Institute of Technology (Cates and Mollaghasemi, 2005). Although this is quite rare in the real world, 249 models help to achieve simplification by making it possible to study, analyze or focus on a subsystem or system component at a time, as if other components of the system are constant. The summation of the behaviour of the entire components is then used to estimate or predict the system behaviour with an acceptable degree of accuracy. 2.5 Digital transformation The increased availability of personal computers and other smart devices, coupled with the development of digital technology fields such as Big Data, Data Science, Analytics, Internet of Things, Edge Computing, Cloud Technology, Machine Learning and Artificial Intelligence has made data available in digital format which makes them easy to store, retrieve, transform, analyze and deployed in various models. Big data is particularly characterized by the 3 Vs, referring to the volume, velocity and variety of data that is being generated by these advanced technologies (Johnson et al., 2017). 3.0 Application of model-based systems engineering This section seeks to examine various areas in which systems engineers have successfully applied modelling techniques in the design, analysis, synthesis and control of modem systems and engineered products. 3.1 Design, prototyping and lifecycle management Models are particularly helpful in the lifecycle management of engineered products, processes and systems (Gemaey and Gani, 2010). Every stage in the life cycle including design, deployment, scaling, failure, recycling, etc. can be effectively modelled before the actual product is launched. This helps to achieve improved planning that gives rise to resilient systems and durable products. 3.2 Simulation modelling Engineers have found an important and increasing use for models in simulating real-life scenarios (Tisza, 2004). Simulation models are used to estimate stochastic or deterministic parameters using random sampling 250 techniques (Ghiocel, 2004). Popular systems that are usually simulated include service queues, equipment failure and availability, quality control, fleet management, software processes and professional training. 3.3 Optimization modelling A very important application of models is in determining the optimal combination of inputs to yield the best desirable output. Optimization models generally consist of the objective function to be optimized by combining the decision variables in a way that satisfies the constraints (Taha, 2017). Optimization models are used in material selection, production planning, structural designs, logistics systems, computer programming routines, as well as government and military operations. 3.4 Data-driven decision making The world today is full of intelligent systems capable of making decisions with little or no assistance from humans (Duan et al., 2019). At the heart of these systems are models that help in guiding the decision-making process of systems like automated guided vehicles, digital assistants and digital maps. Also, Business Intelligence has opened an entirely new frontier whereby the historical data of an enterprise can be mined and wrangled to produce valuable insights that would drive improved business performance (Brynjolfsson et al., 2011), as well as predicting future events such as employee attrition, customer churning and sales outcomes after training and testing machine learning models. 4.0 Conclusion The dimensions that make modelling relevant in systems engineering have been discussed, as well as the areas in which models are deployed to help engineers build and manage effective and efficient systems. As the need for technology-based solutions continues to grow, more complex systems are being built which would require more complex models, or even entirely new modelling approaches, hence, model-based systems engineering continues to grow in definition, scope, acceptance and application. 251 References Adebiyi, K. A., Charles-Owaba, O. E., & Waheed, M. A. (2007). Safety performance evaluation models: a review. Disaster Prevention and Management, 16(2). Brynjolfsson, E., Hitt, L. M., & Kim, H. H. (2011). Strength in Numbers: How Does Data-Driven Decision Making Affect Firm Performance? https://ssm.com/abstract= 1819486 Cates, G. R., & Mollaghasemi, M. (2005). A discrete event simulation model for assembling the international space station. Proceedings o f the Winter Simulation Conference. Charles-Owaba, O. E., & Adebiyi, k. A. (2006). The development of manufacturing safety programme simulator. Journal o fM odelling in Management, 1(3), 270-290. Duan, Y., Edwards, J. S., & Dwivedi, Y. K. (2019). Artificial intelligence for decision making in the era of Big Data - evolution, challenges and research agenda. International Journal o f Information Management, 48, 63-71. Gemaey, K. V., & Gani, R. (2010). A model-based systems approach to pharmaceutical product-process design and analysis. Chemical Engineering Science, 65(21), 5757-5769. Ghiocel, D. M. (2004). Engineering Design Reliability Handbook. Ismaila, S. O., & Charles-Owaba, O. E. (2010). A Review of Manual Load Lifting Models. Leonardo Journal o f Sciences, (16), 47-58. Johnson, J. S., Friend, S. B., & Lee, H. S. (2017). Big Data Facilitation, Utilization, and Monetization: Exploring the 3Vs in a New Product Development Process. Journal o f Product Innovation Management, 34(5), 640-658. https://doi.org/10.1111/jpim. 12397 252 Novak, P., Dvorsky, J., Popesko, B., & Strouhal, J. (2017). Analysis of overhead cost behaviour: case study on decision-making approach. Journal o f International Studies, 10(1), 74-91. Ogren, I. (2000). On Principles for Model-Based Systems Engineering. Systems Engineering, 3, 38-49. Pitt, M., Monks, T., & Crowe, S. (2016). Systems modelling and simulation in health service design, delivery and decision making. BMJ Quality & Safety, 25, 38-45. Sargent, R. G. (2015). Types of Models. In Modeling and Simulation in the Systems Engineering Life Cycle (pp. 51-55). Springer. Taha, H. (2017). Operations Research: An Introduction (10th ed.). Person. Tisza, M. (2004). Numerical modelling and simulation in sheet metal forming. Journal o f Materials Processing Technology, 757(1-3), 58-62. 253 CHAPTER 11 The Impact of Covid-19 Pandemic on Sustainable Supplier Selection Process "Chukwuebuka .M. U-Dominic 'Department of Industrial and Production Engineering, NnamdiAzikiwe University, Awka, Nigeria. Email: bukkvudom @ yahoo.com "Corresponding Author Ifeyinwa.J. Orji 2Research Centre for Smarter Supply Chain, Dongwu Business School, Soochow University, No. 50 Donghuan Road, Suzhou, Jiangsu 215006, People's Republic of China Email: Ifvorii09@yahoo.com Modestus .0. Okwu department of Mechanical Engineering, Federal University of Petroleum Resources Effurun, Delta State, Nigeria. Email: mechanicalmodest@yahoo.com Victor ,M. Mbachu department of Industrial and Production Engineering, NnamdiAzikiwe University, Awka, Nigeria. Email: Profvictor2000@vahoo.ocom Abstract Maintaining a sustainable supplier network is pivotal in businesses that are in pursuit of steady growth and remarkable corporate relevance. The dreadful impact of the COVID-19 pandemic outbreak has grossly shaken the global supply chain networks, and the post-pandemic realities are presumably going to be more severe on the developing economies.A lot of businesses are shutting-down leading to an incredibly high record of unemployment statistics, and inflated delivery cost of products. Panic 254 buying among consumers and firms has distracted the usual consumption patterns and created market anomalies. The supply chains have been adversely impacted and plagued by uncertainties and have defiantly affected the manufacturing supply chains. However, the COVID-19 pandemic has presented opportunities for manufacturing supply chains to shift towards more resilient and authentic sustainable supplier selection. As observed in these recent happenings, organizations that had resisted change suddenly found themselves embracing it. The economic impacts of the pandemic on the emerging economies were adequately described in this work. Most of the recent studies that are related to sustainable supplier selection process in the manufacturing sector during the pandemic situation are detailed. A framework for determining the impact of the COVID-19 pandemic on the sustainable supplier selection process for effective supply chain management in the manufacturing sector was revised and proffered. Illustratively, a multi-criteria decision approach of Analytic Hierarchical Process (AHP) was applied to determine the impact of the pandemic on sustainable supplier selection in the manufacturing sector of the emerging economy. Keyword: Supply chain, COVID-19 Pandemic, sustainability, emerging economy. 1 Introduction The outbreak of COVID-19 pandemic in Wuhan City of China in December 2019 hasvirtually spread all over the world and has become an international health issue (Elavarasan and Pugazhendhi, 2020). The presence of this highly infectious disease has become a serious health and economic problems because of various global social and environmental transformations which have occurred as a result of economic development (Tisdell, 2020). Hence, the scientific research community are making consistent efforts since the onset of the COVID-19 pandemic, to provide insights on various issues that relate mechanism of the spread of the virus, its adaptation plans and policies and of course its impact on various organizations. The COVID-19 pandemic has generated a unique era in the world with consequences in different aspects of our daily life 255 (Rizou et al., 2020), posing a severe threat to the healthy lives and well­ being of millions of people around the world (Pan and Zhang, 2020) even though resulting in positive environmental implications due to the nationwide lockdowns (Sharma et al., 2020). The pandemic has far- reaching consequences beyond the primary health threat. Inflation is witnessed as the cost of local production goes up due to the travel ban, trade and transport restrictions. Noticeably, this disruption has bullwhip effects on incomes, particularly for informal and casually-employed workers. Most businesses have started to engage in cost-cutting measures, withdrawal of some of their employee’s entitlements and even taking slices on dividend payments (Meester andOoijens, 2020). A lot of businesses are shutting-down leading to an incredibly high record of unemployment statistics, and inflated delivery cost of products. Various enterprises are facing serious difficulties as a result of the COVID-19 pandemic including a decrease in demand, supply chain disruptions, cancellation of export orders, raw material shortage, and transportation disruptions, among others (Shafief al., 2020). Organizations that had resisted change suddenly found themselves embracing it. A deep contraction is recorded in the manufacturing sector, with the automotive industry having the lowest production index since 1987. Panic buying among consumers and firms has distracted the usual consumption patterns and created market anomalies. All these observed trade anomalies has influenced many organizations into changing their key business strategies and procedures of doing things(Dwivedi 0) (An et al., 2017; Jaberidooster al., 2015). The pairwise comparison of the identified criterion x, can be shown in Eqn. (1): ' 1 612 ••• blx B ^21 1 •• b2x = A n bX2 •.. 1 . ( 1) Where bij represents the relative importance of the ('''sustainable supplier selection criterion with respect to the / ' ‘sustainable supplier selection criterion. The relative importance of criterion/' can be computed using Eqn. (2): bu = 7 - ; bij> 1 i j = 1, 2, 3, ...x. bV (2) Step 3: Compute the priority weights This step involves determining the pairwise comparison matrices of the dimensions and criteria are used to compute the eigenvalues and eigenvector. This is followed by computing the weights of the antecedents using Eqn. (3): ' 1 b12 • blx ■y/ yi' b2i 1 . • b2x X y 2 = Xmax y 2 bx 1 bx 2 •.. 1 . y x. y x. (3) Where, htiax represents the maximum eigenvalue of the matrix B, which can be computed from the eigenvector Ymax = [yi,y2, ..., yx\ 271 The normalized value of the criteria for sustainable supplier selection in the manufacturing sector during a pandemic can be computed by utilizing Eqn. (4): Y = y i yj.Zf-iVZf-iV (4) Where Y represents the vector coefficient weight while w, denotes the weights of the criteria and x signifies the total number of the criteria in the current study. Step 4: Investigate the ratio o f consistency The ratio of consistency of pairwise comparison matrices can be determined using the equation below: RC = RI/CI (5) Where RC signifies the ratio of consistency, RI signifies the index of consistency and Cl signifies the random index of consistency. The values of the random index of consistency Cl are presented in Table 2. The value that is determined for RC is preferably less than 0.10 in other to attain a greater level of consistency. Thus, the RI values are calculated using the following equation: RI = A m ax m m- 1 (6) Table 2_____ Random index of consistency m 1 2 3 4 5 6 7 8 9 10 0.58 0.9 1.12 1.24 1.32 1.41 1.45 1.49 272 o o C3 3 .2 . A n I llu s tr a t iv e E x a m p le We consider some expert opinions within the manufacturing sector of an emerging economy on the impact of the COVID-19 pandemic on sustainable supplier selection using AHP design questionnaires. A minimum of 10 completed AHP designed questionnaires is considered sufficient for effective and reliable decision making on the impact of the pandemic on the sustainable supplier selection in the manufacturing sector (Dong and Cooper, 2016; Moktadiret al., 2019). A simple arithmetic mean is utilized to aggregate the responses of the experts in the manufacturing sector within the job categories of production manager, operations manager, purchasing manager and general manager into a pairwise comparison matrix. Table 3 shows the initial step in the AHP computations which comprises of the pairwise comparison matrix of the dimensions for the experts. Table 3 Pairwise comparison matrix of the dimensions Dimension EC EV SC PN Relative Rank EC 1 1/3 3 1/3 0.1507 3 EV 3 1 5 3 0.4909 1 SC 1/3 1/5 1 1/5 0.0670 4 PN 3 1/3 5 1 0.2913 2 Maximum Eigen value= 4.1981; RC= 0.0742; RI= 0.0660 Table 3results show that ‘Environmental dimension’ is the most important dimension with a relative weight of 0.4909. This is followed by ‘Pandemic dimension’ which has a relative importance weight of 0.2913. The third in rank is the ‘Economic dimension’ which has a relative weight of 0.1507, while the least ranked is ‘Socialdimension’ with a relative weight of 0.0670. These pinpoint the high impact that the environmental and pandemic dimensions have on the decision to implement sustainable supplier selection in the manufacturing sector of the emerging economy. Following the results in Table 3, the economic dimension might not exhibit a high influence/ impact on the sustainable supplier selection unlike the environmental and pandemic dimension. The least impacting of the dimensions on the sustainable supplier selection process during a pandemic situation is the social dimension 273 according to Table 3 results. Likewise, the pairwise comparison matrix for the criteria in each dimension and their respective relative importance weights were determined by the decision group of experts in the manufacturing sector of the emerging economy using the proposed AHP equations (See Section 3.1). The global weight of the dimensions and criteria are determined from the pairwise comparisons which were developed using the responses of the experts in the study survey. Ultimately,the global ranking of the specific criteria is determined from the global weight by finding the product of the relative weight of the dimension and each criterion and presented in Table4. Table 4 Global ranking of the criteria for sustainable supplier selection during a pandemic_________________________________ Dimension Relative Factor Relative Relative weight weight rank Economic 0.4909 Reduced price/ cost of a 0.1858 2 (EC) product (EC1) Presence of efficient 0.0960 3 production technology (EC2) Financial capability (EC3) 0.2108 1 Environmental 0.1507 Technical competence of 0.0358 4 (EV) employees (EV1) Development of 0.1400 2 \v sustainability abilities (EV2) V- Sustainable product design 0.0890 3 (EV3) i * Regular environmental 0.4482 1 audits (EV4) Social (SC) 0.0670 Health and safety standards 0.1062 3 (SCI) Policy formulation and 0.2605 2 compliance (SC2) Social responsibility (SC3) 0.6333 1 0.2913 Changing regulations (PIN) 0.0716 2 274 Pandemic Health threats (PN2) 0.2620 1 (PN)______________________________________________________ As can be seen from the Table 4 results, the financial capability of the firm, the reduced price of products and health threats are highly critical and impactful on the sustainable supplier selection process during a pandemic situation. This is deduced from the global ranking of the criteria with the highest-ranked criteria notably the criteria that has the highest impact on the sustainable supplier selection process during a pandemic. This further buttresses the fact that health threats are very impactful on company operations particularly the sustainable supplier selection process during a pandemic situation. During the pandemic, health concerns are critical in most firms’ decisions and companies are mandated to make plans to identify and eliminate operations and materials that pose a direct health risk from the COVID-19 to the company’s employees and consumers (Sheth, 2020). Also, firms can imbibe behavioural changes that are related to pandemic outbreaks which seem to be connected with personal protection such as the use of masks (Klemeset al., 2020). The financial capability of the firm is also critical for effective sustainable supplier selection as sufficient budgetary allocation is highly essential in sustainability investments (Kusi- Sarponge? al., 2019). In addition, the reduced price of products can induce sales growth and influence the sustainable supplier selection process during the pandemic that is laden within uncertainties and dynamic product demands. 4 Conclusion Globally, companies are facing increasing pressure from the government regulatory agencies and other relevant stakeholders to actualize sustainability development in their supply chains. Notably, the manufacturing sector is a product system that relates directly and indirectly to economic wealth creation, impact on the natural environment and social systems along the product’s life cycle (Kusi- Sarpongef al., 2019).Sustainable supplier selection remains the initial point of sustainable supply chain management as companies consider 275 ways to effectively implement sustainable supplier selection. The COVID-19 pandemic presents numerous opportunities to implement sustainable supplier selection in the manufacturing sector. This might be attributable to the huge role that manufacturing sector plays in producing a vast variety of products to meet dynamic consumer requirements. The emerging economies of the world have succeeded in generating financial gains through their manufacturing sector as the backbone of the economy; but. it is important to notice that these nations have been far away from achieving sustainability within their system (Yadav et al., 2020). Furthermore, the widely imposed lockdown and movement restrictions have distorted the usual routine business pattern ofmost manufacturing sectors in the emerging economies (Shafi et al., 2020). Manufacturing companies in the emerging economies need to evaluate their sustainable supplier selection process in the current pandemic crisis. The wealth of solutions is expected from this present odd situation, posed by the recent pandemic outbreak, to be best equipped to contain such outbreak in the future and still maintain a sustainable supply chain network. The proposed framework for determining the impact of the pandemic on the sustainable supplier selection process in the manufacturing sector can be applied to other industrial sectors that seek for ways to select the right suppliers with sustainable development in mind. Industrial managers can utilize the framework to evaluate other strategic decisions that might be related to the sustainability dimensions and criteria for improved performance and increased global competitiveness. The pandemic and environmental dimensions are much more impactful in implementing sustainable supplier selection in the manufacturing sector in a pandemic situation. This calls for more theorization and exploration of the issues in various industrial settings in emerging economies for a fair generalization. Specifically, the health threats in addition to the reduced price of products and firms' financial capability also have a huge impact on the sustainable supplier selection process amongst other criteria during the COVID-19 pandemic. 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A major issue in the development of TSP algorithm involves how to handle the large number of subtour eliminating constraints which contribute to the exponential growth of computational time associated with TSP algorithms. In this chapter, basic concepts, development and many numerous research efforts of Professor O.E. Charles-Owaba on TSP were discussed; some of his works on the concept of the TSP set sequencing algorithm were highlighted. Keywords: Traveling Salesman Problem, Subtour, Machine setup problem, Set Sequencing Algorithm, Combinatorial optimization, Sequence dependent setup, Charles-Owaba 1.0 Introduction The need to determine the minimum total length of the route while visiting every point once in a given set gives rise to the traveling salesman problem (TSP). The TSP is an important and popular problem in combinatorial optimization that has attracted a lot of interests in operations research, mathematics, computer science, engineering and other research areas (Ezugwu & Adewumi, 2017; Kieu, 2019; Oladokun & Charles-Owaba, 2011). TSP can be stated as: “Given N cities and the distance or cost between each pair of cities, a salesman starting in one city wishes to visit each of N-l other cities once and only once and return to the starting point. In what order should he 287 visit the cities to minimize the total distance travelled?” Mathematically, the problem can be stated as: Given a ‘cost (distance) matrix’ C = (Ci;), where Qy is the cost (distance) of traveling from city i to city j (i, j = 1, 2, . . n), find a permutation (ix, i2, i i , ..... , in) of the integers from 1 through n that minimizes the quantity C i . i 2 + ^2 * 3 + ' 1 ' + ^ i n i i- Historically, the TSP has assumed many interesting names such as the laundry van problem, and the messenger problem. From a scheduling perspective, TSP is equivalent to the sequence-dependent single machine setup problem or simply referred to as machine setup problem (MSP). The TSP which was first formulated in the 1930s, came to prominence in the United States of America, in the 1950s, when solving a 33-city problem instance was used as a promotional contest by Soap Company for a price of $10,000.00. 2.0 Traveling Salesman Problem and Applications The TSP as a combinatorial optimization problem has an associated decision problem that seeks to determine the cheapest cost route (i.e. route/distance) available to a salesman to visit a specified number of cities and return to the beginning city. This unique problem description of TSP has attracted numerous attention and research efforts from scientists across the globe. Apart from its theoretical importance, countless numbers of practical and interesting problems across several industries have been formulated as a TSP model within the context of optimization. The TSP is popular because of its practical relevance and application in many areas such as routing of vehicle, manufacturing and assembly of parts, manufacturing of electronic board manufacturing, scheduling of jobs in the production system, andgroup technology (GT) approach to manufacturing. The varied applications of the model remain the key motivating factor in the continued interests of many researchers in TSP. For example, in printed circuit boards (PCBs), the objective is to determine an optimal sequence for drilling circuit board holes considered as cities to be visited by drilling machine head (salesman) to reduce machine travel time or its associated cost (Grostchel, et al., 1991). In 288 inventory order picking problem, a server or attendant (salesman) need to travel within the warehouse to collect a series of orders (cities) to minimise lead-time. Given the arrival of an order for a subset of items stored in a warehouse, an attendant/automated vehicle/server has to move strategically to collect these items before shipping it to customers. The objective here is to minimize the lead time of services to customers. Other applications include the sequencing of tasks on a weaving machine with set-up costs, the order spread elimination problem in cutting-stock model encountered in glass manufacturing, the problem of crystal orientation time reduction during the study of the atomic structure of crystals with x- ray diffractometers, efficient manpower utilization associated with the rostering of duties in public transport system (Bard et al, 1994; Foulds and Hamacher, 1980; Keuthen, 2003; Ohno et al, 1999; Rajkumar & Narendran, 1996; Al-Haboub & Shorik, 1993; Madsen, 1988; Ferreir, 1995). Also, there are research work that has emanated from the contributions of Professor Charles-Owaba to the traveling salesman problem. One is the simultaneous optimization of makespan (C max) and the number of tardy jobs (NT) in a single machine problem with sequence-dependent setup time as described in Oladokun et al (2011). Another interesting application of TSP is in the music industry where the problem of generating harmonious song-list was modeled as a single machine setup problem with accompanying solution software (Oladokun et al., 2011). 2.1 The Single Machine Setup Problem In a general-purpose work facility, the set-up time is an interval of time between the end of a job’s processing and the beginning of the next available job. The machine setup can be sequence-dependent and sequence-independent. A schedule maps (or allocates) resources to tasks (or activities) over a specified period while a sequence involves the ordering of activities through machines or resources. The sequence- dependent machine setup problem minimizes a pre-defined cost or time objective of re-setting a facility by determining the optimal sequence required to perform a set of N operations. For a single machine commissioned to process job i and j, the scheduling problem of 289 optimising the makespan, Cmax (or completion time) with sequence- dependent machine setup times S;y (j is processed immediately after /) is the single machine setup problem (MSP). In MSP, the sequence of X (stations) parts being processed by a single machine to minimize Cmax can be likened to the traveling salesman problem. In scheduling, the modeling structure of the TSP is also referred to as sequence-dependent MSP. In many contexts, terms such as MSP and TSP are used interchangeably. In a static single machine scheduling scenario with no sequence- dependent setup times, makespan minimization is a trivial problem because Cmax is the same irrespective of the sequence adopted. However, in many practical scheduling problems with sequence-dependent setup times, makespan becomes a function of the job sequence. A classical example of such a single facility problem is found in the mixing of different paints produced repeatedly on one machine in fixed sequence per production cycle. The setup time corresponds to the cleaning time of the machine between colours changes; this depends on the time required for the colour to be removed, and the start of production for the next colour. Another example is the group technology (GT) approach to manufacturing systems design using TSP set-up time reduction principle, this exploits the sequence dependency of set-up times of some part families (Charles-Owaba & Lambert, 1988; Karabat & Akkan, 2006). 2.2. Other Variants of TSP TSP can be categorised as symmetric and asymmetric. For the symmetric case, the distance (or equivalent cost) of travelling from the station (or city) i to station j is the same as travelling vice-versa (i.e. city j to city i) i.e. Cij = Cji. However, the asymmetric TSP is more generic in that Cij ±Cji, and this portrays the real-life scenarios or problems such as when the to and fro trip fares are different for the pair of cities (Oladokun & Charles-Owaba, 2008). The TSP can also occur as cyclic when the salesman returns to the starting city or acyclic when the salesman stops at last city without ‘return home’ (Charles-Owaba, 2001). The Minimum Latency Problem (MLP) is another variation of the TSP. which aims to 290 minimize the sum of arrival times at vertices, or the sum of clients waiting time to receive service and other many practical applications (Silva et al, 2012). The Time-Dependent TSP is a generalized TSP where the costs between pair of cities depend on their position in the sequence (Abeledo et al, 2013) while in the Time-Dependent TSP with Time Windows variant the time dependence is captured by considering variable average travel speeds Montero etal 2017). There is another variant in the context of maritime transportation called the TSP with Draft Limits (TSPDL) that is modelled to account for restrictions on the port infrastructures (Battarra etal, 2014). 3.0 Solving Travelling Salesman Problem The TSP was infamous amongst scientists in early developmental years due to lack of scientific methodology for solving the problem. In TSP and other real-life instances of combinatorial problems, as soon as the number of cities increases, more computational resources will be required to solve the problem effectively and efficiently. Early solution approach includes a simple method of randomly chosen locations in the Euclidean plane as proposed in 1938 to a TSP application in farm survey, making a finite number of trials, with rules that may reduce the number of trials, and a modified assignment problem algorithm (Robinson, 1949). The TSP camouflage its computational complexity with a deceptively easy to grasp definition and remains a very attractive and productive platform for developing and testing many combinatorial optimization procedures. The invention of the linear programming simplex algorithm ushered in a new world of possibilities when Dantzig et al (1954) formulated the TSP as an integer linear program and used the cutting plane method to find an optimal solution for a 49-city problem. There have been several adaptations of the LP algorithms for TSP, such as the use of dual LP algorithm for LP relaxations and max-flow algorithm for identifying violated sub tour inequalities of TSP model. There were applications of branch-and-bound algorithms that adopted an assignment problem (Eastman, 1958), the minimum spanning trees problem or similar 291 relaxations as lower bounds. The branch-and-bound algorithm by Little et al (1963) was one of the most popular implicit enumeration approaches for the TSP. Other early exact algorithm approaches include dynamic programming algorithm (Bellman, 1960) and integer programming formulation solved with the Gomory's cutting-plane algorithm (Lambert, 1960). For small problem size, exact methods have proven to be effective. However, in TSP and other real-life instances of combinatorial problems, as soon as the number of cities increases, more computational resources will be required to solve the problem effectively and efficiently.Several heuristics have also been developed and applied to solve the TSP (Hossam et al, 2018; Almufti et al, 2019) . Some of the widely known local optimization techniques and variants like simulated annealing, tabu search, neural networks, genetic algorithms and ant colony algorithm have adopted the TSP as a challenging playground for evolution and testing (Xu et al, 2018; Qaiduzzaman, et al., 2020; Rossman, 1958; Tian & Yang, 1993; Walshaw, 2002; Riera-Ledesma, 2005). The cheapest-insertion heuristic (Karg &Thompson 1964), and the Lin Lopt heuristic (Lin, 1965) were some of the earliest heuristic approaches to the TSP. A chronological review of the evolution of these algorithms and heuristics is contained in Oladokun and Charles-Owaba (2011). 3.1 Computational Complexity A computational problem can be defined as a function/required to map each input jc within a given domain to an output / (x) in a given range. Computational complexity considers the number of steps an algorithm needs to take to solve an instance of a problem (Oladokun, 2006; Oladokun & Owaba, 2011). Because the computer execution time required for solving a problem is a function of the number of computational steps, the performance of an algorithm is, therefore, measured as the maximum number of steps it requires for any instance of size N expressed as a function of N. A polynomial algorithm bounded by a polynomial function of instance size N is considered efficient, while an exponential algorithm bounded by an exponential function of instance size N is considered inefficient or computationally expensive (see Cook 292 et al, 1998; Garey & Johnson, 1979; Johnson & Papadimitriou, 1985; Walshaw, 2001; Walshaw, 2002; Saadani et al, 2005). Hence, a problem is considered easy if there is a polynomial-time algorithm to solve it and hard otherwise (Cook et al, 1998; Marcotte et al, 2004; Gamboa et al, 2006). The TSP is classified as a hard combinatorial optimization problem with no polynomial-time optimizing algorithm (see Lawler et al, 1985; Applegate et al, 2004; Zhang, 2004). The TSP and its variants belong to a class of computationally complex problems called NP- complete. The class of P and NP problems can be solved by a non- deterministic polynomial (NP) time algorithm in polynomial time. This implies that if a polynomial-time algorithm is found for the TSP, it means all other NP-hard is solvable in polynomial time. This theoretical importance has been a key driver for the TSP research interests (Roberts & Flores, 1966; Fischetti & Toth, 1992; Dorigo & Gambardella, 1997; Applegate et al, 2004; Zhang 2004). 3.2 Algorithms and Heuristics Like all other NP-hard discrete optimization problems, there are two classes of solution methods for the TSP problem: exact or optimization algorithms and heuristics also known as approximation algorithms. While exact algorithms are designed to contain a proof of optimality of the resulting solution; and have a mechanism to obtain the so called global optimal solution, they are computationally expensive and bounded by an exponential function of instance size N. TSP heuristics or approximation methods, on other hand, are designed to obtain a good solution without the confirmation of optimality and are mostly polynomial-time methods. Many heuristics are modified exact algorithms designed by jettisoning their optimality mechanisms as trade­ off for achieving computational efficiency. Since the TSP is a discrete optimization problem with a finite number of possible solutions, though this number is an exponential function of the problem size N, the complete enumeration is guaranteed to yield an optimal solution. However exponential growth renders this approach not practicable for even 2-digit size problems. For instance, an explicit 293 enumeration algorithm running cn the fastest computer would need about two days to find an optimal solution tor a (N=20) problem size while for a (N=25) problem size the time grows to 400 centuries! Hence, practical algorithms are based on implicit enumeration which does not search through all solution space. Many existing algorithms are based on methods such as Integer Linear Programming method which formulate the TSP as a linear programming problem in zero-one variables and attempt to prove optimality using the concept of cutting planes. The TSP has been solved using dynamic programming formulation, branch and bound algorithm. While these algorithms are not efficient for practical problems they have been the basis for very good non-optimizing heuristics. The Nearest Neighbour Algorithm is an example of such heuristics with easy to implement variations like multi-start approach Nearest Neighbour (see Johnson et al, 1997; Charles-Owaba & Oladokun, 1999; Hurkens & Woeginger, 2004). There are insertion methods (Karg &Thompson, 1964), the 2-opt and 3-opt heuristic which works as tour improvement methods using the deletion and replacement of 2 non-adjacent edges. The Lin-Kemighan k-opt method is a generalized implementation of the 2- opt tour improvement method (Lin & Kemighan, 1973; Chandra et al, 1999; Helsgaun, 2000). There are also search heuristics such as genetic algorithm, simulated annealing, and tabu search. The genetic algorithm and many of its variations developed for the TSP are designed to mimic the biological evolution concepts that support the evolution of improved population of solutions. This improvement is achieved by mathematically mirroring evolution concepts such as survival of the fittest, crossover or reproduction, genetic mutation and migrations and similar evolution concepts (Charterjee et al. 1996; Johnson & McGeoh, 1997). The tabu search is another popular general heuristic procedure used for the TSP. Tabu search solves the problem of infinite cycling associated with improving search procedure by forbidding some moves, ‘taboo moves’, that will return to immediately previously 294 visited point in the solution space (Radin, 1998; Kolohan & Liang, 2000). Simulated annealing is a search technique that controls cycling by mimicking the annealing process for improving the strength of steel (Tian & Yang, 1993; Johnson & McGeoh, 1997; Radin, 1998). 3.3 Feasibility and Sub tours in TSP Solutions Feasibility due to subtour occurrence is a major issue in the formulation of the TSP or similar permutation sequence problem. Design of subtour constraints is a major challenge in model and algorithm development for the TSP. While it is easy to understand subtours, crafting subtour elimination constraints remains a difficult and challenging task (Radin, 1998; Oladokun and Charles-Owaba, 2011). Hence, theoretical principles for crafting these constraints within the context of algorithm development has been the thrust of many TSP works such as Crowder and Paderg(1980) which adopted a linear programming relaxation, Grotschel (1980) which used a cutting-plane algorithm with cuts involving sub tour inequalities, Hong (1972) used the Ford-Fulkerson max-flow algorithm for finding violated sub tour inequalities. In fact, the method for handling sub tour occurrences is what distinguishes one solution method from another and has influenced the various solution approaches. Meanwhile, the large number of sub tour elimination constraints, even for a modest number of points, makes the problem practically intractable. The enormous number of computations required to solve such system of equations does not allow for the direct utilization of the ILP for TSP. However, researchers have adopted the idea of using the ILP to find good lower bound for the TSP. This lower bound procedure can then be used for assessing the effectiveness of heuristics solutions. For example, for the 380 cities record-breaking work of Crowder and Paderg (1980), a linear programming relaxation was adopted. An integer-programming solver was used to carry out a branch-and- bound search on the final linear programming relaxation. If the 295 solution found using this search does not produce a tour, the subtour inequalities violated by the solution obtained is added back again using cutting-plane algorithm (Grotschel,1980). Subtours constraints require huge computational efforts. One approach to minimize these efforts in heuristics procedures is to adopt TSP formulation with simpler constraints such as formulating the TSP as quadratic assignment problem (QAP) and some adaptations of improving search methods on the QAP formulation. Oladokun and Charles- Owaba (2011) described some graph theoretic concepts for dealing with these sub tours constraints within the context of the set sequence algebra. 4.0 The Set Sequencing Algorithm (SSA) Charles-Owaba (2001, 2002) proposed the set sequencing algorithm as a basis for the TSP solution. The set sequencing procedure describes a complete TSP sequence or tour as a set of N TSP matrix elements (links). The procedure then defines as the transformation of a known sequence (Si-0 to a new sequence (Si) by feasibly replacing a subset of its links (Lr) with an equal number (M) of candidate links (Lc) using a recursive function Va(Si) =Va(Si-i) +A(Lr, Lc, M). Where Va(Si) and Va(Si-i) are the respective solution sequence values and A(Lr, Lc, M) is the exact amount Va(Si) is changed by the replacement operation. However, the original SSA had the challenge of feasibility; it sometimes results in infeasible solutions or subtours. The redesign of the SSA to develop a subtour-free set sequencing algorithm was the focus of a PhD thesis (Oladokun, 2006) supervised by Professor O.E Charles-Owaba in the Department of Industrial Engineering, University of Ibadan (see Oladokun & Charles-Owaba, 2011). While implicit enumeration algorithms and heuristics view the machine setup problem in terms of the individual sequences and are designed to search through N factorial possible sequences (Charles-Owaba, 2001). The set sequencing concept addresses the machine setup problem differently, by searching for optimal elements among N(N-l) TSP matrix elements. A set of candidate links are used to replace some or all of the 296 links of a given sequence to iteratively form improved sequences (Kwon et al, 2005). The SSA represents a major contribution of Professor O.E Charles-Owaba to the literature of the travelling salesman problem. 5.0 Conclusion The traveling salesman problem has attracted quite a lot of interests for several decades evident by its wide practical applications such as routing, logistics, drilling, surveying, genetics, manufacturing, telecommunication, neuroscience, scheduling, to mention just a few. In scheduling, the traveling salesman problem or the sequence-dependent machine setup problem is an attempt to determine the minimum- total- length route while visiting every point once in a given set. In this chapter, the numerous research efforts of Professor Charles-Owaba to model and solve the different variants of the traveling salesman, such as the simultaneous optimization of makespan (Cmax) and the number of tardy jobs (NT) in a single machine problem, group technology (GT) approach to manufacturing systems design using TSP set-up time reduction principle, and graph theoretic concepts for dealing with sub tours constraints within the context of the set sequence algebra were highlighted. These research efforts were discussed by considering the single machine set-up problem (MSP) and other variants of TSP, the need to eliminate sub tour occurrences in the search for an optimal tour, which grows exponentially as the size of the problem grows. This difficulty brings to fore the concept of computational complexities, algorithms and heuristics available to solve TSP. 297 References Abeledo, H., Fukasawa, R., Pessoa, A., & Uchoa, E. (2013). 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Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem, Journal o f Artificial Intelligence Research, 21. 471-497. 304 CHAPTER 13 On Safety, Health, Productivity and National Development ‘A Kolawole and 2 A A Opaleye 1,2Department of Industrial and Production Engineering University of Ibadan Ibadan, Nigeria 'Corresponding author: kolawole_adekunle@yahoo.co.uk Abstract Occupational health and safety has become an important subject of discourse globally. The aim is to safeguard the safety, comfort and well­ being of the workforce of any nation. This is applicable to all branches of industry, business and commerce, information technology establishments, recreational facilities without leaving out domestic activities. As a result of the effect of this subject on the economy and national development together with the challenges involved, the issue has attracted the attention of many stakeholders including government, management of work organisation, researchers among others. In this chapter, the combined impact of safety, health, productivity and national development is conversed. It is concluded that for a nation to develop, productivity must grow steadily and one of the key ways to attain this, is that the health, safety and well-being of the workers who are the drivers of development must be guaranteed in any workplace. 1.0 Introduction The issue of health and safety has become a worldwide subject. The reason is that safety, comfort and well-being of the workforce of any nation is very germane to the goal of attaining national development. Safety and health matters are important to any area of human endeavours 305 and are applicable to business and commerce, information technology establishments, recreational facilities and even domestic activities. As a result of the impact of this subject on the economy of any nation and by extension, national development together with the challenges involved, the issue has attracted the attention of many stakeholders including researchers, management of work systems and government agencies. In virtually all countries of the world occupational safety and health is an important subject matter as efforts are made to for the safety and well­ being of people at work. The importance of safety and health cannot be overstressed, so also is productivity. Work as noted by Charles-Owaba (2010) is very vital for any nation to achieve development as it is the only known bridge between human desire and its fulfillment. Hence for an individual or nation at large, any meaningful development cannot take place unless work is done. In this chapter, the synergy between safety, health, productivity and national development is discussed. 2.0 Safety, Health and Productivity Though the keywords stated here may not be unfamiliar to most readers, it may still not be out of place to make attempt to describe them. 2.1 Safety and Health Safety according to OSHA 1800 1 as quoted by Paul (2013) is a tool or device designed to prevent accidents, incidents and injuries which can be achieved by eliminating or reducing hazards and risk involved in every working activities that are conducted on industrial or work premises. In occupational safety and health, safety is seen as state of being safeguarded against occupational accident,damage, injury, death and other detrimental circumstances while at work. Furthermore, it is where known hazards that may be present in a work environment are reduced, Hughes and Ferrett (2011) define health as the protection of the bodies and minds of people from illness resulting from materials, processes or procedures used in workplace, while WHO statedthat health is a state of complete mental, physical and social well-being and not merely the absence of disease or infirmity. Eurofound (2015) was of the view that health and safety is not just prevention of accidents and disease but also consists of every aspect of workers’ comfort. The definition of ILO and 306 the WHO reiterated that health and safety regulations are aimed at advancement and sustenance of: (i) The maximum degree of mental, physical, and social well-being of all employees in every occupation. (ii) The avoidance of workers leaving work as a result health challenges due to their working conditions. (iii) The security of workers in their occupation from risks coming from factors hostile to health; (iv) Every worker is placed in an environment that is adapted to his or her physiological and psychological capabilities (Eurofound, 2015) Based on the aforementioned definitions and others from the literature, Molamohamadi and Ismail (2014) submitted that two major objectives of occupational safety and health and sustainable development maybe highlighted as: (i) Protecting the workers’ mental and physical health by averting work related accidents, injuries, and diseases and making work environment safe. (ii) Focusing on the nature and the environment by forbidding and or ̂ controlling the usage of injurious objects to the environment, decreasing environmental effluences, and using resources prudently. 2.2 Concept of Productivity Like any other subject, productivity has been defined in several ways. European Productivity Agency (EPA) explained productivity as an attitude of mind. It is deliberately making efforts to make progress, constant advancement of what is in existence. It is the conviction of ability to get better than yesterday and always. It is the continuous adaptation of economic and social life to changing conditions and continual efforts to apply new procedures and techniques. Another definition is that productivity is the relationship between the output of a production or service system and the input available to generate this output hence productivity is defined as the efficient and effective use of resources (Charles-Owaba, 2004). And resources include, land, labour, energy, information, materials e.t.c. in the production of goods and 307 services.In addition, itis not only determinedby quantity and quality, but also by the valuethe customer gains. This is particularlytrue for the service industry. Perhaps an all encompassing description of productivity is by Prokopenko (1987) who stated that on a general note, productivity may be seenas a comprehensive assessmentof how an organization meet somestandards stated as follows: (i) Objectives- which indicate the extentto which the objectives are attained, (ii) Efficiency: How wellthe resources are utilisedi.e. doing things rightand (iii) Effectiveness: This is comparing what is achieved to what is possible, i.e. doing the right things. Productivity is important to the life of industrial firm and the economic progress of a country. It is expected thatwhen productivity is growing in every facet of the economy, the standard of living of citizens should improve. 3.0 Work system, Safety, Health and Productivity Workers (man) and workplace are two words that appear common to all the terms either implicitly or explicitly. Safety and health are addressing issues that have to do with man while at work, and productivity has to do with performance of work systems where man works. It is imperative to examine on the roles of man and the work system. 3.1 Man and Work system Production of goods and services take place in a work system. This indicates that productivity would be affected by the environment and the way a work system operates. A work system is a system in which man is one of the main components interacting with facilities, materials, information, energy and finance to perform any of the these objectives: (i) Transform raw materials into finish goods (ii) Extract raw materials in their natural state and (iii) To perform predetermined service or an item or people. Any industrial set-up or establishment would be involved in any of the three objectives of work system. Furthermore in a worksystem, work would either be performed by man or machine and or combination of the 308 two. A combination of the two is termed man-machine work system. Charles-0waba (2010) defines man-machine worksystem as the combination of humans and machines as well as their mutual interrelations in the effort to receive and utiliseinput resources to attain desirable outputs. In another words man-machine system is anarrangement in which one or more human beings together with at least one physical componentwith interrelationship to bring out from given set of inputs, some desired outputs. Itcan vary from a simple structure to a very complex one.Irrespective of whether a worksystem is simple or complex, man at work is the main focus. It is man that drives work systems, hence his safety and health are paramount. 3.2 Man-Machine Work system On a general note, the main goalof designing anywork system is to determine suitable man-machine combinationsthat most effectively and efficiently make use of information, material, energy and finance to accomplish relevant tasks for the achievement of set goals and objectives. . During the designing process, parameters that relate to man should be regarded as constants while those havingto do with facilities, material, energy, information, finance and environment are considered as variables. Hence, to put in place a work system with the desired level of productivity in view, the systems variable values are chosen to suit the nature of man, his abilities, capabilities and limitations. The reasons for this approach aredue to the following: (i) In virtually all work systems, man acts as the controller, to ensure effective and efficient control therefore the designer is constrained by the capabilities and limitations of man. A designed work system that does not take this into consideration may not be controllable or usable. (ii) The designer can at will restructure the machine and the material information system and the environment if need be. However, to redesign a man is an impossible and infeasible task. Thus, man components are regarded as the most critical or importantinany work system and it is necessary that this prominence is given to man in everywork system.In any work system/workplace safety practitioners must be concerned with the operations in the work system 309 in such a way as to ensure that the main principle of Human Factor Engineering/Ergonomics of “fit the task to the man and not the man to the task” is maintained. It should be noted that this principle is applicable in manufacturing and commercial environment as well as service industries including hospitals, education, sports as well as domestic and leisure activities. Upholding this principle in workplace would lead to higher productivity, safety of the workers and reduction in rate of accidents while failure to adhere to this will lead to negative impacts of various forms of musculoskeletal disorder and cardiovascular problems,increases possibility of operator-related health hazards together with decrease in productivity. 3.3 Man-Machine Work system and Environment Whether or not man performs effectively and efficiently in his workplace to ensure increase in productivity and guarantee his safety and health will depend on some factors. These factors to some extent will determine the health, well-being, safety and efficient performance in working place as well as everyday activities. Ergonomists have identified these to include general environment, immediate environment and personal inherent limiting factors in man(Murrell, 1965; Groover, 2007) 3.3.1 General Environment This refers to ambient conditions in the workplace and includes such as lighting conditions, background colour, heat or cold, noise, humidity, pollution, wind velocity, pressure, vibrations, and radiations. These general environments have to be conducive to the body requirement so that man can work effectively and efficiently. One of the tasks of management is to determine the value of the above which will be conducive to the productivity of the work system. 3.3.2 Immediate Environment The immediate environment include such things as tools, materials, machines, space, posture, displays, clothing, controls and other men. In specified immediate environment, the main task is that of stating the number, types, sizes and relative position of each. 310 3.3.3PersonaI Limiting Factor Apart from environmental, anatomical and physiological as well as psychological factors inherent in man that serve to limit or enhance his performance are some characteristics inherent in an individual that contribute to his good or poor performance. Some of these are anthropometric structure, physical work capacity, mental capacity, motivation, gender, age and rest activities. These ergonomic factors interact in affecting human performance. When these factors are appropriate and conducive for a worker in a work system, his safety and comfort would be guarantee and would be productive.Figure 1 presents a summary of how these factors interact to affect human performance and productivity. 311 o General Environment § J2 cc» | rce re CL Fig.l: Human interaction with work environment (source: Charles- Owaba, 2010) 4.0 Safety and Health Programme for Productivity and National development The possibilities of integrating safety and productivity are becoming increasing topical interest in occupational safety (Salminen and Saari, 1995). The desire of most productive system be it production or service system is to increase productivity sometimes at the expense of safety of workers. However, rather thanprioritising productivity abovesafety, the two should be seenas goals that can be attainedconcurrently. Karanikaser al., (2018) observed that generally, when workers are pleased with the conditions and environment where they work and also feel secured from 312 any form of injury, they would be more productive.There is therefore a need to consider how ensuring safety and health programme in workplace would eventually lead to productivity improvement. 4.1Safety and Health Programme In order to have a healthy and safe work system that would lead to increase in productivity, there should be a concerted effort for effective health and safety programme. Avoiding injuries, discomfort and death together with financial pains for employees, their families as well as employers are major concerns of safety and health programme (OSHA, 2016). Ikeoguer al., (2013) identified two approaches to health and safety programme as reactive and proactive approaches. Reactive is responding to injury or illness after occurring with an aim of reducing cost relating to illness and or injury while proactive approaches considers safety and health prior to incidence of any accident. Proactive foresees and make efforts to avoid accidents, it includes all actions directed toward removing accident, procedures used towards managing risks .analysethe environment for any form of hazard, prevent sickness or diseases and ensure that no worker has zero workday. Maintain. Ikeoguef a l,(2013) further stated that reactive is costlier than proactive programmes as it waits for the occurrence of injury or accident before taking any action. This statement of Ikeoguet al., (2013) was corroborated by OSHA (2016) with the submission that proactive method is better than reactive in handling safety and health in workplace as it recognisesthat locating and dealing with hazards before accident occurs is a much more effective approach. 4.1.1 Core Elements of Safety and Health Programme To implement and have an effective safety program that workers would want to embrace without hindering production and services, OSHA (2016) suggested some practices for an effective safety and health programme. These are described as follows. Management Leadership: Top management must demonstrate its commitment to continuous improvement in safety and health, communicates that commitment to workers, and sets program 313 expectations and responsibilities. At all levels, safety and health should be made a core organisational value by managers, establish safety and health goals and objectives, provide adequate resources and support for the programme and set a good example. Participation ofWorker: In setting goals, identifying and reporting hazards, investigating incidents, and tracking progress; workers and their representatives are involved in all aspects. All workers, including contractors and temporary workers, understand their roles and responsibilities under the programme and what they need to do to effectively carry them out. Workers are further encouraged to have means of communicating openly with management and to report safety and health concerns without fear of retaliation. Whatever may serve as barrier to worker participation in the programme should be removed. Hazard Identification: Safety and health hazards from routine, non­ routine, and emergency situations are identified and assessed with procedures put in place to continuously identify workplace hazards and evaluate risks.An initial assessment of existing hazards, exposures, and control measures is followed by periodic inspections and reassessments to identify new hazards. Any incidents are investigated with the goal of identifying the root causes. Identified hazards are prioritised for control. Hazard Prevention and Control: Employers and employees work together to identify and chooseways for eliminating, preventing, or controlling workplace hazards. Controls are selected based on a hierarchy that uses engineering solutions, safe work practices, administrative controls, and personal protective equipment (PPE) in that order respectively. A plan is developed to ensure that controls are implemented, interim protection is provided, progress is tracked, and the effectiveness of controls is verified. Training and Education: Every worker should have understanding about how the programme works and how to perform the responsibilities assigned to them under the programme. Employers, managers, and supervisors receive training on safety concepts and their responsibility for protecting workers’ rights and responding to workers’ reports and concerns. All workers are trained to recognise workplace hazards and to understand the control measures that have been implemented. Safety 314 knowledge which is basically the levelofworkers’ awareness on organisational safety systems, practices, and procedures is determined by the level of education and training that an employee is exposed to (Liu, et al., 2020). It has been found that organisations that increase the knowledge of employee about safety through safety trainingrecord lower rate of accidents and injuries (Tinmannsvik and Hovden, 2003). This stresses the importance of employees acquiring necessary skills through education and training. Programme Evaluation and Improvement: Control measures are periodically evaluated for effectiveness.Processes are established to monitor program performance, verify programme implementation, and identify programme shortcomings and opportunities for improvement.Necessary actions are taken to improve the programme and overall safety and health performance. One other important means for safety and health in workplace is to take advantage of digital tools. Safety and productivity can be improved through technology by upgrading old machinery or making use of digital record-keeping tools that track key safety metrics across all locations. Old machinery not only presents a safety risk but also results in productivity loss. Outdated equipment leads to unplanned productivity loss because most of these machines require frequent mechanical work and maintenance. It also puts workforce in danger. 4.2Relating Safety, Healthand Productivity It is obvious that safety and health compliance activities would impose cost on management of any work system. The question one may want to ask is whether safety compliance really worth it.Several studies have shown that investment in occupational safety and health is very beneficial. For example, Thiede andThiede(2015) stated that Health and safety measures decrease injuries, increase efficiency, and bring income security to workers’ families apart from intangible benefits such as trust, motivation and security. Similarly, Riano-Casallasand Tompa (2018) reported that investment in occupational health and safety per full time 315 equivalent in medium and large companies in Colombia was statistically significant at 1% level. It was estimated that 4,919 injuries were averted through these investments resulting in the avoidance of $3,949,957 in costs. Also,Hendrick (1996) stated that good ergonomics or safety and health programme is good economics. This implies that on the long run benefits to be derived would outweigh the cost. Safety should not be an afterthought and it also does not have to be associated with productivity loss. Proper and continuous safety training at all levels within any work system can reduce costly and dangerous mistakes. Effective management of any method that enhances safety and health such as ergonomics has been linked to accident and incident prevention for decades. Resnick and Zanotti (1997) and Kadefors et al. (1996) noted that a comfortable environment supported operators in performing their job tasks productively, and a safe working environment increased the confidence of personnel, reducing, in turn, the occurrence of injuries. Giving employees with well-designed workstations and training in proper body postures allows them to work more efficiently. On the other hand, poor ergonomics or safety and health practices in workplace have been associated with lower productivity (Clarke,2006; Dianat et al, 2016). Many work and everyday life situations are hazardous to health. Dul and Weerdmeester (2008) notedthat apart from different type of costs that are associated with poor health and safety programmesacross the globe, illnessesof the musculoskeletaldisorders (majorly lower back pain) and psychological diseases constitute the major causes of absence due to illness and of occupational disability. Some side effects of neglecting or non-compliance with safety principles may not manifest in the body system of the workers immediately but latter at old age. Providing the right working environment can assist in reducing these problems. 316 5.0Benefits of Safety and Health Compliance From Hendrick (1996) and OSHA (2016), it canbe deduced that effective implementations of occupational safety and health programmes bring other benefits which are summarised as follows: i. Reduction in turnover as new employees will likely findergonomically designed tasks that are not beyond their physical capacity. ii. Compensation costs and other forms of payment such as illness and engaging new employee are reduced. iii. The self-esteem of workers is enhanced. iv. Productivity would go up by making tasks easier and creating more conducive environment for employees thereby enhance overall business operations v. Workplace illnesses are avoided vi. Compliance with required laws and regulations are improved upon.Enhance their social responsibility goals vii. Absenteeism is drastically reduced as workers will not likely take off time to recover from soreness of muscles, fatigue and other musculoskeletal disorder related problemsA significant decrease in employees’compensation premiums would be achieved 6.0 Conclusion Importance of safety and health of man at work has been enumerated as key to productivity increase and national development.lt has been highlighted that it is people (workers) who are well, mentally and physically fit that would engage in activities that would lead to national development. When people are hale and hearty to perform their jobs in both public and private sectors, there would be development. The prominence placed on the importance of health of workers as explained in this chapter agrees with the saying that though health is not everything, but without health, everything is nothing. It appears safe tostate that health and safety arenot everything but with good health and safety there would be room for growth inproductivity and national development. It is concluded that a growing productivity in every ramification will lead to better standard of living of the citizens and 317 thereby national development. Therefore to attain national development, the health, safety and well- being of the workers who are the drivers of development must be guaranteed in any workplace. 7.0 REFERENCES Charles-Owaba, O.E. (2010).The Men and Machines that change the World. An Inaugural Lecture, University of Ibadan, Nigeria. Ibadan University Press Charles-Owaba, O.E.(2004). A Theoretical Basis for Industrial Ailment Diagnosis and Remedy, Journal of Pure and Applied Sciences, Vol. 7, No 2, pages 271-284. Clarke S. (2006). Safety climate in an automobile manufacturing plant: The effects ofwork environment,job communication and safety attitudes on accidents andunsafe behaviour. Personnel Rev Vol 35 pp413-430. Eurofound (2015). https://www.eurofound.europa.eu/observatories/eurwork/industria 1-relations-dictionary/health-and-safety. Accessed on 15 October 2020. Dianat I, Vahedi A. &Dehnavi S. (2016). Association between objective and subjectiveassessments of environmental ergonomic factors in manufacturing plants. International Journal of Industrial Ergonomics Vol.54 pp26-31. Dul, J. &Weerdmeester B. (2008). Ergonomics for Beginners, A quick Reference Guide 3rd Edition. CRC Press Groover, M. P. (2007).Work systems and the Methods, Measurement, and Management of Work. Prentice Hall, Upper Saddle River, NJ 07458 318 Hendrick, H. W. (1996).Good Ergonomics is good Economics. Proceedings of the Human Factorsand Ergonomics Society, 40th Annual Congress. Human Factors and Ergonomics Society, Santa Monica, CA, 90406-1369 Hughes P.&Ferrett Ed (2011) Introduction to Health and Safety at Work, The handbook for NEBOSH National General Certificate. 5th Edition Elsevier Ikeogu, D., O., Uwakwe, J., O. and Chidolue I.B. (2013). The Efffect of Health and safety Management in National Development. Mediterranean Journal of Social Sciences Vol. 4 No. 7 Karanikas, N., Melis, D. J., and Kourousis, K. I. (2018). The Balance Between Safety and Productivity and its Relationship with Human Factors and Safety Awareness and Communication in Aircraft Manufacturing. Safety and Health at Work Volume 9. Krishnan, S., Hizam S. M., Saffian, A. K. M., Baharun, N. S. andAzman, N. (2017) Safety at Workplace Enhance Productivity. Human Resource Management Research Vol 7 No. 1 Liu, S., Kwame Nkrumah, E. N., Akoto, L. S., Gyabeng, E. and Nkruma, E. (2020). The State of Occupational Health and Safety Management Frameworks (OHSMF) and Occupational Injuries and Accidents in the Ghanaian Oil and Gas Industry: Assessing the Mediating Role of Safety Knowledge HindawiBioMed Research International Volume 2020 https://doi.org/10.1155/2020/6354895. Molamohamadi, Z. and Ismail (2014). The Relationship between Occupational Safety, Health and Environment and Sustainable Development: A Review and Critique. International Journal of Innovation, Management and Technology Vol. 5, No. 3, pp 198- 202 Murrell K. F. H. (1965): Ergonomics Man in his working environment. London: Chapman and Hall 319 OSHA, (2016). Recommended Practices for Safety and Health Programmes. https://vvww.osha.gov/PublicatioTis/OSHA3885.ndf Accessed 15 October, 2020. Paul, S. V. (2013): Safety Management System and Documentation Training Programme handbook. First Edition, CBS Publishers and Distributor, New Delhi Prokopenko, J. (1987): Productivity Management.A practical handbook. Geneva, International Labour Office. Resnick M. andZanotti A. (1997). Using ergonomics to target productivity improvements.Joumal of Computer Industrial Engineering Vol 33, ppl85-188. Riano-Casallas, M. I., and Tompa, E. (2018) Cost- benefitanalysisofinvestmentinoccupationalhealth andsafetyinColombiancompanies. American Journal of Industrial Medicine Vol.61 (11) pp 893-900. DOI: 10.1002/aiim.22911 Salminen, S. and Saari, J. (1995). Measures to improve safety and productivity simultaneously. International Journal of Indutrial Ergonomics. 15 pp 261-269 Thiede, I., and Thiede, M. (2015). Quantifying the costs and benefits of occupational health and safety interventions at a Bangladesh shipbuilding company. International Journal of Environmental Health Vol 21 (2) ppl27-136 Tinmannsvik, R. K. and Hovden, J. (2003). Safety diagnosis criteria— development and testing Safety Science, vol. 41, no. 7, pp. 575- 590 320 CHAPTER 14 Garment Sizing System: A Critical Review of the Past, Present and Future Adepeju A. Opaleye1 and A Kolawole2 1,2 Department of Industrial and Production Engineering University of Ibadan, Nigeria 'opaleye adepeiu@vahoo.com (corresponding author) 2kolawole adekunle@vahoo.co.uk 1.0 Introduction With the desire to remain competitive and customer driven, companies are fast adopting business models, programs and procedures to meet customer’s volatile demand and shortened product lifecycle at efficient cost. Such business model includes mass customization and mass personalisation of products. They are fast becoming effective approach in many manufacturing sectors, such as the automobile, food, textile and garment, cosmetic industry because they offer opportunities for expanding the sphere of influence of a company, widening its customer base and production capacity. Classically, mass customisation business model is described as the production of goods and services to meet needs of a defined market segment at a cost closer to that of the mass production system. It combines the economies of scale in mass production system with segmentation of market demand. Empowered by the internet, digital devices and social networks, customers are increasingly expressing interest in the design, and development of their product while powerful lever such as flexible computer-aided manufacturing system enable companies to customize or adapt standard products which meet many end users tastes and preference without inventory or purchasing delays. Thus, customers are not only treated as a market segment but as an individual entity. This process of personalizing requirements enhances prosumer’s 321 ability to determine their product specification but manufacturers are cumbered with challenges of reducing product life cycle, increased product complexity, and immense pressure from global competition. The garment production industry is not an exception of such developments. The industry has one of the most complex and diverse products. For example, customers desire unique garment design and style specifications suitable to their unique body proportions, specific need, and personality. A report shows that Levi Straus and Co. offers women customised pants of about 49,000 different sizes in 30styles resulting in about one and a half million options available to consumer. In order to significantly impact and drive consumers’ intentions in terms of willingness to repurchase, verbal referrals, commitment and loyalty, garment producers should adopt approach to meet customer’s dynamically changing quality requirements without increasing shopping difficulty and confusion. Lamb and Kallal's (1992) proposed the Functional, Expressive, and Aesthetic (FEA) Consumer Needs Model which provide an overall conceptual framework for designing any type of garment. Consumer’s functional requirements include fit, mobility, comfort, and protection; expressive requirements of a consumer provides an opportunity for the wearer to communicate his or her self-image while the aesthetic requirements are related to appeal of a clothing product in terms of style, colour, appearance, fashionability or attractiveness (Chae, 2017; Kasambala et al., 2016). Consumers are most likely attracted to garment items which satisfy all their intended requirements. However, according to various consumer and designer-mediated perspectives, inappropriate sizing and fitting system often result in return of the garment that they have been purchased (Connell, et al.„ 2006; Otieno, et al.„ 2016; Shin and Damhorst, 2018). Almost every industrialized nation has home-based garment sizing system for each garment type. For instance, there are Canadian Standards, German sizing system, European, American, Japanese, Korean, Chinese, etc (Gupta, et ah, 2006; Lee, 2014; McCulloch,et al., 1998; Tryfos 1986). Essentially, a sizing system takes garment-related 322 anthropometric data from a sample of individuals in the nation’s population as input to produce a number of garment sizes such that each size is for a subset of people who wear the same standard garment size. Thus, instead of dealing with fifty million (50,000,000) sizes for, presumably, fifty million (50,000,000) people in a nation; a tailoring industry may sew only twenty (20) standard sizes, for instance, to adequately cater for the millions (Mpampa, et al., 2010). Each size (a table of garment dimension values), may now have enough demand (2,500,000 potential customers in our case example). The goal of a sizing system is to provide the optimum number ready-to-wear (RTW) garment sizes for a given population with good fit for all individuals (McCulloch, et al., 1998). The literature is however sparse on the existence of garment sizing system for the Nigerian traditional clothing industry. Perhaps, this explains the slackened growth of the industry. At the moment Nigeria is unable to reap from the afore-mentioned benefits from RTW or mass customisation enterprise because it operates a “bespoke” garment manufacturing system. Tailors produce garment patterns by measuring the body size of individual patrons of the firm, and the fitting process involve physical try-on of garment along some correction steps that reflect wearer’s responses to obtain a desired fit. Unlike this production system, online customers do not have the luxury of physically trying-on a cloth and have to rely on the product image and the available size charts to select a product that fits well. As a result, they find it difficult to get garment of excellent fit. When such problem occurs in mass customised or personalised online orders, it can result in more problems than for ready-to-wear garment in mass production. While mass produced garment items can easily be sold to other customers, it may be difficult to sell personalised garment orders because it had been customized to the design, style and size of original orderer (Kim et al., 2019) . This may lead to increase in production costs and inventory management problems. Therefore, research on sizing and fit preferences is very necessary in order to deliver the bespoke customer experiences in the garment mass customisation and personalisation of Nigerian designs, thereby improve customer satisfaction percentage. 323 2.0 Overview of the Garment Sizing Problem Garments are primarily worn to provide shelter, warmth against harsh weather change and it is secondarily worn to give beauty and a sense of expression to the wearer. The application of the principles of cutting, sewing with the nitty-gritty of fabrics and skill results in the accomplishment of garment manufacture. There are criteria that cannot be overlooked in designing and making a fabric that would perfectly suit a customer and they include the type of fabric used, colour of the fabric, the style to be sown, accessories/aesthetic used with the fabric and anthropometric measurement of the consumer. Psychological and social factors are also key factors that can be categorized under the significance of a garment. Garment has over time been used as a means of expressing oneself and a way of portraying social importance (Johnson, et ai, 2014). According to Festinger (1954), human being get satisfied with the opinions made by other persons which can be consciously or unconsciously; Biolcati (2019) also highlighted that the approval of physical appearance of an individual by other persons most likely yields an increase in their self-esteem. Hence, effect of a garment fit on consumer’s appearance and subsequent self-esteem may determine consumers’ intent to repurchase a garment size. Earliest garment sizing systems were dependent on the tailor's very own understanding and first showed up in pattern books before the end of the eighteenth century (Aldrich, 2000). These sizing systems utilized the corresponding scaling technique. The interest for armed force attire brought by wars during the nineteenth and twentieth hundreds of years quickened the production of ready-to-wear (RTW) dress and constrained the improvement in size structure. The proportional scaling technique did not precisely address the issues of the market. During the second half of the twentieth century, sizes started to be created from body estimations utilizing statistical strategies (Aldrich, 2000). From that point forward, anthropometric overviews have been led, and sizing standards have been published in various nations. 324 A sizing system can be characterized as a lot of pre-decided body sizes assigned in a standard way (Winks, 1997) which highly depends on the body measurements taken on a cross-area of the objective population. Winks (1997) implied that the system comprises of a scope of sizes from the smallest to the biggest with fixed interims between nearby sizes. The production of ready-to-wear garments categorized into various sizes has changed fashion from the era of tailor-fitted garments to mass-produced garments (Bums and Bryant, 2000). There are two major issues relating to garment sizing; the classification and measure of fit. Classification relates to identification of criteria required for distributing the target population into size groups. The classification procedure plays an essential role in assessing when a garment is wearable by a consumer or not. On the other hand, the fit is a measure of how well the consumer fit into the assigned group (Xia and Istook, 2017) . However, the latter remain the most important problem in the garment industry and a recurrent issue in the literature. It has been observed that fit problem is a difficult concept to research and analyse as the relationship between body and clothing is complex and often ambiguous (Loker et al., 2005). 2.1 Techniques for Garment Sizing There are various approaches reported in literature that have been applied in solving garment sizing problem. 2.1.1 The Earliest Method The general approach includes individual craftsmen perspective to solving clothing problems i.e. fitting to individual. It is also called ‘haute couture” approach. This is common in the early 18th century, when all attire was handmade and fitted to each client. Professional tailors measured the body measurements of each client, and after that drew and cut the patterns for each piece of clothing and each client. After numerous unique designs were collected, tailors found relationships between body measurements, notwithstanding of individual differences. Tailors slowly created these patterns into a framework of attire production to make dress for individuals with comparable figure sorts (Hsu et al., 2007; McCulloch, et al., 1998). 325 The first sizing system reported in 1941 was based on bivariate classification of about 15000 women according to their hip and bust measurement. This was to ensure sizing uniformity in the garment making industry. Continuation of the work resulted in an empirical sizing system known as the Commercial Standard (CS) 215-58 reported in 1958. This modification of the initial system was based on various manufacturers’ experience through trial-and-error. By the year 1970, another empirical sizing system known as the PS 42-70 Standard of the USA was developed using military anthropometrical data and a “trial- and-error” approach. CS215-58 and PS 42-70 sizing systems were based on out-of-date measurements taken at 1941 (Ashdown, 1998). ASTM D5585-94 is another system developed in 1994 by the American Society for Testing and Materials (ASTM) based on the experience of garment designers and available market information. The first national anthropometric study in Europe started in the twentieth century. The Polish cloth sizing table based on anthropometric measurement of about 180000 was first reported in 1982 and later republished in 1997 while that of the Czech Republic was based on anthropometric measurement of about 400000 persons. These serve as an anthropometric data source for many scientific and industrial researches. However, as the living and medical condition of people begin to improve, there is a significant change in human growth and development in these countries and a significant change in the 21st (twenty-first) century human shape and silhouettes proportion. 2.1.2 Multivariate Statistical Technique Roebuck (1995) and Beazley(2001) described steps involved in sizing systems to comprise among others, selecting appropriate body anthropometric data, select key dimensions and establish number of each size necessary to outfit the intended users’ population. This procedure has been adopted in more contemporary study relating to garment sizing problems. 326 Perhaps, the first multivariate approach to garment sizing was achieved by Salusso-Deonier (1982) using the principal component analysis (PCA). The principal component analysis is a method used to discov the control variables in research; create a basis for classifying th population after identifying the key body measurements in the undertaken study. This approach is valuable in distinguishing the basic body or the fit affecting measurements that can frame the basis of size chart advancement. Salusso-Deonier (1982) considered anthropometric measurements of adult females over fifty five years old. The data analysis showed that there are two important variables; one represent body laterality such as body girth and width while the second represent body linearity such as heights and lengths. A similar study by Gupta and Gangadha (2004) shows that the bust and the hip measurement are key dimensions for the upper body and the lower body garment out of the twenty-one anthropometric data considered. The developed size charts accommodates 95% of the Indian adult females. The model was validated using aggregate loss of fit index. Also, Veitch, et a/.,(2007) used PCA to consolidate twelve anthropometric measurements into the two primary central components for laterality (fullness) and linearity (length). The anthropometric data used consist of 54 measurements of 1265 Australia adult females. The classification results in 36 different size groups. This maximizes information pertinent to setting up a size and shape specification for the production of a bodice. Loker et al. (2005) applied both statistical and visual analysis methods to improve the garment fit of an existing sizing system of a garment company. In another study by Zakaria et al. (2008), multivariate statistical analysis technique was used to explore patterns in anthropometric data and develop a size system. The authors surveyed data of 629 schoolgirls aged between 7 to 12 years belonging to three different ethnic groups, namely, Malays, Chinese, and Indians. Mason et al., (2008) considered sizing by identifying unique body shapes. The analysis of variance (ANOVA) and anthropometric data from female teachers in Africa was used. Esfandarani and Shahrabi (2012) also used principal component analysis to identify variables which partition a heterogeneous population into smaller homogeneous groups. The obtained size chart was evaluated using the aggregate loss of the 327 fitness method. Xia and Istook ^.017) considered integration of natural log-transformation, principle component analysis, multivariate linear regression, size range determination, and measurements calculation for developing the sizing system. Both the residual variance analysis and factor analysis are also multivariate techniques similar to the PCA. According to Salusso-Deonier (1982), the effectiveness of body shape classification technique is highly dependent on the selection of the key body dimensions. 2.1.3 Optimisation Techniques Generally, optimisation technique is a mathematical expression for the quantity to be maximised or minimised such as minimum number of size groups and maximum fit. The size optimisation method develops the optimum sizing system with the availability of anthropometry data and its framework is based on mathematical model of garment fit. Gupta et al., (2006) applied three different solution approaches to the linear programming formulation in order to cluster a given population into homogenous body size groups. In the linear programming model, the constraints and the objectives are describeable by relationships which are straight line or linear type. The desired degree of fit is considered a basis for clustering individuals into size groups and exact number of people covered by the system can be determined. Tryfos (1986) in his work recommended the integer programming approach to optimize the number of sizes of a manufacturing clothing company or shoe company so as to maximize anticipated sales or minimize a record of aggregate distress. He partitions the space of body measurements artificially into a set of discrete conceivable sizes and specify a tolerance value for each critical dimension. For example, if a waist tolerance is+1, a size of 30inches will accommodate customer having a waist girth between 29 and 30 inches. The problem was formulated as a “p median” or “Facility location” problem. Ashdown (1998) and McCulloch et al., (1998) focused on the developing a sizing system better than the ASTM D5585-94. The goodness of the fit experienced by a customer upon wearing a particular 328 size is mathematically captured as a distance between the body measurements of the customer and the dimension of the prescribed size. The larger the variation, the worse the fit of the final garment. A non­ linear optimisation technique, “aggregate loss of fit” and the PCSS method was considered as a solution procedure. The non-linear optimization strategies were utilized to infer a set of conceivable measuring systems from anthropometric information. Results appeared that measure assignment as well as the capacity to identify non- accommodated people leads to significant changes in fit over existing measuring frameworks. However, like any other mathematical optimisation problem, increase in the number of constraints may increase model complexity and compromise the performance of these sizing systems. 2.1.4 Data Mining Increasing use of automatic data collection and storage system necessitates the use of data mining in many areas of science and engineering research domains. Specifically, the clustering methodology for garment sizing problems is a method of organising data based on their relative distances into clusters or natural groups. Clustering is also known as an unsupervised method of mining data which do not depend on any presumption common in statistical strategies. Hsu et al., (2007) integrated Ward’s minimum variance method into the K-Mean technique to cluster eleven anthropometric data of 956 adult females in Taiwan. The Ward’s minimum variance method was used for the first hierarchical clustering while the K-Mean was used for the second non-hierarchical clustering. In a similar study by Viktor et al .,(2009), the body scanned data was clustered into five clusters. The author stated that clustering technique must account for interrelationship between anthropometric data to obtain good clusters. Opaleye et al., (2019) considered a fuzzy based clustering methodology for sizing adult male trousers. This clustering differs from the hard-clustering method by its nonlinear nature and the flexibility of gathering large data in a disciplined manner. It gives more precise and close-to-nature solutions for partitions and in this suggests more possibility of solutions for decision-making. 329 Simbolon (2014) deployed the principal component analysis and fuzzy c-means clustering to create a sizing system for Indonesia adults using anthropometric data of 912 adults. Hamad et al. (2017) defined an exhaustive methodology to obtain a clustering of human morphology shapes representative of a population and to extract the most significant morphotype of each class. The fuzzy clustering technique is applicable in sizing due to vagueness in classification of body types and imprecision in anthropometric measurement. 2.2 Issue of Garment Fit The success of any scheme used in the process of sizing is dependent on the extent to which the scheme satisfies the intended function and fit requirements of the item. All consumers want the best fitting clothing item so they select a size close to their anthropometric measures, try it on and purchase or reject the item. A nice design or expensive fabric is of no use when the clothing item do not appropriately fit. In the study by McCulloch et al. (1998), the sizing system was formulated for the Misses subpopulation in USA. The researchers noted that the common practise of using one or two key body dimensions does not provide a good fit for populations with large variations in body proportions. Therefore, the non­ linear optimization method was formulated as a multivariate sizing system and the fit defined as a measure of the proportional difference of an individual to a prototype (ideal) size. This approach provides a mathematical description of the goodness of fit. Individuals within a defined “cut o ff’ for garment dimensions are automatically assigned into a size group. Ashdown (1998) defined the average of all discrepancies over the given garment dimensions from a specified size as the aggregate loss of fit. This represents how well the sizing system performs in fitting the population. The researchers found that optimized sizing systems better accommodate population with large variation in anthropometric measurement. Gupta et al., (2006) also defined a fit function within which certain proportion of the target population will be accommodated. Similarly, the concept of grouping based on similarity of parts was adapted by Kolawole (2016). A customer pair-wise fit (CPF) model for 330 quantifying degree of fit was formulated using garment sizing variables customer anthropometric dimensions and customers’ tolerance for garment dimension. The fit is considered as a measure of the absolute difference of an individual to an ideal size and tolerance as the numerical value of space that a designer can add or subtract from the value of a particular dimension without hindering the fit of a garment to a set of customers. Given the tolerance, it was found that perfect transitive set of customers will be accommodated in the same size group. The cut-off, fit function and tolerance are synonymous to ease allowance as used in clothing and textile related research. The authors suggest quantitative frameworks for fit estimation; however, none of these researchers provide a clear rationale for quantitative estimation of ease allowance. 3.0 Quantification of Ease Researchers have established that fit is a function of the interaction between body measurement, design/style parameters with the addition or subtraction of an extra dimension, which is commonly referred to as ease. Traditionally, ease estimation during pattern construction is based on practitioner experience without an explicit communication on how ease may be established, or what contributes to its determination. Without clear information and data on ease estimation, emerging CAD/CAM virtual fitting rooms required for online shopping of ready-to-wear, mass customisation or personalisation of clothing items will be practically impossible. Theoretical description of ease is based on two definitions of radial ease allowance (REA) and girth ease allowance (GEA). REA is the distance between the body and the cloth surface measured from the same centre while GEA is the additional girth measurements in a garment that were in excess of the basic body dimensions. Ease can also be defined in terms of measured numerical difference between the garment dimension and wearer’s anthropometric measurement at all points of their relationship. It accounts for other interdependent factors which in turn affect fit satisfaction. In practice, there are three types of ease; standard ease, 331 dynamic ease and fabric ease. Standard ease is the difference between the maximal and minimal perimeters of the body while sitting or standing. Dynamic ease provide enough space for various body movement such as walking, running and jumping while fabric ease takes into account mechanical properties of the fabric used. As such, optimal quantification of ease is a trade-off between many factors which includes; wearer’s body shape, style, fabric used, wearer’s motional and aesthetic satisfaction (Y. Chen et ah, 2009; Kim et ah, 2019). Some research efforts towards the quantification of ease have been made. Ashdown and DeLong (1995) investigate consumer’s threshold of fit based on participant tactile responses to ease variation using sensory evaluation technique. Custom- fitted pants were made for the four participants as the control pant and fourteen other pants varied independently between ±0.5 and ±1.0 for the waist, ±0.5 and ±1.5 for the hip and ±0.5 and ±1.5 crotch were used as the test pants. The test pants were similar in style and fabric material to the control pant except that they were either smaller or larger at one of the identified dimensions. Statistical analysis of the experiment show that all the participants perceived variation at more than one dimension. However, further investigation shows that no consistent interactions exist between the actual and the perceived point of variation. The authors also noticed the operation of kinesthetic after-effects in their perception as participants were unable to recognise the control pants more than 42% of the time. The kinesthetic after-effects may also have effect whenever the difference between the test pants and the control was small. Frackiewicz- Kaczmarek et ah, (2015) suggest a similar evaluation approach for tight, regular and loose shirt, jersey, undershirt and interlock undershirt. They used the factorial analysis of variance with Levene’s test for homogeneity of variance to determine factors influencing the distribution of the air gap thickness and the contact area in selected garments, such as overall garment fit, garment style, body region, and fabric type. The author noted violation of model underlying assumptions. As a result, "the statistical analysis conducted was not reported. 332 Chen et al., (2006) also propose a method of optimising ease allowance of a garment using a combination of fuzzy logic technique and sensory evaluation. Vertical body measurement and girth body measurement critical to garment design were selected using data sensitivity based criterion. These two features and the participants’ sensory evaluations for comfort degree were used as inputs to the fuzzy methodology which permit automatic pattern generation to improve the wearer’s fitting perception of a garment. An extension of the work proposed in (Yu Chen et al., 2008) and (Y. Chen et al., 2009) suggest an aggregated ease allowance using an ordered weighted averaging function. The OWA weights are based on garment design and designer’s criteria on textile comfort and estimation of the ease allowance was based on some fuzzy rules extracted from the learning data. Wang et al., (2006) and Kim (2008) proposed ease estimation by measuring difference between garment size and human body size separately at specified segment of the body circumference. Wang et al., (2006) further developed a mathematical model of ease distribution using surface fitting approach in order to predict ease of X-lined jackets at different point of measurements. Petrova and Ashdown (2008) proposed a body-location based estimation method. Garment ease at different dimension points was measured using the 3D scanned data. The authors observed a decrease in ease as body size increases but a statistical relationship was not suggested. Choi and Kim (2004) used a linear distance approach using the GEA for ease estimation in order to compare two different pattern making methods for women clothing. Subjects who have nearly the same body size were selected for the study. In the result of analysing the space between skin and clothing of each pattern by 3D Scanner, there exist significant differences in the chest and bust parts of the pattern considered. A similar method of ease allowance estimation was proposed by Wang et al., 2007; Kin et a l, 2011 and Su et al., 2015. Perhaps the most interesting approach is by Kim et al., (2019). They developed a linear regression model to estimate preferred ease allowance for a popular type of male jacket among male adults in South Korea as of 333 2014. Six different models were developed for preferred ease allowance on seven different parts measured on the jacket. Ranges of estimated ease allowance were obtained by inputting body size measurements of 62 male customers which showed the highest correlation with the preferred ease allowances. However, the complexity in the relationship between body and garment dimensions renders a straightforward estimation of ease inappropriate. Results of the statistical regression models may be inaccurate, most especially when there are difficulties in verifying distributional assumptions and relationship between the dependent and independent variables is vague. 4.0 Size system validation Gupta and Zakaria (2014) highlight measures of evaluating a good sizing system which includes; cover factor, aggregate loss and size roll. The cover factor is the percentage of sample accommodated under each assigned size within a sizing system. The researchers noted that the systems must accommodate between 65%-80%, of the target population. The higher the number accommodated by the system, the better for manufacturers. The aggregate loss is a measure commonly used by researchers for the validation of proposed sizing system (Gupta, and Gangadhar, 2004; McCulloch, et al., 1998). It is the Euclidian distance of the wearer’s actual body dimensions to the assigned size. If the size fits the wearer well, then the distance from the assigned size to the actual size is said to be minimized. This an index of the absolute value of fit. According to Gupta and Zakaria (2014), the benchmark for an accurate sizing system is an ideal value of aggregate loss calculated as 2.54n /2 , (metric in centimetres) where ‘n’ is the number of key anthropometric dimensions used to segregate the target group. If the actual aggregate loss is less than the ideal, the system is considered good for the target population. The size roll on the other hand is simply the total number of sizes obtained for a sizing system, from the smallest to the largest, with fixed intervals between adjacent sizes. The more the number of sizes, the better the fit but the more customer’s confusion in size selection. 334 Therefore, a trade-off between number of sizes and goodness of fit may be required for optimum size roil. Kolawole and Charles-Owaba (2018) proposed a percentage degree of fit index similar to the aggregate loss of fit. The proposed percentage degree of fit measures the degree (or percentage) to which a certain sizing system “satisfies” the target population. Evaluation of the percentage degree of fit for a sizing system ranges from zero which implies poor fit (no member of the group can wear same size) to 100 which implies perfect fit (all member of the group can wear same size). The measures of fit index enhance the process of individual and group validation of sizing system. 5.0 Conclusion and Future trends The importance of an effective garment sizing and fitting mechanism to the mass production, mass customisation and personalisation system production systems has been emphasized. Conventional sizing system produce garments in sizes that can accommodate a majority of customers within a set of fixed sizes and it enhances the process of fitting garment to the consumer without which the overall objective of garment production cannot be met. The progressively evolving methods of producing a sizing system impact the efficiency of that sizing system. Methods ranging from simple bivariate classification, statistical techniques, multivariate techniques, mathematical programming techniques, data mining techniques and artificial intelligence techniques have been considered. This was made possible by the experience of more than 70 years of exploring and understanding how to develop sizing systems that are efficient for manufacturers, customers and retailers. Research shows that a good sizing system must be developed based on the knowledge of fit and cater for the actual body sizes and shapes of the target population. Gupta and Zakari (2014) and Kolawole and Charles- Owaba (2018) highlight measures of evaluating a good sizing system which include; cover factor, aggregate loss, size roll and percentage degree of fit. 335 Given the research discoveries and the weaknesses of different sizing systems, researchers are finding better ways of developing sizing systems and reduce fit problems by adopting advanced data mining, artificial intelligence methods and computer aided design technologies. It is anticipated that newer systems which integrates customers’ preferences will produce better sizing systems resulting in a greater goodness of fit for clothing customers. Proper implementation of garment mass customisation and personalisation model will require determination of ease from customer’s perceptive. Such model may not be generic as ease allowance is a function of design type and fabric. 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INTRODUCTION Engineering and management decision situations with more than one criterion have been encountered with increasing frequency (Adeyeye&Charles-Owaba, 2008; Adeyeye&Oyawale, 2010a; Biswas et al, 2020; Zizovic, Miljkovic, &Marinkovic, 2020). In multi-criteria decisions, cases where the criteria conflict with each other are more common. In such situations gain in one criterion leads to loss in one or more of the other criteria. Due to conflict among the criteria, it is impossible to find a point at which all the criteria would assume their optimum values simultaneously. Consequently, there is no common optimal solution. What we have is a compromise solution(s). Since the criteria remain in conflict over the decision space, the analysist often elicits and incorporates the preferences of the Decision Maker (DM) in the model such that the DM gets the best compromise solution. The criteria are often of varying degree of importance to the DM. Hence preference elicitation is very important in multicriteria optimisation. The preferences of the DM are often expressed as weights to reflect the relative importance of the criteria. The set of weights is often referred to as preference indices or preference structure. The preference structure is very important because the compromise solution obtained often vary from one set of preference structure to another. There are three possible situations in the case of a priori articulation of DM opinion concerning the relative importance of the various criteria. The DM may be satisfied 342 with the compromise solution obtained with his preferencestructure and may not bother himself/herself about other feasible solutions that may exist. In other instance, the DM may have interest in the trade-off options available to him/her. In that case, the problem is solved repeatedly with different preference structures. In this manner, the DM learns about available trade-off options and is able to know how much he/she has to give up in one or more criterion/criteria to gain improvement in one or more of the remaining criteria. He is then able to intelligently select the most preferred solution from the candidate solutions. In some other instances, the DM may want the analyst to present the Pareto optimal solutions to him/her for evaluation after which the most preferred solution is picked. Pareto optimal solutions are often generated using the weights elicited from the DM(Adeyeye&Oyawale, 2010a, b; Adeyeye, Odu& Charles-Owaba, 2015; Zizovic, et al, 2020; Navarro, Penades-Pla, Martinez-Munoz, Rempling, &Yepes, 2020; Aiello, et al, 2020; Wang, Parhi, Rangaiah, & Jana, 2020). Many methods have been proposed for solving multicriteria optimisation problems. Among the methods are the linear combination of objective functions or weighted-sum scalarization (WSS) method in which criteria are normalised and combined before performing optimisation of the combined objective (Adeyeye&Oyawale, 2010a;Adeyeye& Charles- Owaba, 2012; Oktal, Yaman. & Kasimbeyli. 2020 & Erozan &Caliskan, 2020). Nonpre-emptiveGoal Programming (NGP) is a distance-function approach which uses a certain target point in the decision space which represents the most desired values for the several criteria as a key element in modelling the problem (Adeyeye& Charles-Owaba, 2008; Adeyeye&Oyawale, 2010b;Bakhtavar, Prabatha, Karunathilake, Sadiq, &Hewage, 2020). Compromise Programming (CP) is another distance- function approach for which the target point is a utopian point usually not feasible which corresponds to the ideal value of each criterion (Adeyeye&Oyawale, 2010b;Adeyeye& Allu, 2017; Salman et al, 2020 and Canales,Jurasz, Beluco, &Kies, 2020). Adulbhan andTabucanon, (1977, 1979) and Chen, Wiecek, and Zhang (1998) observed that in multicriteria LP problems, the linear combination of objective functions method is very simplistic and sometimes fail to give the real compromise. 343 According to Adeyeye and Charles-Owaba (2012), this drawback could be due to the lack of sensitivity of the linear combination of objective functions.The Compromise Constraint Bicriteria LP (CCBLP) method was proposed to overcome the limitation of combination of objective functions method for bicriteria case (Adulbhan&Tabucanon, 1977 & 1979). The CCBLP hasnot gained much popularity apart from few applications probably due to lack of evidence on its efficacy (Adulbhan&Tabucanon, 1979;Adeyeye and Charles-Owaba, 2012). The DMs desire to know the relative merits of these approaches so that under any given decision situations they can be properly guided in making the choice of the method that best meet their needs. Since preference indices are often used to determine the best compromise solution, generate the Pareto optimal solutions and carry out trade-off analysis, the sensitivity of any multicriteria method to changes in weight structure could be a good approach of evaluating the usefulness of the method. In this study, the earlier work of Adeyeye and Charles-Owaba (2012) is extended by comparing the CCBLP method with three commonly used traditional weighted criteria methods, namely; WSS, NGP and CP on their sensitivities to changes in the weight structure for bicriteria LP problem. 2. BRIEF DESCRIPTION OF THE FOUR METHODS In this section, the Compromise Constraint Bicriteria Linear Programming (CCBLP) and three traditional methods, namely, Weighted-sum Scalarisation, Nonpre-emptive Goal Programming (NGP) and Compromise Programming (CP) are briefly described. 2.1 Weighted-sum Scalarisation (WSS) Consider a bicriteria problem, with criterion functions f\(x) — Y.je]C\jXj and f2(x) = Y1j&]c2jX), respectively and gt(x) is the constraint function of ^constraint while bt is the righthand side of the t th constraint. The elicited weights that reflect the relative importance of criteria are wlf w2 > 0 and vvx + w2 = 1. The weighted-sum or linear combination of objective functions is given by; Maximise, F = f i ( x ) + f 2 (x) 344 Subject to; (1) 9t — > < — b t't li 2 , T Where A "W = and f 2 (x) = f 2 (x) also the respective coefficients of criteria 1 and 2.2 Compromise Constraint Bicriteria LP The CCBLP is a modification of the weighted-sum approach. The objectives are normalised and combined into one. Next, the compromise constraint is derived and added to the structural constraints of the problem. The compromise constraint is expressed as; 0(2) The combined criteria or any of the original criterion may be used as the criterion to be optimised subject to the compromise and structural constraints as shown below. Maximise (any one of the three criterion A W = / ^ cijXj A W = ZjejCyXj, 345 9t bt, t = l ,2 ,... ,T Where f t and f t are the respective ideal values of criterion 1 and 2 when optimized individually. 2.3 Nonpre-emptive Goal Programming (NGP) The bicriteria model may be transformed to a GP model by assigning targets to each criterion. In some cases, a priori determination of goal may not be easy. Arbitrary setting of targets may lead to computation dominated or suboptimal solution. Hence, the potentials provided by the objectives are explored by solving them individually and using their optimum values as the target levels. The GP method seeks to minimise the distance between the desired aspiration levels and the compromise solutionobtained according to the preference structure.The general NGP model is given as; Minimise, a = ^ W £ (d f + d~) i Subject to ; (4) f i t o + d f - d t = f t , i = 1,2 ,... / 9t £ .= .£ bt, t = 1, 2 , . . . ,7 346 Where dt ,d f > 0 anddt x df+ = 0, Vi 2.4 Compromise Programming (CP) Compromise Programming (CP) has received a lot of attention since it was proposed by Zeleny (1973, 1974). The best compromise solution is identified as the solution that give the shortest distance to a utopian point where all the criteria simultaneously reach their ideal values. The utopian point is not practically attainable but is usually used as a base point. First, the ideal (i.e. the best or anchor) values, (/j*) and anti-ideal (worst or nadir) values, (ff*) are computed for each criterion and are often used for the construction of pay-off matrix. Next, the distance function (fi* — /;(x))between the outcome/achievement of each criterion and its ideal/optimum value is defined. This distance gives the degree of closeness of the outcome/achievement of the criterion to its ideal. The distance is usually normalised for dimensional consistency. The normalised distance is given by; (5) The combined distance (Dp) for all the criteria which expresses the closeness of the solution of the problem to the utopia is expressed as; (6) Where, p is a metric and real number belonging to the closed intervalfO, oo]. The value ofp = 1, when the distances are of equal concern to the DM and p = ooif only the largest distance is of concern. Observe, that all other solutions fall between the solutions obtained by solving the CP model with p = 1 and p = oo. For instance, if the DM weighs the distances in proportion to their magnitude, then, p = 2 and the resulting model is solved to obtain the compromise solution. The general CP problem is as presented below; 347 Minimise, Dp Subject to: When only the largest distance(L) counts, then,p = oo,and the problem becomes a min-max problem. The model is stated as; Minimise, Dra = L Subject to: (7) 3. EXPERIMENTAL A bicriteria production planning problem from literature is used (Adeyeye and Charles-Owaba, 2008). The two criteria considered are (i) minimisation of production cost (ii) maximisation of capacity utilisation of production facilities. Cost minimisation criterion was converted to maximising criterion by multiplying by -1. The major production facilities with their respective capacities and cost of processing one unit of materials are presented in Table 1. The model developed by Adeyeye and Charles-Owaba (2008) were used for the experiment see Eq. 8 . The problem was solved using the WSS, CCBLP, NGP and CP methods. For WSS method, the normal forms of the criteria were combined into one objective and solved using the existing constraints of the problem. In the case of CCBLP, apart from adding the normal forms of the criteria, the compromise constraint was derived and added to the structural constraints of the problem before solving it. In the case of the NGP and CP, the two criteria were solved individually to determine their ideal and anti-ideal values. For the NGP, the ideal values were set as the target 348 while in the case of CP, the ideal and anti-ideal values were used for the computation of normalised distances. Various weight structures were used to perform experiment to see the response/sensitivity of the CCBLP and the other three traditional approaches to the changes in the weight structure (see Table 2). The total production costs and capacity utilisation of each production facility was determined. The utilisation of production facilities was computed using the production facilities capacity constraints in Eq. 8 . For instance, the respective capacity utilisation of PMV1 and ST3 are X 9 , 6 0 0 100%) and x 100%). The utilisation of the remaining facilitieswas computed in similar manner. In this study, the deviations were weighed equally, hence the Dx distance metric is used to identify the solution that is closest to the utopian and the corresponding preference structure. The Dt distance metric in its discrete form is mathematically expressed for bicriteria decision situation as Dx = wx A*-AW I A*-A** | + w2 lA’-A W I A*-A" Table 1: Facilities Capacities and Processing Costs Stage of Facility Name Capacity Processing Production kg/month cost per unit Premix Premix Vessel 1 9,600 2.00 (PMV1) Premix Vessel 2 14,400 1.20 (PMV2) Premix Vessel 3 24,000 1.00 (PMV3) Processing Processing Vessel 25,000 2.00 1 (PLT1) Processing Vessel 25,000 1.80 2 (PLT2) Processing Vessel 40,000 1.40 3 (PLT3) 349 Processing Vessel 30,000 1.60 4 (PLT4) Storage Storage 1 (ST1) 80,000 0.30 Storage 2 (ST2) 45,000 0.45 Storage 3 (ST3) 20,000 0.20 Minimise, Cost — 2*111 2*211 2*311 1*2*121 1*2*221 + 1.2x321 + x131 + ^231 + *331 + 2 y12 + 2*412 4" 2-̂ 512 + 2*612 + 2 * 712 + 1 .8y22 + 1 .8x422 + 1 .8x522 + 1.8x622 + 1.8x722 + 1.4y32 + 1.4* 432 + 1 .4 * 532 + 1-4*632 + 1-4*732 + +1.6y42 + 1.6*442 + 4 .6*542 + 1.6*642 + 1.6*742 + 0-3y13 + 0.45y23 + 0.20y33 Maximise, Capacity Utilisation — 4.17*m + 4.17*2ii + 4.17*3ii + 2.78*i2i + 2.78*22i + 2.78*32i + 1-67*131 + 1.67*231 + 1 .67*331 + 1 .6y i2 + 1 .6*4i 2 + 1 .6*5i 2 + 1 .6 * 5 1 2 "I" 1 .6 *7 i 2 4* 1 .6 y22 + 1.6*422 + 1.6*522 + 1-6*622 + 1.6* 722 + 732 + *4 3 2 + *532 + *6 3 2 + *732 + 1.33y42 + 1.33*442 + 1-33*542 + 1 .3 3 * 5 4 2 + 1 .3 3 * 7 4 2 + 0.5y13 + 0.89y23 + 2 y33 Subject to: (8) Production facilities capacity constraint *111 + *211 + *3i i < 9,600 {PMV1) *121 + *221 + *321 < 14,400 {PMV 2) *131 + *231 + *331 < 24,000 {PMV3) y \ 2 + *412 + *512 + *612 + *712 5s 25,000 (PLT1) y22 + *422 + *522 + *622 + *722 ^ 25, 000 ([PLT 2 ) ^ 3 2 + * 4 3 2 + * 5 3 2 + * 6 3 2 + * 7 3 2 — 40,000 (PLT3) ^ 3 2 + * 4 3 2 + * 5 3 2 + * 6 3 2 + * 7 3 2 Ss 30,000 (PLT4) y i3 £ 80,000 (STl )y23 < 80,000 (ST2) y 23 < 20,000 (ST3) Firm’s full capacity constraint * 1 1 1 + * 2 1 1 + * 3 1 1 + * 1 2 1 + * 2 2 1 + * 3 2 1 + * 131 + * 2 3 i + * 331 = 48,000 Material proportions constraint * 1 1 1 — 0 . 1 * 3 1 1 = 0 * 1 2 1 — 0 . 1 * 3 2 i = 0 * 1 3 1 — 0 . 1 * 3 3 ! = 0 fc * 2 1 1 - 1 . 3 * 3 i i = 0 * 2 2 1 ™ 1 . 3 * 3 2 1 — 0 * 2 3 1 ~ 0 . 1 * 3 3 i — 0 * 4 2 2 ~ 0.0625y22 := 0 *432 0.0625y32 — 0 * 4 4 2 - 0.0625y42 = 0 *si2 ~ 0.01042y12 = 0 *522 — 0.01042y22 = 0 351 *532 — 0 .01042y 32 — 0 *542 ~ 0 .01042y 42 = 0 *612 — 0.96y 12 = 0 *622 — 0.96y 22 = 0 *632 — 0.96y 32 = 0 *642 — 0.96y 42 = 0 ^ 7 i2 — 0 .0521y 12 = 0 *722 — 0.052 l y 22 = 0 *732 — 0 .0521y 32 = 0 *742 - 0 .0521y 42 = 0 Material balance constraint * 1 1 1 + * 2 1 1 + * 3 1 1 + * 1 2 1 + * 2 2 1 + * 3 2 1 + * 1 3 1 + * 2 3 1 + * 3 3 1 ~ 7 1 2 — y 22 - y 32 — y 42 = o y i2 + *412 + *512 + *612 + *712 + V22 + *422 + *522 + *622 + *722 + y 32 + *432 + *532 + *632 + *732 + y32 + *432 + *532 + *632 + *732 ~ y i3 ~ y23 — y33 = 0 Table 2: Relative Importance of Criteria S/N Preference Structure 1 w, = 0.25, w2 =0.75 2 3 w, =0.75, w2 =0.25 4. RESULTS AND DISCUSSION The summary of results of experiments with different preference structures are presented in Table 3 below. All the four methods have been 352 JS II II o Ln able to assist the DM to determine the utilisation of the production facilities and the associated costs for the different weight structures. However, the usefulness of the various methods as tool for the DM in making intelligent trade-off decisions vary because of the difference in their sensitivity to relaxations in the objectives. The Di-distances were not computed for the WSS, NGP and CP when Wi = 0.75 andw2 = 0.25 because their solutionsare identical to the ideal solution of the minimum cost objective (see Table 3). Their so called “best compromise solutions” could mislead DM because they did not reflect the relaxation provided by the DM. Only the CCBLP responded to the small relaxation in the costminimisation objectives with improved capacity utilisation of production facilities but with a decrease in the achievement of minimum cost objective. The utilisation of the least utilisedfacility improved from 0.18% to 20.32% while production cost increased by 1.8%. The increase in the utilisation of production facilities was achieved at the detriment of production cost because the objectives are in conflict.Also, when wx = 0.25 andw2 = 0.75, the NGP and CCBLP responded to the relaxation in the capacity utilisation objective while that of WSS and CPare identical to the ideal solution of the maximisation of capacity utilisation objective. It is only in the case where the objectives are of equal importance (vvx — w2 = 0.50) to the DM that all the four approaches responded to the relaxations in the objectives. In terms of sensitivity of the approaches, WSS and CP were the least sensitive, followed by NGP while CCBLP is the most sensitive. In terms of the Di-distances, the compromise solution provided by CCBLP is the closest to the utopia and the corresponding preference structure is w1 = 0.25, w2 = 0.75). 353 Table 3: Results of Simulation with Different Preference Structure Facil wt Wx = 0.75, w2 Wx = w2 0.25, w2 ity = 0.25 0.50, 0.75 = 1 Nam e Id W N C C W N c c W N c c Ide e s GP C P S G c p s G c p al al s BL s P B s P B h{ C P L L x) o P P Ca St pa f. cit (x y ) uti lis ati on PM 1 1 1 10 10 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PM 2 1 1 10 10 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PM 3 1 1 10 10 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 PP 1 2 2 20 . 20 . 2 2 2 2 2 1 1 5 1 10 0. 0. 32 32 0. 0. 0 . 5. 0. 0 0 8 . 0 0 3 3 3 3 3 2 3 0 0 4 0 2 2 2 2 2 0 2 0 PP 2 1 1 10 10 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 354 II II £ S PP 3 1 1 10 10 1 1 1 9 1 5 1 7 5 50. 0 0 0 0 0 0 0 7 0 0 . 0 6 . 0 . 20 0 0 0 0 0 0 2 0 2 2 0 0 0 PP 4 1 I 10 10 1 1 1 1 1 1 3 1 1 10 0 0 0 0 0 0 0 0 0 0 3. 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 ST 1 1 1 10 66 . 1 4 4 4 4 4 4 4 4 43. 0 0 0 80 0 3. 3. 3. 3. 3. 3. 3. 3. 90 0 0 0 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 ST 2 0 . 0 . 0.1 59. 0 . 1 1 1 1 1 1 1 1 10 1 1 8 10 1 0 0 0 0 0 0 0 0 0 8 8 8 0 0 0 0 0 0 0 0 ST 3 1 1 10 10 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Cost 2 . 2 . 2.4 2.5 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2 . 2.6 m 4 4 8 x 2 x 4 5 5 5 5 6 6 6 6 7x 8 8 1 0s 1 0 5 8 4 4 5 4 7 2 0 7 10s X X X X X X X X X X X 10 ! 10 ! 1 0 : 10 ! 10 ! 10 ! 10 ! 10 ! 1 0 : 1 0 ! 1 0 ! Dista 0.3 0 . 0 . 0 . 0 . 0 . 0 . nee 37 3 3 3 3 3 3 Metr 8 8 9 8 6 2 ic 8 8 1 8 6 6 (Li) Incre 0 . 0.0 1.8 2 . 2 . 3. 2 . 7. 5. 5. 7. 7.5 ase 0 7 7 0 7 5 9 0 5 In Cost (%) 355 The feasible solution space defined by the constraint sets determines the sensitivity of the methods to the changes in the preference structure. In the case of WSS, NGP and CP, the compromise solution is limited to the vertices of the solution space. Such solutions could be misleading because in some cases the real best compromise solution may be in other parts of the solution space other than the vertices. This could be the reason why WSS and CP were giving identical solutions for all the cases studied. The addition of goal constraints to the NGP model changes the feasible solution space of the bicriteria problem by introducing new vertices and eliminating some of the existing vertices. This could be the reason why the solution of the NGP was different from that of WSS and CP for Wi = 0.25 andw2 = 0.75.It is possible that the NGP picks one of the new vertices introduced by the goal constraints. Once the goal constraints are added to the structural constraints, the feasible region for the problem has been defined and does not change with relaxations in the criteria and the solutions are limited to the vertices. In the case of CCBLP, the preference indices are used to derive the compromise constraint which is added to the original constraint set and it forces the criteria to settle on a common point on any part of the boundary of the solution space. The CCBLP is able to identify the real compromise solution because it is not limited to the vertices of the constraint set. Although the CCBLP approach is the most sensitive to changes in preference structure, its application is limited to bicriteria case whereas WSS, NGP and CP can handle more than two objectives. The CP approach has a means of incorporating the concerns of the DM over the deviations through the use of the topological metric, pwhich is a real number belonging to the closed interval [0 ,oo]. The choice of which of the approaches the DM should use in a given situation depends on the number of criteria, sensitivity to relaxations in the criteria and the concerns of the DM on the deviation from utopian solution among others. 5. CONCLUSION Simulation with different preference structures showed that CCBLP is the most sensitive to the changes in the preference structures and gives 356 the real compromise solution. It is able to identify the real compromise anywhere on the boundary of the feasible region either on the vertices on not. The CCBLP is limited to bicriteria while WSS, NGP and CP can handle more than two criteria. This provide a guide for Decision Maker on the choice of method to use for his decision problem. REFERENCES Adeyeye A. D. And Allu A. (2017). 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Zizovic, M., Miljkovic, B., &Marinkovic, D. (2020). Objective methods for determining criteria weight coefficients: A modification of the CRITIC method. Decision Making: Applications in Management and Engineering, 3(2), 149-161. 359 CHAPTER 16 Preventive Maintenance Interval Prediction: Application of a Cost- Based Approach with Lost Earnings Consideration in a Manufacturing Firm *O.A. Adebimpe and O.E. Charles-Owaba Department of Industrial and Production Engineering, University of Ibadan, Nigeria. Corresponding Author: oa.adebimpe@yahoo.com Abstract In this work, the pertinent maintenance parameters in manufacturing firms were identified and used to develop a cost function for machine maintenance. In the cost tunction, the lost earnings due to corrective maintenance and preventive maintenance were considered alongside machine reliability to determine an optimal interval for preventive maintenance. Thereafter, the model was evaluated by applying it to a cash crop processing company in Nigeria.The model application considered the two lost earnings cost parameters that were identified in the determination of the preventive maintenance interval and their influence on the total maintenance cost. Numerical examples were presented to demonstrate the solution techniques and the results were presented accordingly. 1. Introduction Preventive maintenance is central to addressing the availability and useful life of machines. According to Dhillon (2006), maintenance can be defined as the combination of appropriate actions for retaining and/or restoring components/equipment/part to its designated functions.Every action directed towards keeping equipment or facility in a proper working condition is regarded as maintenance (Sobamowoer al., 2012). This includes both technical and administrative efforts to ensure the functioning of a system (Reason, 2000; Swanson, 2001).In preventive 360 maintenance, there is a set of organized activities which are performed on machinery to achieve its best operational condition. More specifically, the activities are targetted towards the preservation of equipment conditions, prevention of equipment failure, and repair of broken equipment(Jardine& Tsang, 2013). Through adequate maintenance of facilities, production loss, downtime, environmental hazards have been greatly reduced in manufacturing firms. Maintenance actions not only have a direct effect on machine availability but also influence the profit-making of the manufacturing firms. That is, when the machine meant for manufacturing activities are in a good working condition, it promotes the organizationalgoals. Also, issues bothering on the machine downtime, defective products, production loss, personnel injuries and accidents which could arise from a poor machine condition can all be avoided. Inlight of this, maintenance actions have become very important and strategic part of anymanufacturing business. However, executing preventive maintenance actions always come at an inevitable cost and, directly competewith the savings of the manufacturing firms.For example, costs of failure and the cost incurred as a result of the time spent to execute the maintenance actions affect the useful production time.While the maintenance actions resulting in these costs have become inexorable, it increases the cost of business of the manufacturers. And so, manufacturershave decisions to make onwhen to execute themaintenance actionsat a minimal cost while achieving machineavailability. In this study, we present a model for the determination of the preventive maintenance interval in a manufacturing firm and specifically considered the influence of lost earning duringmaintenance actions. 2.Review of Maintenance Studies ^ Maintenance in the past has been viewed as a necessary evil by manufacturing companies (Paz & Leigh, 1994). However, this has changed from being a necessary evil to an integrated part of manufacturing and business in general (Adebimpe, 2014). The recent 361 I consideration of maintenance as an important aspect of the business has been spurred by the increased requirements in machine performance, environment and safety for businesses to gain competitive advantages in the manufacturing market. Maintenance can be classified into two: Corrective Maintenance (CM) and Preventive Maintenance (PM) (Alaswad& Xiang, 2017).The corrective maintenance allows the machine to operate until it finally breaks down. This type of maintenance activity is also referred to as breakdown maintenance or failure based maintenance. In this type of maintenance, no work is performed on the machine until the machine fails. Though this maintenance policy wasconsidered to be feasible in cases where profit margins are large (Sharma et al., 2005), the strategy could lead toan unpleasant circumstance for the business. It could cause serious damage to machine, environment, personnel as well as production downtimeand machine unavailability (Basnet al., 2017). On the other hand, preventive maintenance is planned and aimed at optimal machine availability. Preventive maintenance refers to every action executed on a machine before it fails. These are activities which are directed towards the reduction of the rate of machine degradation and consequently to extend the useful life while the machine is still functional. One main objective of preventive maintenance is to reduce the rate at which a machine fails (Vilarinhoef al., 2017).According to Angiuset al. (2016), preventive maintenance has shown a great contribution to the quality of product or service delivery, environmental and personnel safety. However, the time spent for PM actions often affects the useful production hours of a manufacturing firm and as a result, affects the production target. The two main classifications of maintenance techniques are presented in Figure 1 alongside a further classification of preventive maintenance as described by(Avontuur, 2017). 362 Figure 1: Types of Maintenance Techniques Source: Peters, 2018. 2.1 Preventive Maintenance Though maintenance has been part of human life since inception, the understanding of the importance of preventive maintenance (PM) policies can be dated back to the early 1950s (Murthy et al., 2002). In the past, corrective maintenance was popular. However, the current stringent business policies, competitive market, change in focus of business executives and decision-makers as well as the furtherance of improved methodologies to enhance the effectiveness of manufacturing systemshas led to the adoption of preventive maintenance. In PM, maintenance tasks are predetermined and are derived from the equipment or machines component lifetimes and basic operations. For that reason, certain actions are planned to replace some parts before they eventually fail to function. In Simoeset al. (2011), PM was viewed from both the managerial perspective and the operational perspective. In a managerial perspective, issues bothering on decision making and support received towards the analysis of maintenance data are considered. This includes inputs such as objectives of preventive maintenance, maintenance planning, systems performance and the adopted problem­ solving techniques. Thus, the viewpoint is referred to as the outer process 363 because historical data and analysis are used for the execution of PM actions and decisions. Meanwhile, the operational perspective is viewed as the maintenance action which is executed for sustaining a system (Bjorklundetn/., 2010). Consequently, it is referred to as the inner process because it considers the technical aspect of PM based on inputs. However, these two viewpoints are considered to be very important towards achieving effectiveness and efficiency of a manufacturing system. The roles of the two viewpoints are crucial to attaining efficient and effective manufacturing systems. 2.2 Overview of Preventive Maintenance Models Numerous approaches have been applied in maintenance studies, especially to predict preventive maintenance. For instance, Sim and Endrenyi (1988) developed preventive maintenance model which was aimed at minimization of machine unavailability as a result of frequent breakdown while Bottazi et al. (1992) analysed the preventive and corrective maintenance strategies of a collection of buses for a range of five years.A Monte Carlo simulation approach was applied to evaluate the maintenance policies using a developed updatable database. In Chareonsuket al. (1997), a multi-criteria approach was applied to determine optimal preventivemaintenance interval considering age- based failure rate of components, cost and reliability of the components. Meanwhile, Percy et al. (1998) developed models to address preventive maintenance schedules in complex systems. Also, Kardon and Fredendall (2002), Chen et al. (2003), Juang and Anderson (2004), Das et al. (2007) applied mathematical principle and modeling to solve the problems of preventive maintenance interval. Similarly, in predicting the preventive maintenance intervals, authors such as Zequeira and Be'ren-guer (2006), Wangand Pham (2006), Das et al. (2007), Taboadae? al. (2008), Castro, (2009 )have applied cost- basedapproach with the reliability of the machines under consideration. However, the cost function has not captured lost earnings during 364 maintenance activities. Thus, Ojeih (2011) and Adebimpeer a/.(2014) considered the lost earnings and developed a cost-based model to predict an optimal preventive maintenance interval in a manufacturing firm. Also, Adebimpeer al. (2015), included the cost of inventory of the required spare parts for the preventive maintenance as part of the cost function. They applied the model and establish its applicability in manufacturing firm. However, there is a need to further demonstrate the application and, the impact of lost earning as an important cost parameter in the totalmaintenance cost. Thus, we considered the lost earnings during corrective maintenance and preventive maintenance as a factor in the cost-based approach. 3. The Model The model developed by Adebimpeer al. (2015) was adapted for this study and the development process is presented.The developed model is a cost-based model which considers related cost involved in carrying out preventive maintenance in a manufacturing company and the lost earning that results from carrying out the maintenance activities. The basic cost parameters that wereidentified in this model are; the preparation cost for the preventive maintenance activities, cost of executing the preventive maintenance, cost of executing corrective maintenance and lost earnings while executingcorrective maintenance and preventive maintenance. 3.1 Model Notations The following describes the representation and the meanings of the notations used in the model development; 1. tPM: preventive maintenance interval (Hours). 2. TC: total maintenance cost for a planning horizon. 3. C0: cost of executing a planned preventive maintenance (Cost/Maintenance). 4. CPM: average cost of preventive maintenance (Cost/Maintenance). 5. CF: average cost of corrective maintenance during the interval tPM. 365 6 . CBM\ cost of executing corrective maintenance. 7. LEbm\ lost earnings resulting from corrective maintenance. 8 . LEbm\ lost earnings due to planned preventive maintenance. 9. Dm: average duration for corrective maintenance. 10. PL: estimated profit per hour. 11. Dt : average duration for planned preventive maintenance. 12. /?andoc: shape and scale parameters of Weibull distribution for the machine. 3.2 Model Assumptions The following are the assumptions made for the model development; 1. The machine failure is characterized by Weibull distribution. 2. The cost of carrying out preventive maintenance is known. 3. The preparation cost of performing preventive maintenance is known. 4. The average number of machine failure within a PM interval is known. 5. The average cost of executing corrective maintenance is known. 6 . The minimum acceptable reliability of the machine is known. 7. The average time taken for corrective maintenance and preventive maintenance is known. 8 . The labours used for the maintenance are the employees of the company (i.e. operators). 3.3Cost Functionand Reliability Adapting from Adebimpeet al. (2015), the cost function is described as follows; Total Maintenance Cost = {Preparation Cost o f Preventive Maintenance + Cost o f Executing Preventive Maintenance + Cost o f Executing Corrective Maintenance + Lost Earnings During Corective Maintenance + Lost Earnings During Preventive Maintenance} (1 ) 366 The mathematical expression for the cost components that makes up the Total Maintenance Cost as described in equation 1 is now described. i. Preparation Cost for the Preventive Maintenance C0: this describes all the costs associated with the mobilization of all resources and set-up. ii. Cost of Executing Preventive Maintenance CPM: this describeslabour cost (which is a percentage of employees’ salary) of maintenance personnel, material and tools used in preventive maintenance. iii. Cost of Executing CorrectiveMaintenance CBM: this describes the cost of tools, labour and materials used for corrective maintenance within a preventive maintenance interval ( tPM). This is further expressed as shown in equation 2 ; Cbm = CP (2) iv. Lost Earnings during Corrective Maintenance LEBM: this accounts for the money lost as a result of downtime caused by sudden machine failure. Thus we expressed this in equation 3 as the average number of failures that occur within an interval of preventive and the average duration of failure before the machine is restored to its normal working condition; LEbm = DmPl ( ^ ) P (3) v. Lost Earnings during Preventive Maintenance LEPM: this accounts for the money lost as a result of planned downtime as a result of preventive maintenance. It is expressed as equation 4 below; CEPm = ^jPi (4) Thus, by aggregating equations 1-4 we have the total cost TC as described in equation 5 and 6 367 TC — C0 + CPM + CBM + LEbm + LEpm (5) t c = c 0 + c PM + c F ( ^ y + D M p L y ^ y + dt pl (6) Now that the objective function has been demonstrated, the cost function is subject to the reliability of the machine under consideration. Therefore, we expressed the reliability function of the machine as expressed in Das et al. (2006) using the cumulative probability function of Weibull when the upper bound for the failure probability is set by the firm; (tPMy E(tPM) 1 — e v a ) ; where tPM, a, /? > 0 (7) And by manipulating equation 7,tPMis made the subject of the equation and we have equation 8 as; tPM < a ( in f— j — -)] (8) F (tPM) < Upperbound (9) Equation 10 describes the cycle of preventive maintenance in a year given a specific preventive maintenance interval. To predict the cycle of preventive maintenancen activities in a year, we considered the time lag between the start of the preventive maintenance and the completion of the activityDr . Thus, we expressed nin equation 10 as; n = is an inte«er ( 10) Thus after aggregating equations 1 to lOwe have; Optimal Interval 368 Min TC(T) = n C0 + Cpm + Cf ( * ? ) ' ] + n Dm Pl (^ff/ + (DTPl) Subject to tpM —K (/n [ V l — F(tPM)] //?> ( 12)( 11) Upper Bound (13) 3.4Algorithm Step 1: Input C0, CPM, CF, PL, DM, DT, Upper Bound. Step 2: Compute the tPM using the reliability function in equation 7. Step 3: Substitute the tPM in the objective function to estimate the total cost TC in the model at minimum reliability and the computed preventive interval tPM. Step 4: Repeat steps I to 3 for a range of reliability and checks for the tPM value at minimum cost. Then, end the procedure. 4. Model Application In this section, the model was applied using the data that was collected from a manufacturing firm. The model application considered the influence of the two parameters of lost earnings in the numerical example and the subsequent analysis. The first numerical example considered the lost earnings due tocorrective maintenance and the second considered lost earning as a result of corrective and preventive maintenance todemonstrate the solution technique. 4.1 Manufacturing Firm Data 369 Table 1 represents the data of a critical machine in a cash crop processing company. The company under consideration is located in South-Western Nigeria and has one of the biggest beverage companies whose products are widely consumed in Nigeria and all neighbouring country as its major customer. That is, the company under consideration has a high volume of demand and is engaged in a competitive market and as a resultof these, an optimal interval for planned preventive maintenance is required. Table 1: Data from the Manufacturing Company Parameters Values P 1.21 oc 199.61 Co 1400 Naira CpM 2560 Naira CF 15190 Naira PL 4500 Naira Dj1 8 Hours (9.13 x 10'4 year) Dm 2.5 Hours T 8760 Hours (1 Year) 4.2 Numerical Example 1 The example demonstrates the prediction of the preventive maintenance interval using the presented model and algorithm. In the example, only the lost earning during corrective maintenancewithin preventive maintenance interval was considered. The approach applied the data in Table 1, with the Upper Bound of F (tPM) being set at 0.25, t , M < 199.61 {/n [1/ (1 _ 0 25)]Vl M} tPM< 1 9 9 .6 1 { /n [7 (0 7 5 )]Vl21} tPM < 199.61X0.3573 370 tPM < 70.66 Hours Thereafter, we estimate n = — — and substitutes tPM = ID t + tpM l 70.66 Hours with the inputted parameters into the cost equation as described below; 8760 ” “ L8 + 70.66. n * 112 Min TC(T) = n c0 + cPM + c F + dmpl ( 70.66 ̂1.21 TC(T) = 112 1400 + 2560 + 15190 Vl99.6lJ ( 70.66 ^ + 2.5 X 4500 V199.61J TC(T) = 112[3960 + 15190(0.2846) + 11250(0.2846)] TC(T) = 112[3960 + 4323.66 + 3201.75] TC(T) = 112[11485.41] TC(T) = 1,286,365.92 Naira Table 2: Result of Preventive Maintenance Interval and Total Cost Upper Preventive Cycle of Total Cost of Bound Maintenance Preventive Maintenance Interval Maintenance TC(T) ________ (dt + £pm)______ (ra)_________________ 371 0.25 78.66 112 i,286,365.92 0.27 84.84 104 1,278,073.38 0.29 90.6 97 1,265,896.39 0.31 96.11 92 1,268,613.05 0.33 101.5 87 1,263,364.83 0.35 107.75 82 1,261,288.06 0.37 113.81 77 1,249,435.14 0.39 119.61 74 1,261,303.04 0.41 125.18 70 1,248,719.77 0.43 131.58 67 1,257,003.27 0.45 138.69 64 1,267,057.50 0.47 145.46 59 1,268,544.95 0.49 151.91 58 1,261,868.33 0.51 158.94 56 1,277,561.22 0.53 166.45 53 1,269,588.36 0.55 173.58 51 1,277,460.42 0.57 181.83 49 1,289,982.76 0.59 189.63 47 1,294,671.06 0.61 193.7 46 1,296,611.34 0.63 206.66 43 1,300,656.06 0.65 215.78 41 1,300,315.45 0.67 225.36 39 1,297,562.65 0.69 235.43 38 1,327,029.63 0.71 246.08 36 1,320,649.00 0.73 257.38 35 1,350,066.70 0.75 269.42 33 1,339,982.01 0.77 282.35 31 1,369,916.73 0.79 296.3 30 1,356,382.46 0.81 311.49 29 1,387,855.17 0.83 328.18 27 1,371,457.23 0.85 346.75 26 1,406,631.53 0.87 367.72 24 1,389,144.25 0.89 391.89 23 1,432,790.87 0.91 420.49 21 -i;419,479.83 0.93 455.74 20 1484639.654 372 0.95 502.05 18 1,496,153.05 0.97 570.67 16 1,545,768.54 0.99 715.47 13 1,640,505.77 4.3 Numerical Example 2 In this example, we predict the preventive maintenance interval with consideration for lost earning due to both corrective and preventive maintenance. The approach illustrated the model and algorithm using the data in Table 1, with the Upper Bound of F (tPM) being set at 0.25; t™ < 1 9 9 .6 1 { ;n [V ( 1 _ 0.25)] ,/l21} tP„ < 1 9 9 .6 1 { /n [ 7 (0.75)] /l21) tPM < 199.61 X 0.3573 tPM < 70.66 Hours Thereafter, we estimate n = L—- - — and substitutes tPM =dt + tPMJ 70.66 Hours with the inputted parameters into the cost equation as described below; 8760 n = 8 + 70.66 n 112 Min TC(T) = n Co + CPM + CF ( - ^ ) /?] + n [dmPl ( ^ L ) * + (DtPl) 373 / 70.66 X1'21] TC(T) = 112 1400 + 256u -i- 15190 V199.617 ( 70.66 ̂1.21 + 112 2.5 X 4500 + 4500 X 8V199.61/ TC(T) = 112[3960 + 15190(0.2846) + 11250(0.2846) + 36000] TC(T) = 112[3960 + 4323.66 + 3201.75 + 36000] TC(T) = 112[47485.41] TC(T) = 5,318,365.92 Naira Table 3: Result of Preventive Maintenance Interval and Total Cost of Maintenance with Lost Earnings Due to Corrective Maintenance and Preventive Maintenance Upper Preventive Total Cost of Bound Maintenance Maintenance Interval (DT + tPM) TC(T) 0.25 78.66 5,318,386.80 0.27 84.84 5,022,073.38 0.29 90.6 4,757,896.39 0.31 96.11 4,580,613.05 0.33 101.5 4,395,364.83 0.35 107.75 4,213,288.06 0.37 113.81 4,021,435.14 0.39 119.61 3,925,303.04 0.41 125.18 3,768,719.77 0.43 131.58 3,669,003.27 0.45 138.69 3,571,057.50 374 0.47 145.46 3,464,544.95 0.49 151.91 3,349,868.33 0.51 158.94 3,293,561.22 6.53 166.45 3,177,588.36 0.55 173.58 3,113,460.42 0.57 181.83 3,053,982.78 0.59 189.63 2,986,671.08 0.61 193.7 2,952,611.34 0.63 206.66 2,848,656.06 0.65 215.78 2,776,315.45 0.67 225.36 2,701,562.65 0.69 235.43 2,695,029.63 0.71 246.08 2,616,649.00 0.73 257.38 2,610,066.70 0.75 269.42 2,527,982.01 0.77 282.35 2,521,916.73 0.79 296.3 2,436,382.46 0.81 311.49 2,431,855.17 0.83 328.18 2,343,457.23 0.85 346.75 2,342,631.53 0.87 367.72 2,253,144.25 0.89 391.89 2,260,790.87 0.91 420.49 2,175,479.83 0.93 455.74 2,204,639.65 0.95 502.05 2,144,153.05 0.97 570.67 2,121,768.54 0.99 715.47 2,108,505.77 375 Table 4:Lost Earnings due to Breakdown Maintenance and Preventive Maintenance Upper Preventive Lost Earnings Lost Earnings Bound Maintenance During CM During PM Interval (DT + (Naira) (Naira) tpM) 0.25 78.66 3,201.75 4,032,000 0.27 84.84 3,543.99 3,744,000 0.29 90.6 3,867.92 3,492,000 0.31 96.11 4,182.27 3,312,000 0.33 101.5 4,493.80 3,132,000 0.35 107.75 4,859.78 2,952,000 0.37 113.81 5,219.26 2,772,000 0.39 119.61 5,567.40 2,664,000 0.41 125.18 5,905.34 2,520,000 0.43 131.58 6,297.81 2,412,000 0.45 138.69 6,738.84 2,304,000 0.47 145.46 7,163.50 2,196,000 0.49 151.91 7,572.20 2,088,000 0.51 158.94 8,022.05 2,016,000 0.53 166.45 8,507.49 1,908,000 0.55 173.58 8,972.87 1,836,000 0.57 181.83 9,516.62 1,764,000 0.59 189.63 10,035.73 1,692,000 0.61 193.7 10,308.47 1,656,000 0.63 206.66 11,185.25 1,548,000 0.65 215.78 11,809.53 1,476,000 0.67 225.36 12,471.52 1,404,000 0.69 235.43 13,174.00 1,368,000 0.71 246.08 13,924.09 1,296,000 0.73 257.38 14,727.69 1,260,000 0.75 269.42 15,592.36 1,188,000 0.77 282.35 16,530.31 1,152,000 376 0.79 296.3 17,552.70 1,080,000 0.81 311.49 18,677.84 1,044,000 0.83 328.18 19,927.78 972,000 0.85 346.75 21,334.67 936,000 0.87 367.72 22,942.94 864,000 0.89 391.89 24,821.17 828,000 0.91 420.49 27,075.86 756,000 0.93 455.74 29,900.14 720,000 0.95 502.05 33,681.76 648,000 0.97 570.67 39,422.03 576,000 0.99 715.47 52,009.02 468,000 P reventive M aintenance In terval (Hours) Fig 1: Graph showing the relationship between Total Maintenance Cost and Preventive Maintenance Interval with CM Lost Earning Consideration. 377 Fig 2: Graph showing the relationship between Total Maintenance Cost and Preventive Maintenance Interval with CM and PM Lost Earning Consideration. Preventive Maintenance Interval (Hours) Fig 3: Graph showing the relationship between Lost Earnings During CM and PM and Preventive Maintenance Interval. 378 Upper Bound Fig 4: Graph showing the relationship between the Cycle of Preventive Maintenance in a Planning Horizon with the Upper Bound 5. Discussion The numerical examples 1 and 2 showcase the step to step approach of the algorithm.In example one, the preventive maintenance interval tPM is computed as70.66 Hours. However, when the average time for executing the preventive maintenance activities is considered, then DT + tPMis 78.66 Hours. The corresponding total cost of maintenance in a year with the predicted preventive maintenance interval is 1,286,365.92 Naira. In the case of the numerical example two, the computed preventive maintenance interval tPM appears to be the same preventive maintenance activities is considered, and thenDr + tPMis 78.66 Hours. The corresponding total cost of maintenance in a year with the predicted preventive maintenance interval is 5,318,365.92 Naira while the machine will undergo preventive maintenance during the planning horizon for n = 112 times. This result shows that lost earnings due to 379 preventive maintenance increase the cost incurred by manufacturing firms. The resultsfrom the subsequent analysis with the Upper Bound of F (tPM) being set at 0.27 and above are presented in Tables 1-3 and Figures 1- 4.In Table 2, the work first considered the lost earnings due to corrective maintenance among other cost factors. The results show a minimum Total Maintenance Cost TC of 1,248.719.77 Naira at which preventive maintenance can be performed. The optimum preventive maintenance interval at this minimum cost is 125.18 Hours. Considering the estimated optimal preventive maintenance in Table 2, the cycle of preventive maintenance within the planning horizon of a year is 70. Table 3 and Figure 2shows the result for lost earning during preventive maintenance alongside the lost earning during corrective maintenance. As presented, it was observed that there is an increase in preventive maintenance interval when the Total Maintenance Cost (TC) decreases. That is, an inverse relationship exists between the preventive maintenance interval and the Total Maintenance Cost when the lost earnings due to preventive maintenance actions were considered. While, the manufacturing firm losses a specific amount of money during the period of the preventive maintenance, the result suggests that lost earning during the period of executing preventive maintenance should be considered as a planned loss. However, if the decision-maker tries to save the preventive maintenance hours for production, the result shows that the machine reliability will be affected. The machine failure rate would increase as seen in Table 3 and could reduce the useful life of the machine. Comparing the cost incurred due to corrective and preventive maintenance as presented in Table 4 and Figure 3, we observed an increasing lost earning as a result of corrective maintenance. Meanwhile, when the preventive maintenance interval increases, the lost earning due to preventive maintenance decreases. This implies that the wider the preventive maintenance interval, the more the lost earning that could be incurred as a result of the loss of production time. Although there is a 380 notable decrease in lost earning due to preventive maintenance while the lost earning due to corrective maintenance increases, the result didn’t justify economic savingsif the PM is ignored. This is because a decrease in lost earning during preventive maintenance shows an increase in failure probability and thus making the machine reliability to be very low. 6. Conclusion The application of a cost-based approach to predict the preventive maintenance interval in a manufacturing firm has been demonstrated and this has revealed the applicability of the model. The identification of some cost factors including the lost earning due to corrective maintenance and preventive maintenance in determining the total maintenance cost for a production cycle has helped to capture the necessary costs that are incurred during maintenance. Also, we have been able to demonstrate the impact lost earnings could have on the determination of the optimal preventive maintenance interval and how each lost earning factors influences. Thus, this showsthe real-life situation and can serve as a quality decision support system for the maintenance team. 7. References Adebimpe, O.A (2014). Spare Parts Inventory and Lost Earning Based Preventive Maintenance Interval Predicting Model. 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Procedia Manufacturing, 11, 1170-1177. Kardon, B. &Fredendall, L.D.(2002).Incorporating overall probability of system failure into a preventive maintenance model for a sehalsy stem Journal o f Quality in Maintenance Engineering 8 (4), 331-345. 384 Wang, H. & Pham, H. (2006). Availability and Maintenance of Series Systems Subject to Imperfect Repair and Correlated Failure and Repair. European Journal of Operational Research, 174, 1706- 1722. Zequeira, R.I.&Berenguer, C. (2006).Optimal scheduling of non-perfect inspections. IMA Journal o f Management Mathematics, 17(2), 187- 207. 385 CHAPTER 17 Supply Chain Modelling: A Discrete Event Approach Ajisegiri G.O, Department of Industrial and Production Engineering, Faculty of Technology, University of Ibadan. go.aiisegiri@ui.edu.ng Ajisegiri, A. H. Department of Industrial and Production Engineering, Faculty of Technology, University of Ibadan, oluokunhumhaery@gmail.com Akande S. Department of Mechanical and Mechatronics Engineering, Afe Babalola University, Ado Ekiti. Sakandel @abuad.edu.ng Abstract The present world direction in automating everything has effect on barely every sectors including the logistic section of an industry. However, many company are still lacking behind with the use of low level description in regards to their global Supply Chain Network (SCN). In this work, an agent-based model is developed for modelling supply chain risk management (SCM) with focus on price and demand variation are the considered emerging properties of all the agents interaction. Agent- based Modelling (ABM) has been used extensively as a promising computational tool that depicts entities with autonomy and dynamic behaviour. The supply chain network consists of different agents e.g. manufacturers, inventory policy, retailers, transporters, etc. Reseau.py, built in Python modelling environment was used for the computational development. Based on the agent’s autonomy and their respective objectives, simulations of supply chain network were carried out to 3 8 6 investigate price variation effect among the agents. The results show that fluctuation in price is an established factor to be consider among agent’s interaction in the SCN. Keywords: Supply Chain Network, Supply Chain Management, Agent- based Modelling, Python. 1.0 Introduction A supply chain can be defined as a network of autonomous or semiautonomous business entities collectively responsible for moving a product or service from supplier to customer (Swaminathan et al., 1998). In order to achieve a reliable logistic network, a number of researchers have developed different models to describe units and activities of a supply chain (Ran et al., 2009). The present world direction in automating everything has effect on barely every sectors including the logistic section of an industry. However, many companies are still lagging behind in the use of low level description (Cohen & Lee, 2020) with regards to their global Supply Chain Network (SCN). Supply chain modelling methods that have been used for several periods are likely to be increasing company cost of operations, as they could be missing out on different opportunities. Missing out on different opportunities is likely due to unreliable model being used by the organisation. Supply chain reliability means the likelihood of performing supply chain activities in accordance with plans and expectations. Preparation for demand adequately, reducing inventory, and increasing reliability top supply chain professionals agenda. There have been several approaches to model supply chain reliability by researchers; for example, control theory approach is based on operational research, and differential equations approach, which depends on algorithms and optimization theories (Yildiz, 2013). However there are few or no works on modelling the reliability of supply chain using discrete event simulation. In 387 particular, the use of an agent-based modelling approach is limited. Based on the gaps highlighted, there are still many research opportunities that can be pursue in the complex adaptive system of interactions of the individual agents within supply chain network. Agent-based Modelling (ABM) has been used extensively as a promising computational tool (Borshchev & Filippov, 2004a, 2004b) to model supply chain reliability with features like uncertainty, partial information sharing, and dynamics (Long & Zhang, 2014). ABM, an agent-oriented approach to model and simulate complex adaptive systems, depicts a new development in supply chain area of research that has been regarded adequate for studying supply chain management (Chen et al., 2013). In order to bridge the research gap in literature, this work focuses on the use of ABM for modelling supply chain reliability in order to unravel the complexity of supply chain system. We analyse supply chain complex adaptive attributes considering energy flows, materials, and the related demand-supply match for each output products (by-products, useful waste and finished goods) and also simulate the effect of supply and demand, and price variations to depict how ABM is a promising tool in modelling supply chain reliability. The remainder of this work is structured as follows. Section 2 presents works related to modelling supply chain management as well as the gaps that exists in this research area. Section 3 to 4 is.an overview of the modelling method (ABM) as well as how it can benefit supply chain management and the model description. Section 5 gives a numerical example to the problem and Section 6 gives the conclusion. 2.0 Literature Review Increasingly, companies are viewing reliability problems as part of their organization goal to improve their daily operations. Most industries continues to reduce lead time, attain Just-in-Time delivery and lower inventories. An insightful research such can be found in (Bernstein & 388 Federgruen, 2005; Lee & Billington, 1993; Perakis & Roels, 2007) showing current direction supply chain management practices. Moving beyond that and toward high performance level, is not possible without reliable equipment, processes, and people. All the elements (people, equipment, tasks etc.) must be reliable to give higher percentage of reliable supply-chain process. From a supply chain management view, the goal is to improve lead-time each step of the supply chain tasks. Just as this is important is also to know the ability of how products will last long, while the aim is to achieve maximum return on investment (ROI) from management perspective. Recently, researchers have carried different studies on the complexity of supply chain management using couple of evolutionary approaches. Some of these works can be found in (Isik, 2011; Perona & Miragliotta, 2004; Wilding, 1998) to mention few of these papers. Agent-based modelling (ABM) has been used extensively as a promising computational tool that depicts entities with autonomy and dynamic behaviour (Kuhn et al., 2010). ABM is being used in science, social science, and other fields like engineering. It involves simulating the interaction the behaviour of many autonomous agents or entities over time (Ghali et al., 2017). ABM is also known as bottom-up (Albino et al., 2016) approach method. ABM look promising and useful tool that can be use to model large scale system (Kogler & Rauch, 2020), by incorporating the system with corresponding rules with assumptions that is most relevant within the supply chain network, the interaction among the agents, and possible emerging behaviour from the agents' interactions. (Tah, 2005) used ABM to simulate the emergence of industrial network focusing on modelling and simulation platform, which provide a risk-free environment and low cost for organisations to experiment with emerging SCM practices prior to implementation. In addition to their work, a prototype system was developed to explore the possibility of modelling and simulation of project procurement using multi-agent. They were able 389 to conclude that multi-agent approach in modelling SCM is adequate for the simulation of supply chain network construction. Kim et a/.(2012) developed an ABM method for end product exchange network between sellers and buyers in an industrial network. Their proposed solution method has limitations because setting off was not investigated. Yazan et al. (2016) approach modelling industrial networks with the aid of enterprise input-output for the design and simulation of a reliable supply chain network. However, their results were static and therefore not reflecting real life situation. (Abideen & Mohamad, 2020) work focus on dynamic quantification and visualization of the future state of a warehouse supply chain value stream map using discrete event simulation (DES) technique. The DES simulation was able to mimic the future state lead time reductions successfully. In this work, the focus is on using a descriptive event approach called agent-based model to model supply chain risk management (SCRM) reliability with focus on price and demand variation. We analyse supply chain complex adaptive attributes considering energy flows, materials, and the related demand-supply match for each output products (by­ products, useful waste and finished goods) and also simulate the effect of supply and demand, and price variations to depict how ABM is a promising tool in modelling supply chain reliability. 3.0 Reseau-SCM Agent-Based Model There are many approaches of simulating a complex system and one of the applicable methods is through agent-based modelling (ABM). ABM is extensively used within complexity theory and springs from object- oriented programming and distributed artificial intelligence. The agent formulations used in this work extend on the basic formulation by (Ajisegiri, 2019). The model was named Reseau, which means a network. The Overview, Design Concepts and Details (ODD) protocol proposed by (Grimm et al., 2010) is used for its description. It was designed so that ABM publications would be more complete, quick and 390 easy to understand, and organized in a manner that allows for presenting information in a consistent order (Grimm et al., 2010). The details of ODD adaptation in Reseau can be found in the extra supplement information (ESI) section. The model is an integrated agent-based model and input-output approach and was developed using Python platform, which is a general-purpose programming language. Simulation Flow The logic flow of Reseau agent-based model for the problem identified above is described below. The logic flow is divided into four distinct heading and the high level of how the mode runs is explained below for each of the header. System logic flow • Initialised agents • Load all agent parameters from external file Begin trading Step 1 • Randomise all agents in the list • Agents produce • Agents predict requirements Step 2 • Randomise all buyers • Each buyer checks all sellers and complete transaction Step 3 • Randomise all sellers • Each seller checks all buyers and complete transaction Step 4 • The histories are collated and stored Step 5 • Each agent records its transaction in an external file 391 Seller logic flow Step 1 - Production • The production quantity for each product is assumed equivalent to the production quantity. Step 2 - Predict requirement For each product: • Product sales quantity SQt is asummed to follow Gaussian distribution with mean, p and sigma, a. For each product • Check history and get average price in the market over 10 periods • If condition is random: product price p* is asummed to follow Gaussian distribution with mean, p and sigma, a. o If condition is risk based and average price equal zero: delta p equal p; o If condition is risk based: get product price Step 3 - Sell product • Create an empty list to append buyers • For each product, if the storage capacity is less than sales quantity o Randomize all the buyers o For buyer in buyers list: make deal for each product o If deal is valid o Append buyer in the list of deals o Sort the deal based on highest price: Initialize the count n = 0 o While the sales quantity is greater than storage capacity and n is Less than length of the deals list: execute trading and increase n by 1 Buyer logic flow Step 1 - Production 392 For each raw material: If list of raw material equal empty then raw material quantity equal zero Step 2 - Predict requirement • The raw material demand Di is asummed to follow Gaussian distribution with mean, p and sigma, cr. Step 3 - Buy raw material • Create an empty list to append sellers • For each raw material, randomize all the sellers • For seller in sellers list, make deal for each raw material. If deal is valid, append seller in the list of deals and then sort the deal based on lowest price • Initialize the count n = 0. While raw material demand is greater than zero and n is less than length of the deals list then execute trading and increase n by 1 Factory logic flow Step 1 - Production For each raw material obtain PC = m in im um (q^,R M C ) (2) »For each raw material obtain RMQi = RMQi - PC X RMUt (3) For each raw material SQi = SQi + PC x PUi (4) PQ = SQ (5) Step 2 - Predict requirement Total capacity C is asummed to follow Gaussian distribution with mean (p) and sigma (ct). 393 For each product sales quantity SQi = SQi + C x PUi (7) For each raw material demand RDi = C x RMUi x SQi - RMQi (8) • For each product o Check history and get average price in the market over 10 periods o If condition is random ■ Product price p; is assumed to follow Gaussian distribution with mean, (j. and sigma, a. ■ If condition is risk based and average price equal zero ■ Delta p equal p* o If condition is risk based ■ Get product price Step 3 - Buy raw material ■ Create an empty list to append sellers ■ For each raw material, randomize all the sellers. ■ For seller in sellers list: make deal for each raw material ■ If deal is valid, append seller in the list of deals and sort the deal based on lowest price. ■ Initialize the count n = 0. While raw material demand is greater than zero and n is less than length of the deals list then execute trading and increase n by 1 Where PC is production capacity, RMQ is all raw material quantity, RMU is all raw material usage, RMC is all raw material capacity, RMQt is each raw material quantity, RMUt is each raw material usage, is each raw material demand, SQi is each sales quantity, PU is product usage, PQ all product quantity and SQ all sales quantity. 394 4.0 Numerical example To demonstrate the effectiveness of the proposed methodology and gain some managerial insights a case study is conducted for only one input- output factory type. We believe that if a single input-output system works perfect for the model, it will surely represent a multiple input multiple output system which is a representation of a real problem. Sensitivity analysis is further conducted to provide deep understanding of the proposed hypothetical SCM system. The proposed structure of the SCM system studied in this work is shown in Figure 1. The factories consist of three combined heat and power plant (CHP) differentiated by their unique identifier, CHP1, CHP2, CHP3. The CHP’s main raw material input is biogas apart from other input which are not included in this simulation. This demonstration is strictly for single input-output scenario. The CHP’s main output is electricity. The other made up industries/factories are, anaerobic digester (AD), that is, ADI, AD2 and AD3. The anaerobic digester uses electricity as its main raw material input to generate biogas. The SCM system is made up of six different industries/factories with the possibility of transacting business among themselves. Each of the industries/factories can also make possible connection with external environment if external agent supplier’s price is favourable compare to any of the factory agents. Apart from the factories, the SCM also contains three infinite sink agents (market buyers B 1, B2 and B3) that willing to buy from the source agents r at a considerable price and also infinite sink agents (market sellers, SI, S2 and S3). The infinite market agent either buys or sells directly from/to the factory agents. o 395 Figure 1: Hypothetical supply chain management (SCM) o f energy based system. The initial data for the anaerobic digestion and combined heat and power plants were obtained from (Gonela & Zhang, 2014). The three CHP plants separately have demand capacity for biogas (methane) ranging from 80,000 - 500,000 cubic meter per month while the AD plants utilizes food and bio-solid wastes in the range of 0.3 million tons and required energy within 30 - 65 megawatt. Simulation results and discussion Based on the numerical example described above, a single simulation run was carried out and the results is as shown in Figure 2 - 3 . The supply and demand evolution of the three CHP’s are shown in Figure 2. It should be noted that a time period of one month stand for one simulation cycle. This was found to be enough to give a stable final configuration. It can be seen that CHP2 has a higher demand evolution with average value around 480,000 cubic meter per month. CHP3 demand for biogas is the 396 lowest. CHP1 has a demand in between the value of CHP2 and CHP3. This is understandable based on the demand capacity of each of the three combined heat and power plant. However, Figure 3 shows the electricity demand on monthly basis by the AD plants. AD2 has the highest demand on monthly basis. ADI has the lowest. The demand by each plant is based on their demand capacity. From these results, it can be established that price variation over a period of time is a determinant that need to be consider in modelling of supply chain risk management. Figure 2: Biogas demand/month for CHP plants. \ 397 Figure 3: Electricity Demand/month for AD plants. 398 V Figure 4: Average demand and mean error over 30 time-steps. Figure 4 (b), (d) and (f) show the average biogas demand. It can be seen that the demand for biogas by CHPI with a mean of 340,000 cubic meter and standard deviation (SD) of 40. CHP2 has an average demand of 440,000 cubic meter and SD of 50 while CHP3 has an average demand of 120,000 cubic meter and SD of 60 cubic meter. 399 A single run simulation for the evolution of price are as shown in Figure 5 - 6 . The price of electricity sales per month for each CHP plant is as shown in Figure 5. It can be seen in the figure that the CHP with lowest average price per step is CHP2 and its price dominate the other two CHP’s. On the part of the AD factories, Figure 6 indicate that the sales price of biogas per month. In the same vein, AD2 has the best price and that dictates why it dominates the transaction in the SCM. From these results, it can be established that price variation over a period of time is a determinant that needs to be considered in the modelling of supply chain risk management. Figure 5: Price/Unit o f Electricity 400 time-step ("month") Figure 6: Price/Unit o f Electricity. 5.0 Conclusion In this work, supply chain risk management reliability with focus on price and demand variation are the considered emerging properties of all the agents’ interaction. A hypothetical SCM of six. different process plants acting as market sellers and buyers were developed. The source agents sell to the sink agent based on the lowest price at any period. Results revealed that ABM is a promising computational tool for modelling and simulating periodic supply and demand. It was determined that variation in price is one of the deciding elements in modelling reliability of supply chain risk management. 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Afolabi2 1 (Department o f Industrial and Production Engineering, University o f Ibadan, Ibadan, Nigeria) 2 (Department o f Agricultural and Bio-Environmental Engineering, Federal College of Agriculture, Moor Plantation, Ibadan, Nigeria) *Corresponding Email address: engrakanbi@yahoo.com Abstract In place of the combine harvesters, stationary grain threshers are the most common among the farmers in the developing countries, many are being produced locally to meet up with the local demands by the farmers which they find to be relatively cheap and affordable. To ascertain the level of their user friendliness, two threshers of heights 92 cm (Ml) and 161.5 cm (M2) with capacities 3000kg/hr. and 6500kg/hr. respectively were selected for evaluation to determine the possible biomechanical strain that may result from working with these locally fabricated threshers. Questionnaire and physical measurements were employed for data collection of thirteen randomly selected operators, with ages ranged in- between 20 and 35 years. The results of machine performance tests showed that quantity threshed on average ± SD per minute are 12.59kg ± 2.41 (Ml) and 20.38kg ± 3.84 (M2),corresponded to the mean (SD) of weight per lift of 1.75kg (0.44) and 2.06 (0.22), and mean; SD of frequency of lift/minute of 71ift/min;1.59 and 101ift/min;1.81. The body kinematics analysis showed flexion, extension, lateral deviation and abduction with respective highest mean values of 167.750 at kneel (Ml), 111.500 at ankle (Ml), 24.750 at neck (M2) and 72.000 at shoulder (M2) at the end of lift. Regression analysis of biomechanical parameters, and frequency of lift and weight per lift gave F-value of 425.987 (R2 =0.974), 405 which shows no relationship at a= 0.01. Subjects’ indications of body parts discomforts showed highest percentages of 78.3%; 84.6% and 72.9%; 80.8% for M l; M2 at shoulder and lower back respectively. Conclusively, the overall result showed that the two machines need to be ergonomically modified to prevent the users from the risk of musculoskeletal disorder (MD). Keywords: biomechanical strain, developing countries, ergonomics, local demands, operators, stationary grain thresher 1.0 Introduction The industrialization of agriculture has introduced new equipment with little attention paid to ergonomic design. Most machinery turned out in the developing nations to meet the need of the farmers are products from artisans with little or no consideration to operators but the operations of the machinery. As many technological approaches in solving associated problem with manual operations in agriculture are on the increase, the need for application of ergonomics/ human factors in machinery development become indispensable. There are diverse forms of occupations carried out by men and women; hence, the risk of musculoskeletal injuries as a result of occupational vulnerabilities may vary by sex (Messing et al., 2009). An ample of occupational risk factors existing in the course of working life are regarded to be detrimental to musculoskeletal health that resulted to various forms of musculoskeletal disorder diagnosis and eventually damages the physical functioning of workers in their latter lives (Prakash et al., 2017) The aim of this study is to evaluate the level of ergonomic factor consideration in the design and fabrication of locally manufactured agro­ processing machinery and to determine biomechanical strains that may result through the performance evaluation of the selected grain threshers. 2.0 REVIEW OF LITERATURE In contempt of the existing information on the corresponded work-related disorders in musculoskeletal systems, a profound number of occupations 406 are still linked to poor working postures and awkward body movements in association with a heavy physical work load (Karla et al., 2012). Competition and increased work demands have also increased farmer’s exposure to risk factors through increased work pace and/or duration. In American, Mazza et al. (1997) recorded that of the thirteen most common agricultural health related problems reported by rural health care providers, heavy lifting was the most common exposure of patients, while repetitive motions was fourth. External loads are given rise to in the physical work environment and are communicated through the biomechanical forces of the body, specifically the limbs and trunk, to produce intramural loads on tissues and bodily structures. Biomechanical variables include posture of the body, bodily strain, intensities and movements, as well as individual factors such as age, strength, agility and dexterity, and additional components that mediate in the transferal of outer loads to inside loads on bodily structures. Tissue injury may transpire when the applied load transcends the inner forbearance of the tissue and resulted to tissue irritation and pain, impairment or disability. As with most biomechanical systems, loading is influenced greatly by the external moment imposed on the system. However, because of biomechanical disadvantage at which the torso muscles operate relative to the trunk fulcrum during lifting, very large loads can be generated by the muscles and imposed on the spine (Marras, 2006). In occupational setting human anatomy can be affected by traumas that lead to musculoskeletal disorders, these are; acute trauma (this can transpire when a single application of a force is so huge that it transcends the endurance limits of the body structure during occupational task) and cumulative trauma (this refers to repeated application of force to a structure that tends to wear down the structure, thus, lowering its tolerance to the point where it is exceeded through a reduction of this tolerance limit). The latter type of the trauma may of necessity common in the threshing of grain with stationary thresher, in that the process of manual loading of un-threshed grain into the threshing machine is more of repetitiveness. The repetitive application of force can affect either the 4 0 7 tendons or the muscles of the body, the process which results in terrible joint discomfort and a chain of musculoskeletal reactions such as decrease strength, lower tendon movement, and decrease mobility. A disorder, as presented by musculoskeletal disorders, has a slow start as juxtaposed to an acute injury, which is as a result of a single distinguishable occurrence. A disorder is essentially arbitrated by some pathogen or pre-pathological progression (Kurmar, 2001). Kasey et al. (2014) reported that musculoskeletal disorders are non- harmful soft tissue disorders, which may resulted from and/or heightened by workplace exertions. Sergey et al. (2017) presented that diverse forms of damage to the bones and soft tissues of the elbow joint are corresponded with particular postures of flexion and turning of the forearm on the elbow during injury. Mechanical degradation of tissue may occur due to exposure over time from mechanical stresses that are repetitive, prolonged or forceful. The expression “load” is habitually used to relate the physical stresses at work on the body and structures inside the body. These stresses comprise kinetic (force), kinematic (motion), oscillatory' (vibration), and thermal (temperature) energy sources (Radwin et al., 2001). Repetitive tendon motion is thought to promote shear damage at the tendon sub-synovial connective tissue (SSCT) interface, which is supported by the finding that fibrosis is exacerbated in SSCT layers adjacent to flexor tendon (Aaron et al., 2014). Loads can originate from the external environment or result from action of the individual. 3.0 MATERIALS AND METHOD Thirteen physically active subjects (11 males, 2 females, age = 24.8 ± 3.2 years, height = 173.91 ± 5.96 cm, weight = 63.38 ± 7.86 kg) volunteered as subjects. Individuals with self-reported health problems related to head injury in the recent past were excluded from the study. All subjects completed 3 iterative testing operations on the selected machine, during which sagittal-plane kinematics and lifting distances were recorded while they performed the threshing from the origin of the lift to the end of the lift, also, individual body temperature was taking before and after the 408 CHAPTER 18 Evaluation Of Mechanical Strain Resulting From Working With Two Locally Fabricated Engine Powered Stationary Grain Thresher O.G. Akanbi1* and B.O. Afolabi2 1(Department o f Industrial and Production Engineering, University o f Ibadan, Ibadan, Nigeria) 2 (Department o f Agricultural and Bio-Environmental Engineering, Federal College o f Agriculture, Moor Plantation, Ibadan, Nigeria) ^Corresponding Email address: engrakanbi@yahoo.com Abstract In place of the combine harvesters, stationary grain threshers are the most common among the farmers in the developing countries, many are being produced locally to meet up with the local demands by the farmers which they find to be relatively cheap and affordable. To ascertain the level of their user friendliness, two threshers of heights 92 cm (Ml) and 161.5 cm (M2) with capacities 3000kg/hr. and 6500kg/hr. respectively were selected for evaluation to determine the possible biomechanical strain that may result from working with these locally fabricated threshers. Questionnaire and physical measurements were employed for data collection of thirteen randomly selected operators, with ages ranged in-between 20 and 35 years. The results of machine performance tests showed that quantity threshed on average ± SD per minute are 12.59kg ± 2.41 (Ml) and 20.38kg ± 3.84 (M2),corresponded to the mean (SD) of weight per lift of 1.75kg (0.44) and 2.06 (0.22), and mean; SD of frequency of lift/minute of 71ift/min;1.59 and 101ift/min;1.81. The body kinematics analysis showed flexion, extension, lateral deviation and abduction with respective highest mean values of 167.750 at kneel (Ml), 111.500 at ankle (Ml), 24.750 at neck (M2) and 72.000 at shoulder (M2) at the end of lift. Regression analysis 409 of biomechanical parameters, and frequency of lift and weight per lift gave F-value of 425.987 (R2 =0.974), which shows no relationship at a - 0.01. Subjects’ indications of body parts discomforts showed highest percentages of 78.3%; 84.6% and 72.9%; 80.8% for Ml; M2 at shoulder and lower back respectively. Conclusively, the overall result showed that the two machines need to be ergonomically modified to prevent the users from the risk of musculoskeletal disorder (MD) Keywords: biomechanical strain, developing countries, ergonomics, local demands, operators, stationary grain thresher 1.0 Introduction The industrialization of agriculture has introduced new equipment with little attention paid to ergonomic design. Most machinery turned out in the developing nations to meet the need of the farmers are products from artisans with little or no consideration to operators but the operations of the machinery. As many technological approaches in solving associated problem with manual operations in agriculture are on the increase, the need for application of ergonomics/ human factors in machinery development become indispensable. There are diverse forms of occupations carried out by men and women; hence, the risk of musculoskeletal injuries as a result of occupational vulnerabilities may vary by sex (Messing et al., 2009). An ample of occupational risk factors existing in the course of working life are regarded to be detrimental to musculoskeletal health that resulted to various forms of musculoskeletal disorder diagnosis and eventually damages the physical functioning of workers in their latter lives (Prakash et al., 2017) The aim of this study is to evaluate the level of ergonomL factor consideration in the design and fabrication of locally manufactured agro-processing machinery and to determine biomechanical strains that may result through the performance evaluation of the selected grain threshers. 2.0 REVIEW OF LITERATURE 410 50 -i £ 1— . B i m m f f m m m m m m m m m BMI 5 21 21 21 22 2 4 2 4 24 25 25 28 29 29 30 CO AGE (YEAR) AND SEX Fig. 1: age, sex and respective body mass indexes (BMI) of the subjects 4.2 Occupational Lifestyles of the Subjects The occupational lifestyles of the subjects are; Farming, Mechanical work, Driving, Hawking, and Schooling. The percentages distribution are 23%, 15%, 8%, 15%, and 39% respectively as shown in figure 2. It can be deduced that energy requirements for this group of works ranges from lOKJ/min to more than 30KJ / min, from student through to farming (Rowett, 2008). ■ Farm ing ■ M ech a n ica l W ork ■ D riv in g ■ H aw k in g ■ Student Fig 2: percentage of occupational description of the subjects 4.3 Relative Anthropometry Measurements for the Study Table 1 shows the parameters that are essential in the process of threshing by stationary grain thresher. Mean (SD) of height/stature is 173.91 (5.96), and the subjects’ weight ranged from 53kg to 78kg. Arm reaches can explain the degree of flexion and extension of the different parts of the body and it ranged from 69.5cm to 83.5cm; hand length and hand width 4 1 1 explain gripping effect with mean ±standard deviations of .19.75cm ± 1.13 and 9.19cm ± 0.46; ankle height ranges from 8.3cm to 9.2cm with mean ±standard deviations of 0.31cm ± 8.71, these are indispensable as all joints play important roles in operations that involves dynamic movement of the body parts. Table 1: Anthropometric data of the Subjects (cm) Parameters Mean S.D Min. Value Max. Value Height 173.91 5.96 165 186 Weight* 63.38 7.86 53 78 Arm Reach (Front) 77.04 4.14 69.5 83.5 Overhead Reach 203.88 21.09 139 223 Shoulder Height 142 12.9 106 159.5 Hand Length 19.75 1.13 18 21.2 Hand Width 9.19 0.46 8.7 10 Elbow Height 108.92 5.07 101 118 Shoulder Width 44.07 2.09 40.2 47 Leg Length 100.62 4.47 90 107 Lower Leg Length 50.42 4.29 43.5 58.5 Lower Arm Length 34.23 2.49 30.5 39 Arm Reach (From Floor) 73.85 3.92 68.5 80.5 Ankle Height 8.71 0.31 8.3 9.2 412 SD = standard deviation *kg 4.4 Determination of Frequency of Lift, Weight per Lift as Corresponded to Quantity Threshed on M l And M2 The frequency of lift per minute and weight per lift together with quantity threshed per minute are as shown in the Table 2 in terms of their mean and standard deviations. Statistical analysis indicated that on the average, frequency of lift per minute (7 lift/ min ± 1.59 SD) while working with machine 1 is lesser compare to machine 2 which is lOlift/min ± 1.81 SD. In the same way, weight per lift and quantity threshed are 1.75kg ± 0.44 SD and 12.59kg ± 2.41 SD for M l, and 2.06kg ± 0.22 SD and 20.38kg ± 3.84 SD for M2. These results attested to the machines capacities and efficiencies (Table 2). Table 2: Frequency of Lift per Minute, Weight per Lift, and Quantity Param eters M ach in e 1 M ach in e 2 F req u en cy o f lift M ean 7 .0 0 1 0 .00 per m inute (lift/m in ) S D 1.59 1.81 W eig h t per lift (K g /L ift) M ean 1.75 2 .0 6 S D 0 .4 4 0 .2 2 Q uantity T hreshed M ean 12.59 2 0 .3 8 per m inute (K g /m in ) S D 2.41 3 .8 4 Shelled Per Minute S D = standard deviations N = 13 Replication = 3 4.5 Indication of Body Discomforts before and after Operations on M l and M2 by the Subjects Table 3 gives details about the expressed opinions of the subjects regarding body parts discomforts experienced before and as a result of threshing grain with stationary threshers. Before evaluation it was discovered that 61.5% of the subjects has no body discomforts, 15.4% has shoulder and neck pains with lowest percentage of 7.7% for low-back and wrist as shown in Table 3. 413 The two machines were said to have produced some level of discomforts by all subjects. When interviewed about the severity of the pain, the subjects commented on how the pain was moderate before commencing shelling and more severe afterwards. Comparing all types of body discomforts, working with machine 2 (M2) proved to be more unfit ergonomically in that it has greater percentages except on wrist where percentages for Ml is 31.2 and 30.8 for M2. Shoulder strain has lesser percentage of body discomfort for Ml, 78.3% compare to 84.6% for M2, while upper leg and ankle have the least percentage of 6.0% and 7.7% respectively for Ml and M2 (Table 3). 4.6 Analysis of the Degree of Variations from Neutral Position while working with M l and M2 The posture adopted to operate the Ml and M2 may have resulted in pain or discomfort over much of the body since they involved considerable spinal flexion (Table 4). This was particularly observed with the subjects at initiation of lift in stooping posture and the termination of lift. Results from the measured angles of variation from the neutral position during the evaluation of Ml and M2 suggested that this subsequently resulted in an increase in the incidence of pain or discomfort in most body parts. 414 Table 3: Subjects’ Indication of Body Parts Discomfort Percentage of Subjects Affected After Evaluation (%) s/ Body Before Ml M2 N Discomfor Evaluatio ts n (%) 1 Lower 7.7 72.9 80.8 Back 2 Shoulder 15.4 78.3 84.6 3 Wrist 7.7 31.2 30.8 4 Forearm nill 14.1 15.4 5 Neck 15.4 9.8 11.5 6 Upper Leg nill 6.0 7.7 7 Ankle nill 6.0 7.7 8 None 61.5 nill nill A stooping posture, as adopted during threshing operation, is generally considered to be undesirable, with spinal flexion causing deformation of the intervertebral disc and exerting a risk of the nucleus being extruded (Pheasant, 1991). Any mechanical advantage from the weight of the body through a tilted trunk will thus be offset by the risk of cumulative musculoskeletal damage or overexertion from such a posture. Repetitive lifting of load involves asymmetrical movement that further increases the risk of musculoskeletal damage. With spinal rotation there will be an increase in the loading on the spine, causing further deformation of the discs (Pheasant, 1991). 415 Table 4: Results of Different Degrees of Variation from Neutral Position Stooping Standing M l Standing M 2 Mean SD Mean S D M ean S D Lumb- 102.25* 7.72 28.75* 15.22 2 2 .5 ** 3.7 osacral Knee 129.25* 33.05 167.75* 3.86 164.25* 6.45 Neck 101.50* 28.10 16.00* 11.43 24.75d 7.27 Ankle 17.57* 98.00 1 11 .5 0 ** 8.27 84 .00* 27.65 Elbow 139.75* 24.66 115.00* 14.14 136.25* 23.53 Wrist 54.41* 133.5 145.50* 8.43 145.75* 23.81 Shoulder 70.50* 16.9 84 .50* 9.15 72.003 9.09 l S D = standard deviation N = 13 * flexion ** extension d= lateral deviation a = abduction l i shelled (Table 5). Considering the impact of each predictor variable, on the criterion variable (Weight per lift and frequency per lift), the following findings were deduced. The weight per lift, and frequency of lift per individual subject was negatively related to quantity shelled per individual and was significant at 1% level respectively (Table 5). This indicates that the factors are significant to the study and have significant effect on the quantity shelled per individual on the two machines. This suggested that the oxygen consumption is somewhat higher in the evaluation of the two machines than would be expected for the weight lifted at the observed frequencies 416 Table 5: Result from Regression Analysis for Biomechanical P a r a m e t e r s ___________________________________________ M odel U nstandardized C oefficient Standardized C oefficient B Standard E rror Beta t Sig. C onstant -15.986 1.16 -3.784 0 Frequency o f L ift 1.956 0.082 0.811 23.95 0 W eight P er Lift 8.141 0.456 0.604 17.845 0 F 425.987 R2 0.974 Dependent variable: quantity shelled per individual N = 13 5.0 CONCLUSIONS AND RECOMMENDATION This study has brought to the limelight how agricultural machinery developed for use in a developing country can be improved by employing human factors/ergonomics approach to design. The so called technological interventions in agriculture have revealed how would be users are exposed to hazards through ergonomics evaluation. By incorporating ergonomics into the design process, drudgery associated with the machine will be reduced and productivity, user comfort and satisfaction will be increased. Improving the posture and manual handling to be adopted to operate the machine will result in a significant reduction in physical strain and incidence of body-part discomfort and can be expected to reduce the risk of musculoskeletal damage. 5.1 Conclusions The study had shown that biomechanical strain resulted through the performance evaluation results. On this premise, the following conclusions were drawn: 1) Machines capacities and heights, hopper shapes and orientation and concave sizes as well as personal limiting factors of individual subjects may be the determinant for frequency of lift and weight per lift as they varied across the machines. 417 2) Lifting process in repetitive manner by the operators has shown some significant deviations from neutral position, the accumulation of which could result in musculoskeletal injury, therefore make the use of the types of the evaluated machines ergonomically unfit and hazardous to human. 5.2 Recommendation Based on the results from the evaluation, the following recommendations are hereby suggested in order to correct and improve on the existing locally developed stationary threshers and to prevent likely work related musculoskeletal disorder (WRMSD). 1. Incorporation of adjustable plat-form on which the unshelled crops will be put to check stooping posture involved in the initiation of lift. 2. Design and development of stationary grain thresher involving height adjustable mechanism, capable of accommodating 5th to 95th percentile of the operators’ population to check repetitive variations from neutral positions. 3. The importance of ergonomic/human factors intervention in the design and fabrication of agricultural machinery produced locally. REFERENCES Aaron M. Kociolek, Jimmy Tat, Peter J. Keir (2014) B iom echanical R isk Factors and F lexor- T endon Frictional W ork in the C adaveric C arpal Tunnel Jo urna l o f B iom echanics, p p 449- 456. Elsevier Ltd. h ttp ://dx .doi.O rg/10 .1016/i.ib iom ech.2014.12 .029 0021- 9290/& 2014. Karla G. G., Gabriel I., and Juan L. H. (2012) Biomechanical Analysis of a Manual Material Handling Tasks in a Local Manufacturing Company, Proceedings o f the 1st Annual Conference of the Society for 418 Industrial and Systems Engineering, Washington, D.C, USA September 16- 18. K asey C ., A shish D. N., X iaopeng N. and M ajid J. (2014) A B iom echanical S train Index to E valuate S houlder Stress P roceedings o f the 2014 Industria l an d System s E ngineering R esearch C onference Y. G uan an d H. Liao, eds. Kumar S. (2001) Theories of Musculoskeletal Injury, Ergonomics. 44(1), 17-47. Marras W.S. (2006) Basic Biomechanics and Workstation Design (Handbook of Human Factors and Ergonomics (ed. Salvendy, G.), John Wiley and Sons. Mazza J. J., Lee B. C., Gunderson P.D., and Stueland D.T. (1997) Rural Health Care Providers’ Educational Needs Related to Agricultural Exposures, Journal o f Agricultural Health and Safety. 3(4), 1997, 207- 215. Messing K., Stock S.R. and Tissot F. (2009) Should Studies of risk Factors for Musculoskeletal Disorders Be Stratified by Gender? Lessons from the 1998 Quebec Health and Social Survey. Scand J Work Environ Health. 35(2):96—112. Pheasant S. (1991) Ergonomics, work and health, (Macmillan, London) Prakash K. C., Subas N., Paivi L., Mikaela B. von Bonsdorff, Taina R., Monika E. von Bonsdorff, Jorma S., Juhani I. and Clas-Hakan N. (2017) Work-Related Biomechanical Exposure and Job Strain as Separate and Joint Predictors of Musculoskeletal Diseases: A 28-Year Prospective Follow-up Study. American Journal o f Epidemiology Vol. 186, No. 11DOI: 10.1093/aje/kwxl89 Advance Access publication: June 2, 2017 419 Radwin R.G., Marras W.S. and Lavendar S.A. (2001) Biomechanical Aspects o f Work-Related Musculoskeletal Disorders (Theoretical Issues in Ergonomics Science. 2(2), 153-217. Rowett Research Institute (2008) “Energy Expenditure.”http://www.rowett.ac.uk/edu-web/sec-pup/energy- expenditure. Sergey S., Ievgen L ., V asily M . and Jan A. (2017) C om parative B iom echanical A nalysis o f S tress—Strain S tate o f the E lbow Jo in t A fte r D isp laced R adial H ead F ractures. Journa l o f M ed ica l B io logy E ng ineering (2018)38:618-624 420 CHAPTER 19 Team-based Material Selection for a DC Machine Armature Design Using Compromise Programming Optimization Odu, O. Godwin Department of Mechanical Engineering, Delta State University, P.M.B. 1, Abraka, Oleh Campus, Nigeria. oduudwin @ gmail.com or odugodwin® delsu.edu.ng Abstract: Concurrent engineering design which emphasizes team decisions has created new challenges. The process of selecting a single material type from many varieties to best satisfy all product specifications and stakeholders’ requirements is one such challenge in team design. The literature is sparse on team decision-support instrument to enable Design engineers reach consensus on such contentious design issues. This study was designed to develop a compromise programming optimization model of a team-based material selection for a DC machine Armature design. A team-compromised instrument (TCI) for computing criteria weights that collates inputs from individual rankings was developed, and combined with material selection optimization function and solved as multi-criteria compromise programming (MCP) algorithm. This was applied to select materials for the design of a DC machine armature Core, armature shaft and armature windings and the results were compared to those of a popular non-team based Existing Algorithm (EA) known as Technique of Ranking preference by Similarity to Ideal Solution (TOPSIS). The results obtained show that both algorithms selected the same materials when the team-compromise instrument was used with associated compromise gain, such as Carbon Steel SAE 1090 (59.34%), Oxygen-free electronic copper UNS C10100 (59.81%) for DC armature shaft and armature windings respectively. However, for the armature core, the MCP selected JG-core Grain-oriented electrical steel (59.01%) while EA selected AK steel DI-Max HF-10 421 non-oriented electrical steel (51.25%).The model can therefore be used conveniently for making design decisions and reduce the possible conflicts that may arise from the design team and design requirements. Keywords: Team-compromise instrument. Material selection, Multi­ criteria optimization, Compromise programming, Design criteria. 1. Introduction: Material selection is one of the foremost functions of effective engineering design as it determines the reliability of the design in terms of industrial and economic aspects. A good design may fail if unable to find the most appropriate material combinations. Therefore, it is crucial to ascertain the best materials that would be suited for a particular design. Hence, material selectionis the act of choosing the material best suited to achieve the desire requirements of a given application. It is also regarded as the foundation of all engineering applications and design. Though many factors are involved into determining the selection requirements, such as mechanical properties, chemical properties, electrical properties, ability to manufacture and cost, but the selection process can be described with respect to application requirements, possible materials, physical principles and selection method. This task is compounded by several material types from which a single material has to be selected for a particular design. However, apart from the numerous existing material types that are available today, there are a large number of design specification related material characteristics which have to be simultaneously satisfied in the process of design (Al-Ogla, et al. 2015). These design characteristics is yet another major challenges in material selection equation because selecting material to meet a single property requirement is known as single criterion material selection problem. A solution based on a single criterion may provide worst solution value for other criteria, for example, the selection of material with minimum density may not provide for the desired ductility and hardness; another with maximum toughness may not counter for the 422 electricity conductivity and cost requirements. So, a situation may arise where several combinations of these opposed requirements which render the one-criterion solution approach unsuitable. Therefore, for several properties to be simultaneously satisfied, there exists a multi-criteria optimization problem. Apart from the material criteria requirements problem, there is also disagreement arising from team of designer as stakeholders in taking decisionssuch that each individual of the design team may have a certain preference of a certain criteria over the others. The behaviour of team members in an organization is crucial to its performance because each individual should be capable of doing his/her job and perform team roles in a way that will moves the entire team towards achieving their objectives (Nestsiarovich and Pon, 2020; Megan, et al. 2015).Hence, the roles that members take can affect the team outcomes due to conflicts that may exist among them.Therefore, teamwork is very important due to the fact it has the will to compromise and work jointly with others and with the intention of reaching a common goal and purpose (Odu and Charles-Owaba, 2017). Within the design team, role expectations must be determined to allow members to work effectively and reduce delays due role conflicts (Terpstra, 1989).Design team interactions requires planning as always applied to nominal group technique. Such techniques as meeting agendas and decision-making procedures can make team projects more effective. However, with careful planning, team interactions may lead to interpersonal conflicts. Members must find a way to share their professional expertise and beliefs (Xuan and Du, 2003), and also willing to compromise on issues to settle conflicts procedures for handling compromises and unresolved conflicts may need to be determined. This view can be expressed with the concept of design for assembly, design for safety, design for cost, design of manufacture, etc., (Thankachan et al., 2010), where each team members wants their 423 point of view be noticed. In Engineering design, there is always a high risk of possible failure due to the wrong choice of material selection which may have huge costs in product design, building construction, automobiles, and other engineering products (Dev et al., 2020). One possible reason a lot of engineering design may face the risk of failure is the fact that a va ilab ility o f so m any alternatives has often led to poor material selection, therefore, there is need for scientific approach to the material selection process. Besides, new materials are continually being developed due to pressures from domestic and foreign competition, increased demand for quality and serviceability, or negative customer feedback and changes in prices. Moreover, decision-making by an individual judgment in the choice of material has always been biased most times, and this has led to improper material use. However, whenever this individual member comes together as a group, conflicts arises because their opinions are different. There is the need to develop a mathematical model that will compromise their individual decision and eventually eliminate the conflicts among the stakeholders so that consensus on issues can be reached. Therefore, this book chapter focuses on the development of a compromise programming optimization model for multiple criteria material selection using team-based approach for a DC machine armature component. However, the objectives of the study include: (1) develop a team-based compromise instrument for effective collation of DC machine input data from different design professionals, (2) develop a compromise programming optimization model for team-based multi-criteria material selection, and (3) formulate a model for comparing the quality of multi-criteria optimization material selection procedures. In the past one or more years, majority of the traditional materials that were used for engineering product design for some time now are being restored with newly found materials so as to make weight reduction possible and improve their outcomes (Rao, 2008). The variation of materials available exist in abundance (Roth et al., 2002, Ashby, 2010).It is estimated that the number of materials available to 424 the designers for consideration is vast, over 120.000 are at his or her disposal. This comprises of metallic and its alloy, and non-metallic materials for example, plastics, composite materials, ceramics, semi­ conductors, and glasses. This numerousnumbers of materials, along with the complex relationships between the different selection parameters, frequently makes the selection of a material for a given component a difficult task. 2. Materials and Method 2.1 Selection Methods Material selection includes three stages: Initial screening, determining the relative importance of material property, and determination of best solution (Ashby, 2010; Balanli et al., 2019). The initial screening of materials and processes can be very tedious task if performed manually from handbooks and supplier catalogs. This difficulty has prompted the introduction of several computer- based systems for materials and/or process selection (Farag, 2006). One of the important characteristics needed for initial screening of materials is the critical requirements of each part which defines the performance requirements of the material. First, start with all materials available and narrow down the choices on the basis of the rigid properties. Having specified the performance requirements of different parts, the required material properties can be established for each of them. These properties may be quantitative or qualitative, desirable or non-desirable. The desirable material properties should be maximized, while the non-desirable properties that should be minimized. All these properties should be achieved at a reasonable cost. In such cases, alternatives must be made possible through redesign, compromise of requirements, or development of new materials. 2.2 Criteria weights Determination The second stage of the material selection process involvesdetermination of relative importance of material 425 property/criterion.lt is required of the designer to find a suitable method of computing the relative importance of material property. In this study, a modified nominal group technique will be adopted such that selected material reflect the concept of design for assembly, design for manufacturing, design for maintenance, design for safety, design for cost, etc. This is more reason why a team-based material selection model is developed to minimized conflicts that may arise within the design team. Though, the proposed model will not only specify the weights, but will at the same time evaluate the criteria weights through a mathematical function referred to as team- compromise instrument. The model itself is very adequate because of its robustness, flexibility, accountability and simplicity. 2.2.1Team-Compromise Instrument Development Team-based approach to design has been the usual practice in an integrated product development in response to customer satisfaction. This approach is sometimes referred to as concurrent engineering. However, in the recent times, there has been few challenges, especially in the area where different team members of experts or professionals in a team has find a common ground on some contentious issues that relates to design requirements is one of such problem. And due to these challenges, conflicts seem to emanate from the following: Lack of information or input data on the product requirements to enable the stakeholders make the right decision; adoption of ‘traditional’ practice of design in decision-making process; trust issues between individual team members and team leaders in the design decision process; and individual stakeholders with strong professional learning. In order to develop a team-based compromise instrument that is well structured, it is important that instrument allow individuals to acquaint themselves with the following: 1) A comprehensive data of material related design requirement will be sent to each team members. Also, information on the inputs resulting from each of the component in terms of operation, 426 aesthetics, process manufacturing, component’s specifications and operating environment etc., are documented. The above information is independently studied without interference. 2) Individual team members are to rank the criteria independently with ordinal scale of first, second, third, etc., without having the same outcome. Now, a mathematical functioncapable of receiving the inputs from all the stakeholders in (2) above is developed; and a set of criteria preferences is generated. The team-compromise instrument is developed as follows: And for the purpose of promoting team-spirit, it is very important to add that the following conditions must be satisfied: (1) Enter the data for criteria weights computation, received from each of the team member, where w ., is the value of team preference index for criterion j, (2) I$mlwj = 1 (3) wj > ovy In order to satisfied the above conditions, the theoretical aspect of group decision-making approaches, such as Brain writing, Brain storming, Delphi, Analytical hierarchy process (AHP), and Nominal group technique (NGT)) reported in the literature (Al-Ogla&Salit, 2017; Abdullah and Rafikul, 2011; MacPhail 2013) was critically investigated. However, the structure of the NGT decision-making looks more acceptable for the mathematical modeling of team- compromise instrument and hence, satisfying simultaneously the three conditions earlier stated. The followingnominal group technique beneficial properties will be considered for the purpose of this study. (1) The possible number of criteria should be known (AO (2) Agreement on team size cannot be changed and minimum required number is seven (7) members; (3) Individual team member is allowed some time toindependently evaluate the information provided on the criteria and the ranking procedure; 427 (4) The ranking of criteria is carried out by individual team member without interference; (5) Team members are to rank the criteria using ordinal scale of first, second, third, etc., without having the same outcome, and zero rank is not allowed. (6 ) The ordinal scale ranked in (5) are changed to relative scores so that criterion having the highest score becomes first, N\ and 2,K| position criterion takes N-l, 3rd position takes N-2, etc.; (7) Decision made from all team membersare recorded according to a peculiar ranking pattern, such that the individual values form Arithmetic Sequence of(7, 2, 3.....N-2, N-l, N). (8) Accumulated scores for a certain criterion are the addition of scores from all theteam members.Note thatcombination of scores with values between 1 and N is most likely to depend on independent ideas of members; (9) The overallscoresgotten fromthe combination of all team members, Z with the use of ordinal scale to rank the set of N criteria is given by the expression in equation (1). SC = N( 1+2+3+........ +N) = ZN(N+1 )/2 (1) Therefore, the use of nominal group techniquecharacteristics are utilized in deriving a mathematical model which will meet the initial mentioned properties of criteria weightswy Let Rkj be the associated score a n d ^ b e the relative rank assigned by team member i to criterion j. Hence, the maximum possible score on any criterion is N and the minimum score by an individual is given as l.Thus, the relationship between Rkj and if/tj is given in equation (2). Rkj = N - i p kj + 1 (2) By assigning ordinal ranking asfirst, or second, or third, etc., in equation (2) it indicates that higher the rank, the same goes for the scoretoo. The system of ranking by individuals gives room for each team member to have better decision according to the laid down rules. Note that, making use of an ordinal scale of lsl, 2nd, 3rd, etc., without having the same outcome,it is difficult for just a member to arrive 428 with a score of more than 2 criteria that has the same value.As a result of these.the scores of any member aligns with the following arithmetic sequence. RkJ = {1, 2. 3 , ...... N-2, N-l, NJ (3) It is mandatory for all members to rank a criterion by making use of the rank indicator (TSj), then the sum of the scores of criterion j, TSjby all participants in the team is given in equation (4) TSj = I £=1 RkJ (4) Note that the set of scores received from all team members on a particular criterion must not always be arithmetic sequence in nature as illustrated in item (8) of the nominal group technique property. Since equation (4) represents the team ranking of criterion j. then, a team preference index of criterion j, w; , will be a function of T S j . This can be expressed as follows: T S i w, X£=lZ”=lflfc; £k=lE"=i Rkj (5) where the sum of all the scores from Z team members can be expressed as: S Z Rkj = ZN(N+iy2 (6) k=I 7=1 Substituting into (5), gives i x W; = ' k=1 ZN(N + l)/2 (7) In terms of the ranking variable (y/ k]) in expression (2), X (N - ̂ kj +1) w = — --------------- (8) ' ZN(N + l)/2 Expressions (7) and (8) are referred to as team preference index assigned to criterion j, and are used to determine the common values of the criteria weights w; , thereby avoiding possible team conflicts. This is achieved by giving each team member ample time to 429 independently go through the information as regards to the components that required material selection. Note that in this case, team members do not meet face-to-face. 2.2.2 Team-based Compromise Criteria Weight Assigning Instrument In view of the above team-compromise instrument analysis, the following procedure is taken to assist the team of designers to come up with appropriate decision on the set of criteria weights for the components under consideration. Item 1: The leader of the design team should document all necessary information on the DC machine requirements, including information regarding the design process, component function, process manufacturing. Also, stating clearly the ranking system procedure. Item 2:Once item (1) is completed; the team leader sent the prepared document to individual team member asking them to rank and return the set of data{ y/ kJ} back on a specific timeline for collation. Item3: Using equation (8) above, the set of criteria weights are then computed for N design criteria Hence, the material selection problem may be expressed by combining the team compromise instrument (TCI) preference indices and the mathematical programming compromise (trade-off) to form a multi-criteria compromise programming (MCP) model as follows: n Min F, = • 7 [ /v J2 • ; (for minimization ^[n{n + 1)] problem) (9) 430 , S ( n - ^ + D Max Ft = £A=L----------- - U f ; (for maximization /=1 [n(n +1)] 2 problem) (10) {= 1, 2 , ..., m; j = 1, 2 , . . . , n; k = 1, 2 , .... z 2.3 Selecting the Optimum Solution The selection of an optimum solution is the third stage of material selection process. It involves various mathematical programming and operation research principles. Various mathematical programming and optimization principles were utilized to develop the process of material selection (Jahan, et al., 2011).Optimization is an engineering discipline where extreme values of design criteria are sought. However, quite often there are multiple conflicting criteria that need to be handled. Satisfying one of these criteria comes at the expense of another.Generally, multi-criteria optimization deals with this type of conflicting objectives, and It provides a certain level of mathematical structure for an optimal solution to be reached so as to accommodates the various objectives required by the application.The process of optimization involves choosing the best solution from a pool of potential candidate solutions such that the chosen solution is better than the rest in certain aspects (Odu and Charles-Owaba, 2013). In the case of a single objective problem, we are maximizing or minimizing a single output and/or constraining a set of outputs to stay within a certain range (Van der and Koch, 2010).In the present- day situation, multi-criteria optimization is no doubt a very popular topic for both researchers and engineers. But still there are many open questions in this area. In fact, there is no globally acceptable definition of ‘optimum’ as regards to single criteria optimization, it is more difficult in trying to compare solutions of one method to 431 another, s ince in rea lity the decis ion about the best op tion i s s i m i l a r to that of the decision-maker. (Ashish and Satchidananda. 2004). Over the past few years, several researchers have applied different multi-criteria optimization methodsfor solving material selection problems in various engineering applications. Amongst those methods are: Technique for Order Preference by Similarity to Ideal Solution, (TOPSIS) -(Shanian &Savadogo, 2006;Shanian &Savadogo, 2009; Jahan et al., 2012; Kumar et al., 2014;andBabanli et al., 2019); Multicriteria Optimization and Compromise Solution (VIKOR) - (Rao, 2008; Chatterjee et al., 2010; Cavallini et al., 2013); Elimination and Choice Expressing the Reality (ELECTRE) - (Chatterjee et al., 2009; Peng at al., 2015); PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation - (Caliskanet al., 2013; Peng & Xiao, 2013); Complex Proportional Assessment (COPRAS) - (Ayrim et al., 2018: Sahin, 2019); and Preference Selection Index (PSI) Method - (Kahraman and Otay 2019; Maniya and Bhatt. 2010; and Madic et al.. 2017). In this book chapter, a compromise programming optimization model will be developed and utilized to develop the process of selecting the best material incorporating the team-compromise instrument detailed in section (2 .2 .1); and compared to one of the most popular and existing algorithms (TOPSIS) in selecting material for a DC machine armature design. Material candidates with the highest performance indices canbe used to develop a detail design. 2.4 Development of objective function for material selection performance measure for a compromise programming model Let yCand y /b e the performance index or actual value for minimization and maximization criteria of material / in a particular property j desired for engineering design property for non-beneficial and beneficial criteria respectively. And let yy'™"and y;"ux to be the ideal value based on the fact that single criterion is used in solving 432 minimization and maximization problem respectively.Also, let Fi be such a performance measure that may need to be optimized and F "orm is anaggregate function capable of combining different material properties into single function. Ife , = (y „ , y i2, y i3.... y 0 .... y in\ be the set of performance index of n distinct number of desired properties for material /,then it is desirable to express Ft as a combination of e , . To do this Fi an> has to be normalized by converting each element of €, has to be converted into a dimensionless quantity. But because we want to simultaneously satisfy two or more criteria with one material, it is difficult to adopt a single optimization; therefore, there is need to compromise in order to satisfy all the criteria/objectives at the same time by deviating from the ideal value. This implies that the deviation or distance from the ideal is the loss due to compromise. For minimization problem, the deviation or distance (dmin) from ideal value is expressed as: d-min = y[j ~ y jnin (for minimization problem) ( I D Hence, normalized distance, d ^ in from ideal is given as: min _ y ir yj ( 12) The degree of closeness (dC'[) to the ideal value may be expressed as 1-Normalized deviation or 100% - Normalized deviation. Mathematically, dCL~ = 1 - (13) This can be simplified further to 433 dCL~ = yf^-yis y.,jm ax_-V.,mj in (14) The expression in equation (14) shows how close the actual value is to the ideal. Similarly, for maximization problem, the deviation from ideal value is expressed as: dmax = y j 10* - ytj (15) Then, the normalized deviation from ideal is w T n n r mm. ax_..+dN = Vij yj ax ..m in (16) Hence, the degree of closeness, dC£+ to the ideal is given by 1 — dmaxi and is expressed as ..m ax ..+ d c r = i - y i ~y i (17) By simplifying equation (4.7), we have „min d C ^, ++ = ..mViai x y ‘.._m_irn- y i y J (18) where y" ““ = ma\imj um \yu}, is the maximum value of materialJ J property 7and y j m = min imum{yiJ }is the minimum value of material property j 434 Therefore, the equation in (14) and (18) may be expressed in terms of the following objective functions such that they are dimensionless in order to form a mathematical programming com p rom ise or trade­ off. For minimization problem, fij = 1= 1, 2 , . . m; j = 1, 2 , . . . , n (19) For maximization problem, y + _ y ,n(n fij = ymL Jymin > = U ........ m; j = 1, 2..........n (20) where f tj is the normalized objective function of the material 1 for property j ; Therefore, FiT = fil + fi2 + /i3+---+/i;+---+/in (21) Usually, in almost all multi-objective optimization problems including compromise programming requires information regarding criteria preference of each criterion to bring about desirable properties. In order to establish and satisfy a multiple measure of performance across all the criteria selected, thus providing a basis for identifying the best or preferred options. Therefore, in this case, the normal approach of compromise programming model is to introduce criteria preference index, w; according to how important each is regarded in relation to each other obtained from the stakeholders. Thus, the compromise programming model can be expressed by introducing Wj into equation (21), we have FiTw = w j n + w2/ i2 + w3/ i3+ . .. +Wjfij+... +wnfin 435 (22) Hence, combining all the properties, we have, r TW _ vm ... f ' i - L j = l w j J i j (23) The model determines the best compromise solution formulation by solving: For minimization problem, M i n F (24) For maximization problem, M a x F (25) 2.5Compromise Gain (CG) Inmulti-criteria optimization, the normalized objective function may differ for differentalgorithms because different algorithms may adopt different normalization process.For instance, two different algorithms may select the same material for a particular problem situation, but with different optimal values of objective functions. This makes it difficultto compare qualityof solutions from optimal value of objective function perspective. Thiscalls for the use of a different concept which may allow quality of different solutions tobe compared. One such rational is 436 the concept of compromise gain/loss. Notice that f i} is the value of the normalized algorithm solution as defined in expression (21) and (22), and /y"““ is the ideal value (for maximization problem) or f jjma (for minimization problem). The closer f {j gets to ideal value, f ^ o x fj""" the greater the gain the algorithm has achieved with respect to criteria j for material Hence, the goal of any solution procedure is to drive f it to the ideal for all criteria for a given material. Whenever f tj is equal to f j ,TU' or f ljmm it implies that the algorithm solution is 100 percent gain. Unfortunately. there is a limiting criteria value for every material. For material /, for instance, if its value for property j is f j 1, then f tj cannot be greater than f j . In acase where/y' isalsoless than the ideal, f™ ' then there is a compromise loss to this solution. In terms of distance, this may be expressed as follows: Compromise loss = f,™ ' - f tj While the corresponding compromise gain is / tf. To illustrate this concept. consider the diagram in Figures 1 and 2. 437 Minimum Algorithm (Ideal or value solution maximum value f n / maxii ) T Compromise gain Compromise loss (Ideal or Algorithm maximum Minimum. solution value value /■in / maxT ii ) - r i ‘ Compromise gain Compromise los Fig. 1 Compromise gain/Ioss for maximization problem (beneficial criteria) 438 (Ideal or minimum , min Algorithm Maximum value, jjj ) solution value f i(I Compromise |os-s-_--_-_--_--_-_--C--o--m--p--r-o-mTi-s-e- -g--ai—n (Ideal or minimum min A .,lgorithm / Maximumij ) solution value f ,in L T Compromise loss CompronJse gain Fig. 2. Compromise gain/loss for minimization problem (non- beneficial criteria) Observe that if f v‘ were equal to the ideal value, or f j mn then the compromise gainis maximum while compromise loss is zero. From this point of view, the quality of solution maybe measured as the amount of compromise gain/loss attained by the solution procedure (algorithm). In terms of degree of closeness to the ideal, compromise gain may be defined as follows: Definition 1: Degree of Compromise Gain (CG) Degree of Compromise gain of a known solution is the ratio (ptercentage) of the sum of all 439 the elements in the set. {/„ },to the sum of the ideal values. I / . i That is I / . CG (solution) = ------x 100 S /* maxJo i=i (26) where v™“ - v™" f = Z i_____ Zi__ • / = / 2 ;r ” j y i Substituting into the expression in (26), we have tr. CG(solution) = —— xlOO (27) n Similarly, for minimization problems, the same expression (27) for computing degree of compromise gain holds. 440 3. Results and Discussion 3.1 Possible Materials and their properties for a DC machine Armature Design Each of the DC machine components have a specific product requirement where the upper/lower limits of each property for the design specifications of three armature DC machine components are identified and materials are sourcedfrom the web (Matweb) as shown in Table 1, 2, and 3 for the DC armature core, armature shaft and armature windings respectively. Table 1: List of Candidate Materials and their Properties for Material Selection of Armature Core of a DC machine. Alt. D UT YS DU H ER ML C Mat. g/cm3 MPa MPa (%) Vickers ( l l .m i 10~8) W/kg (S/kg) ACI 7.65 370 340 14 195 4.8 0.83 20.15 AC2 7.65 490 359 23 130 5.0 1.20 35.10 AC3 7.68 565 450 25 215 5.2 3.05 40.00 AC4 7.75 400 265 34 137 3.2 4.50 25.25 AC5 7.65 352 331 9 153 5.1 0.56 15.50 AC6 7.70 483 345 32 114 4.3 3.42 25.50 AC7 7.60 369 302 35 188 4.8 1.45 23.50 AC8 7.65 359 345 11 159 5.0 0.87 27.50 AC9 7.65 450 350 20 144 5.4 0.50 20.55 Alternative Materials H 085-27 Grain oriented electrical Steel - AC1 AK Steel DI-MAX M-15 Non-oriented electrical Steel - AC2 ASTM A677 (36F155) Non-oriented electrical Steel - AC3 JN-CORE(50JN600) Non-oriented Electrical Steel - AC4 AK Steel CARLITE M-4 Grain oriented electrical Steel - AC5 AK Steel DI-MAX M-43 Non-oriented electrical Steel - AC6 JG-CORE Grain-oriented electrical Steel - AC7 H-lCarlite DR Grain-oriented electrical Steel - AC8 441 AK Steel Dl-Max HF-10 Non-oriented Electrical Steel - AC9 Table 2: List of Candidate Materials and their Properties for Material Selection of Armature Shaft of a DC machine. U E D Alt. T YS M U H D TC TD TE C Mat M MPa GP Vicke(% g/cm W/m. (xlO (20°Cxl (S/k Pa a rs .1 ) K !> 0 ‘ ) g) AF 33 1 0 285 20 15. 6 20 98 7.87 64.9 1.71 12.6 90 AF 47 400 212 5 0 12 143 7.85 49.8 1.32 11.5 17. 08 AF 36 3 5 301 20 0 20 107 7.87 51.9 1.35 12.6 17. 59 AF 52 4 5 440 20 0 12 150 7.85 48.7 1.27 11.7 15. 94 AF 69 540 205 6 2 10 195 7.85 49.8 1.32 11.5 14. 57 AF 71 605 206 0 0 10 200 7.87 51.2 1.33 11.5 24. 05 AF 42 7 0 350 18 15 126 7.87 51.9 1.35 11.7 20.6 60 AF 64 8 0 420 20 5 26 176 7.85 44.6 1.38 12.0 25. 50 AF 44 370 209 0 5 15 131 7.75 51.9 1.37 12.0 24. 60 AF 42 18 10 0 350 6 15 126 7.85 47.7 1.26 11.7 25. 06 Alternative Materials 1 Carbon Steel SAE 1006-AFI 2 Carbon Steel S AE 1117 - AF2 3 Carbon Steel SAE 1010 - AF3 4 Carbon Steel SAE 1030-AF4 5 Carbon Steel SAE 1090 - AF5 6 Carbon Steel SAE 1547-AF6 7 AIS1 1020 low Carbon Steel - A R 442 8 Alloy Sied SAH 4027 - AF8 9 AISI 1080 Steel-AF9 10 AISI 1040 Carbon Steel - AFI0 Table 3: List of Candidate Materials and their Properties for Material Selection of Armature Windings of a DC machine. D UT Y D SM U M TC TD MP ER M A CAlt. Mat. (g/cm MP GP GP W/m. (xlO (°C) (fi.m x (S/k 5> a (% <%a ) a K -s) io - 9) ) g) AW1 8.94 380 ii 1. 44 388 11.3 1085 5 0 3 1.72 20 27.7 0 AW2 8.94 260 II5 25 44 388 11.2 108 7 3 1.72 20 26.7 0 AW3 8.94 310 II 20 44 386 11.2 108 1.74 20 26.85 1 3 0 AW4 8.89 240 II 35 44 388 11.3 1085 0 0 1.72 20 28.7 5 AW5 8.89 240 II5 45 44 234 11.3 105 0 0 2.44 20 25.5 0 AW6 8.89 455 II5 55 44 391 11.2 108 0 3 1.71 20 29.5 5 AW7 8.89 525 12 1. 10.7 25.49 5 40 367 2 980 1.86 20 5 AW8 2.80 290 73.1 20 28 134 5.44 507 5.15 20 25.7 0 AW9 2.81 400 71.7 19 27 154 6.23 521 4.32 30 25.2 5 AW1 2.70 140 68. 7. 25. 200 8.23 632 23.40 2 3 9 3.30 20 5 Alternative Materials Code Oxygen-free Silver bearing Copper (Temper wire) UNS CI0500, H04 AW1 443 Oxygen-free Silver bearing Copper (Temper wire) UNS CI0700, HOI AW2 Oxygen-free extra-low phosphorus Copper, UNS CI0700 H80 AW3 Silver-bearing tough pitch Copper, UNS CI 1300 AW4 Silver-bearing tough pitch Copper, UNS CI 1600, H08 AW5 Oxygen-free electronic Copper UNS C 10100 AW6 Zirconium Copper (Amzirc Brand Copper) wire UNS C 15000 AW7 Aluminium 2014-T4, 2014-T451 AW8 Aluminium 2025-T6 AW9 Aluminium 5005-H12 AW10 3.2 Criteria Preferences for the Design Product Specifications Table 4, 5, and 6 shows thepossiblecandidate materials data with the achievement level for the Armature core, Armature shaft, and Armature windings design.The criteria preferences resulting fromthe team-compromise instrument indicates that electrical resistivity and magnetic core loss are the most ranked properties/criteria with a value of 18.0 and 16.4 percent respectively for the DC Armature core as shown in Table 4. A low value of electrical resistivity is required and it indicates a material that readily allows movement of electric Charge and is measures the material ability to conduct an electric current, while on the other hand, for magnetic core, a soft magnetic material is needed to provide an easy path for flux in order to facilitate flux linkage between two or more magnetic elements. Also, in the design of a D.C armature shaft, the criteria preferencesare shown in Table 5, and the result shows that yield strength (14.4%), ultimate strength (14.4%) and hardness (11.6%) has the highest 444 ranked criteria preferences. It is seen from the results that these three properties/criteria are very important in the design of armature shaft. The shaft must able to withstand an appreciable load and should have the ability to resist denting and wear. And in terms of the armature windings, it is obvious that electrical resistivity and thermal conductivity were mostly ranked with a weight value of 14.4 and 13.3 percent respectively. Thermal conductivity is an important factor when designing and exploring any electromagnetic device due to heat generation and dissipation in the windings. 445 Tablc 4 Material Selection Data for Armature Core with Criteria Preferences Criteria Criteria Aspiration Veto Criteria type Level threshold Weight (%) Yield strength 10.4 (YS) - (MPa) Beneficial 450 265 Hardness (H) - (Vickers); Beneficial 215 114 12.2 Ductility (DU) - Beneficial 35 9.0 9.6 (%) Ultimate tensile strength (UT) - Beneficial 565 352 11.2 (MPa) Density (D)- Non- (g/cm3); beneficial 7.60 7.75 10.0 Magnetic core loss (ML) (W/kg Non- @ magnetic field beneficial 0.5 4.5 16.4 1.50 Electrical resistivity (ER)- Non- (ß.m); beneficial 3.2 5.4 18.0 Cost of base material (C) - Non- (S/kg) beneficial 15.5 40.0 12.2 446 Table 5. Material Selection Data for Armature Shaft with Criteria Preferences Criteria Criteria Aspiration Veto Criteria type Level threshold Weight (%) Ultimate tensile strength (UT) - Beneficial 710 330 14.4 (MPa) Yield strength (YS) - (MPa) Beneficial 605 285 14.4 Elastic modulus (GPa) Beneficial 210 186 11.0 Ductility (DU) - (%) Beneficial 26 10 8.4 Hardness (H) - (Vickers) Beneficial 200 98 11.6 Density (kg/m3) Non-beneficial 7.75 7.87 6.2 Thermal conductivity Beneficial 64.9 44.6 9.2 (W/m-k) Thermal diffusivity (m2/s x Non- IO'5) beneficial 1.26 1.71 6.7 Thermal expansion Non-beneficial 11.5 12.6 8.8 r c x i o - 6) Cost of base material (C) - Non- 14.57 25.50 9.3 (S/kg) beneficial 447 Table 6: Material Selection Data for Armature Windings with Criteria Preferences Criteria Criteria type Aspir Veto Criteri ation thres a Level hold Weight (%) Density (kg/m3) Non-Beneficial 2.7 8.94 8.0 Ultimate tensile strength (UT) (MPa) Beneficial 525 140 8.1 Young modulus (GPa) Beneficial 129 68.2 7.4 Ductility (DU) - (%) Beneficial 55 1.5 9.1 Shear modulus (GPa) Beneficial 44 25.9 5.7 Thermal conductivity (W/m-k) Beneficial 391 134 13.3 Thermal diffusivity (m2/s x 105) Beneficial 11.3 5.44 9.7 Melting point (°C) Non-Beneficial 507 1083 8.2 Electrical Non- 14.4 resistivity(/2.m x 10-8) beneficial 1.71 5.15 Machinability (%) Beneficial 30 20 6.9 Cost of base material (C) - Non- beneficial 23.45 29.55 9.2($/kg) 3.3Selection of Optimum Material for the DC Components The developed compromise programming model to select material for the DC armature core, armature shaft, and armature windings. The result shows that the model selectedJG-CORE Grain-oriented electrical Steel; Carbon Steel SAE 1090; and Oxygen-free electronic Copper UNS C lOlOOas the bestmaterial with highest performance index of 65.61, 78.35, and 72.33 448 percentfor the D.C. armature core, shaft and winding respectively as shown in Table 7, 8 and 9. Table 7.Performance index value (%) for a D.C. Armature Core for the Compromise Programming Algorithm Mat Material Identity Performa nee Co Index Rank de (%) AC H 085-27 Grain oriented electrical 1 Steel 61.31 3rd AC AK Steel DI-MAX M-15 Non- 2 oriented electrical Steel 52.12 7'h AC ASTM A677 (36F155) Non-oriented 2nd 3 electrical Steel 64.74 AC JN-CORE (50JN600) Non-oriented 4 Electrical Steel 57.01 6,h AC AK Steel CARLITE M-4 Grain 41h 5 oriented electrical Steel 60.03 AC AK Steel DI-MAX M-43 Non- 91h 6 oriented electrical Steel 49.77 AC JG-CORE Grain-oriented electrical p. 7 Steel 65.61 AC H-lCarlite DR Grain-oriented 8 electrical Steel 51.14 8S1 AC AK Steel DI-Max HF-10 Non- 9 oriented Electrical Steel 59.91 5lh 449 Table 8. Performance index value (%) for a D.C. Armature Shaftfor the Compromise Programming Algorithm Mat. Material Identity Performanc Code e Index (%) Rank AF1 Carbon Steel SAE 1006 52.24 6th AF2 Carbon Steel SAE 1117 61.28 41h AF3 Carbon Steel SAE 1010 42.05 8,h AF4 Carbon Steel SAE 1030 58.41 5,h AF5 Carbon Steel SAE 1090 78.65 is« AF6 Carbon Steel SAE 1547 76.76 2nd AF7 AISI 1020 low Carbon 91hSteel 40.49 AF8 Alloy Steel SAE 4027 63.77 3* AF9 AISI 1080 Steel 50.10 71h AF10 AISI 1040 Carbon Steel 40.24 10,h 450 Table 9. Performance index value (%) for a D.C. Armature Windingsfor the Compromise Programming Algorithm Mat. Material Identity Performance Code Index (%) Rank AW1 Oxygen-free Silver bearing 64.33 6th Copper (Temper wire) UNS C I0500. H04 AW2 Oxygen-free Silver bearing 64.76 3rd Copper (Temper wire) UNS C I0700, H01 AW3 Oxygen-free extra-low 64.47 5lh phosphorus Copper, UNS C I0700 H80 AW4 Silver-bearing tough pitch 64.55 4* Copper, UNS CI 1300 AW5 Silver-bearing tough pitch 56.29 91h Copper, UNS CI 1600, H08 AW6 Oxygen-free electronic Copper 72.33 lsl UNS C 10100 AW7 Zirconium Copper (Amzirc 68.98 2nd Brand Copper) wire UNS C 15000 AW8 Aluminium 2014-T4, 2014-T451 56.35 8ih AW9 Aluminium 2025-T6 63.16 7lh AW10 Aluminium 5005-H12 54.81 10,h 3.4 Solution Quality Assessment The quality of Solutions of the model’s procedure was tested, where the compromise gain was computed for the material selection Solutions as presented in Table 10. Table 11, and Table 12. This indicates that the compromise gain for the best material is the same as that of the material selected by the proposed model for armature core, armature shaft, and armature windings 451 respectively. In comparing the model’s solution procedure to know which model is better in terms of performance, analysis was carried out based on three different weighting methods. First, with equal attribute preference, secondly, using the instrument attribute preference by adopting the modified nominal group technique, and lastly, with the existing attribute preference method. In each of the category, the DC machine components were used to test the performance of the models’ procedure comprising: Compromise programming model, and Existing Algorithm (TOPSIS).However, with the use of the team-based compromised instrument, the compromise programming algorithm selected the same material types as the use of equal criteria weights. The selected material types areJG-Core Grain- oriented electrical Steel, Carbon Steel SAE 1090, and Oxygen-free electronic copper UNS C10100 with compromise gain values of 59.01, 59.34, and 59.81 percent for armature-core, armature- shaft, and armature-winding respectively. While with the existing attribute generated preferences, the proposed model selected different material type (ASTM A677 Non-oriented electrical Steel) with a lower compromise gain of 56.69 percentcompared to the equal weights, andinstrument attribute preferences for the DC armature core. Table 10: Compromise gain (%) associated with each material for the DC Armature Core Code Material Identity Compromise Gain(%) AC1 H 085-27 Grain oriented electrical steel 51.89 AC2 AK Steel DI-MAX M-15 Non- oriented electrical Steel 46.58 AC3 ASTM A677 (36F155) Non- oriented electrical Steel 56.69 452 AC4 JN-CORE (50JN600) Non- oriented Electrical Steel 37.71 AC5 AK Steel CARLITE M-4 Grain oriented electrical Steel 44.13 AC6 AK Steel DI-MAX M-43 Non- oriented electrical Steel 45.34 AC7 JG-CORE Grain-oriented electrical Steel 59.01 AC8 H-lCarlite DR Grain-oriented electrical Steel 40.67 AC9 AK Steel DI-Max HF-10 Non- oriented Electrical Steel 51.25 Table 11: Compromise gain (%) associated with each material for the DC Armature Shaft Code Material Identity Compromise Gain (%) AS1 Carbon Steel SAE 1006 43.37 AS2 Carbon Steel SAE 1117 46.34 AS3 Carbon Steel SAE 1010 27.22 AS4 Carbon Steel SAE 1030 42.99 AS5 Carbon Steel SAE 1090 59.34 AS6 Carbon Steel SAE 1547 51.97 AS7 AISI 1020 low Carbon Steel 28.53 AS8 Alloy Steel SAE 4027 47.73 AS9 AISI 1080 Steel 42.15 AS 10 AISI 1040 Carbon Steel 22.05 Table 12: Compromise gain (%) associated with each material for the DC ArmatureWindings 453 Code Material Identity Compromise Gain (%) AW1 Oxygen-free Silver bearing Copper (Temper wire) UNS CI0500, H04 51.65 AW2 Oxygen-free Silver bearing Copper (Temper wire) UNS C10700, H01 54.26 AW3 Oxygen-free extra-low phosphorus Copper, UNS C I0700 H80 45.08 AW4 Silver-bearing tough pitch Copper, UNS CI 1300 52.59 AW5 Silver-bearing tough pitch Copper, UNS CI 1600, H08 52.26 AW6 Oxygen-free electronic Copper UNS C10100 59.81 AW7 Zirconium Copper (Amzirc Brand Copper) wire UNS C I5000 58.20 AW8 Aluminium 2014-T4, 2014-T45I 32.25 AW9 Aluminium 2025-T6 47.62 AW10 Aluminium 5005-H12 37.84 On the other hand, the TOPSIS (Existing) algorithm selected different material types: JG-core Grain-oriented electrical Steel, Alloy Steel SAE 4027, and Oxygen-free electronic copper UNS C10100 with corresponding compromise gain of 59.01, 47.73, and 59.81 percent respectively when equal criteria weights was applied. Moreover, with the use of team compromise instrument and existing attribute generated preferences, the existing algorithm selected material types: AK Steel DI-Max HF-10 Non- oriented Electrical Steel, Carbon Steel SAE 1090, and Oxygen- free electronic copper UNS C10100 with corresponding compromise gain of 51.25, 59.34, and 59.81 percent respectively. The results also show that with the use of the compromise programing performs better than the TOPSIS algorithm when the 454 equal criteria weights, TCI, and TOPSIS generated preferences were applied for the DC armature core, DC armature shaft, and De armature windings as indicated with the compromise gain of 59.01, 59.34, and 59.81 percent compared to 59.01, 47.73, and 59.81 percent respectively. Also, from the result it was observed that for the design of DC armature core adopting the team- compromise instrument preferences, a lower compromise gain of 51.25 percent is obtained when the existing algorithm (TOPSIS) is applied compared to the compromise gain of 59.01 percent for the compromise programming. This suggest that the compromise programming algorithm has a higher gain than the existing algorithm (TOPSIS), which makes it better. The results obtained when Existing criteria preferences was applied to the three components shows that a lower compromise gain of 59.01, 47.43, and 37.84 percent as compared to the compromj^e gain of 56.69, 59.34, and 59.81 percent for the proposed model (compromise programming algorithm). This also confirms that the proposed model is better in terms of performance. Therefore, the quality value of 59.34% and 59.81% of the ideal value is better when compared to 47.73% and 37.84% of the ideal value for the design criteria for DC armature shaft and DC armature windings respectively because of the higher gain. 455 Table 13. Summary of Materials selected and their corresponding Compromise Gainon the Product/Components M odels M ulti-criieria C om prom ise Existing A lgorithm (EA) W eigliling C om poncnü P rogram m ing (M C P ) M odel (T O P S IS ) M cthod C om prom ise C om prom ise M ateria l S clectcd G a in (% ) M aterial S cicctcd G ain (% ) D C JG -C O R E ü ra in - JG -C O R E G rain- Arm ature orien ted e lectrical 59.01 59.01 o rien led e lectrical sleel C ore Steel Equu! DC C arb o n S teel SA E 59.34 A llo y S leel S A E 4027 47 .73 Attribute Arm ature 1090 Preference Shaft DC O xygen-free 59.81 O xygcn-frcc e lectronic 59.81 A nnalu re e lec tron ic C oppcr C o p p cr U N S CIOIOO W inding» U N S C 10100 DC JG -C O R E G rain- A K S t e e l Ü l-M ax H F -10 A rm ature orien ted electrical 59.01 N o n-orien ted E lectrical 51.25 C ore slecl S te e l Instrum ent DC C atbon Steel SA E 59.34 C arb o n S teel S A E 1090 59.34 A ttribute A rm ature 1090 preference Shaft D C O xygcn-frcc 59.81 O xygcn-frcc electronic 59.81 Arm ature electronic C oppcr C o p p cr U N S C I 0 I 0 0 W indings U N S CIOIOO ix : A S T M A677 (36F 155) N oo- JG -C O R P O rzin- A rm ature 56.69 59.01orien ted e lectrical o rien ted e lec trical »teel Core Steel Ex isting A ttribute DC gcncratcd A rm ature C arbon S leel SA E preference» Shaft 1090 59.34 A lloy S teel S A E 4 027 47.73 D C O xygen-free A rm ature clecironic C oppcr W indings U N S CIOIOO 59.81 A lum inum 5005-1112 37.84 A compromise programming optimization model is primarily developed to solve the material selection problem of a EX? machine armature design using a team-based approach. The 456 material selection problem is faced with two major issues: Firstly, the design conflicts that often arise in engineering design environment because of team members may not be willing to compromise their point of view; secondly, the difficulty of comparing the quality of solution procedures from different multi-criteria approaches. In view of the above challenges, a procedure was formulated by adopting nominal group technique through which input data from experienced individual product design team members were translated into material selection Parameter relevant to the proposed model in resolving the conflicts; and a model for comparing the quality of other multi- criteria optimization material selection solution procedures was developed and investigated. The results indicate that the compromise programming optimization model is capable of identifying the best material among the various alternatives considering the design specification related material criteria for the DC armature core, armature shaft, and armature windings. The model also gives an opportunity for the design team or stakeholder’s participation in the decision-making process. Also, a model for comparing the quality of model’s solution procedures was established. This was achieved by comparing the compromise gains of known solution. This indicates that some significant difference in the power of achieving compromise gains in the use of the models’ algorithms, which shows that the existing algorithm (TOPSIS) that was investigated had a lower performance compared to the compromise programming algorithm. References Abdullah M. B., and Rafikul I., (2011). Nominal Group Technique and its Applications in Managing Quality in Higher Education. 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Orji3, Victor Mbachu2, Ayomoh Michael4 1Department o f Mechanical Engineering, Federal University of Petroleum Resources Effurun, Delta State, Nigeria. 2Department o f Industrial and Production Engineering, Nnamdi Azikiwe University, Awka, Nigeria Research Center for Smarter Supply Chain, Dongwu Business School, Soochow University, No. 50 Donghuan Road, Suzhou, Jiangsu 215006, People's Republic o f China 4Department o f Industrial and Systems Engineering, University of Pretoria, South Africa. Abstract One of the biggest challenges faced by manufacturing Companies today is the significant increase in ränge of supply chain (SC) problems that must be solved. Unfortunately, the traditional planning approach cannot match the diversity of these complex problems. There is a huge place for leveraging new technologies in supply chain and logistics. Industry 4.0 aims to link smart operations and supply chain design and processes to salvage some of the operational shortfalls in the supply chain. Industry 4.0 is expected to be driven by emerging technology breakthroughs to help facilitate network of interaction of products and Services with interconnection of robots and artificial intelligence. This technology is gaining so much attention in virtually all sectors particularly in manufacturing operations which require product flow at inbound and out- bound operations. This research is an exposition of Industry 4.0 technologies and how it can aid advance Supply Chain operations in manufacturing settings. The conclusion drawn from this research further 463 reiterates on the gains of attaining high level of performance improvement with the implementation of innovative technologies in all aspect of supply chain network(s). Thus, effective Integration of the Industry 4.0 technologies into supply chain operations will greatly improve productivity, product delivery, cost optimization, asset management, reliability, efficient processes, better sales and Overall performance of manufacturing Systems. Keywords: Industry 4.0; supply chain; emerging technologies; in-bound and out-bound manufacturing operations. 1 Introduction Recently, manufacturing organizations are faced with issues of business sustainability that may have significant impact on business operations (Luthra & Mangla, 2018). Another issue confronting manufacturing Organization has to do with the complex processes involved in launching into digitization or managing new technologies. There is fundamental transformation in technology from classical to advanced high-tech innovations as a result of intricate rapidly evolving market conditions and consumer demand. There is equally need for organizational versatility and responsiveness (Oberg & Graham, 2016). The value of technical innovations has been recognized by organizations and technology is seen as a powerful Strategie tool to ensure total sustainable efficiency and radical progressive change (Chavez et al., 2017; Shrivastava et al., 2016). In Order to streamline business processes, several industries are already implementing e-business technology. High level of convergence and new innovations are required to boost operational efficiency in Systems, (Srinivasan & Swink, 2015). The fourth industrial revolution require aggressive innovations which has to do with investing extensively in automation and robotics, and to incorporate more sophisticated technical philosophies and concepts to achieve total transformation (Uchechi et al., 2020). 464 This transformation will result into major production advantages, consequential in the development of smart factories by consenting to comprehensive Integration of processes (Rashid & Tjahjono, 2016). Integrating effectively will in no doubt lead to profitability, cost optimization, higher reliability, improved management control and efficiency. Industry 4.0 requires great transformation in every aspect of business Operation. Substantial investment and considerable time for effective planning is required to achieve this transformation. Since many Companies are struggling to be at the top of the game in the new revolution, competitive strategies which require aggressive approach to responsiveness and diversity in every aspect of supply chain Operation is significant (Um, 2017). As the world’s population continues to increase, the need for sustainability in terms of resource utilization becomes necessary (Islam & Managi, 2019; Gorman & Dzombak, 2018). Rahman et al., (2020) anticipated that the fourth industrial revolution will focus on the economic, social and environmental dimensions of sustainability. They equally believe that continuous study focused on technology developments should be strongly supported especially from the economic perspective. Karadayi-Usta (2019) stated that the adaptation of the fourth industrial revolution processes entail high level of adjustment of workforce and infrastructure. Companies operating traditionally must Start looking deeper for solution to transformation in all aspect of their production process (Ku et al., 2020). 1.1. The Fourth Industrial Revolution (Industry 4.0) Industry 4.0 is making rapid progress as a transformational process and this is happening at an exponential speed. The first industrial revolution which surfaced in the eighteenth Century (1800) brought about significant improvements to the industries as a result of breakthrough in the steam engine discovery which was used as a source of electricity. This led to migration of people from rural to urban area. The second industrial revolution was witnessed in late 1800, with the implementation of 465 scientific management theories to accelerate production in factories; this led to perfect arrangement of assembly line for mass production. The third industrial revolution witnessed around 1950 to I960 led to the incorporation of Computers and intemels in Offices and factories which facilitated timely completion of tasks and fast delivery of information and products. (Machesa et al. 2020). The fourth industrial revolution as a current viewpoint, is gaining attention globally (Uche et al., 2020). This current technology and its enabling proficiencies, however, are believed to have the ability to manipulate avaiiable machines thereby making factories and organizations smart, this will gveatiy facilitale major changes in our society especially the eas. of na .mg products in supply chain and logistics operations (Baur & Wee, 2015) Technology study dwells on exposition of current technologies l improve supply chain performance in manufacturing operations. Other section of this article cover: Supply chain at inbound and outbound operations; enabling technologies to enhance supply chain in the new revolution; the importance of industry 4.0 technologies in supply chain manufacturing and operations; challenges of industry 4.0 technologies; benefits of adopting the technologies; other industry 4.0 technologies which can bring about changes in supply chain network for advancement in manufacturing operations; conclusion and Suggestion for further studies. 1.2. Supply Chain Supply chain is a global network for delivery of products and Services from source of raw materials to end customers. As the network of product interaction continues to get complex, new technologies are needed to match the complexity of the System. According to Govindan et al., (2017), good number of Companies are currently participating and investing in high-tech innovations to help facilitate and develop collaboration mechanisms and active communication channels which will greatly improve performance of supply chain through improved and sharing of vital information. Supply chain performance improvement is vital in manufacturing organizations (Datta, 2017). For effective information exchange in any Organization, supply chain integration is 466 considered important and critical especially in end to end business process (Chavez et ai., 2017). For great performance and improvement in supply chain network interaction, flexibility enabled by teamwork or strong collaboration is required (Datta, 2017). Altay et al.. (2018) also confirmed that dexterity and flexibility in supply chain have great impact on supply chain performance. Swift et al., (2019) further pointed out that transparency and higher perceptibility in supply chain network of interface will meaningfully improve effective performance. In supply chain management (SCM), traditional pattern of supply chain operations will not yield great result, therefore, implementing the fourth industrial revolution-enabling-technologies is a positive strategy lo revolutionise SCM (Kache & Seuring, 2017). According to Luo et al.. (2018), many organisations are currently adopting the new technologies through Electronic business Solutions for total enhancement of their integration, capabilities and operational excelience. 1.3. Digitalized Supply Chain and Technologies of Industry 4.0 The fourth industrial revolution as earlier explained is a transformational process which involves the use of Contemporary smart technologies to facilitate production, Service delivery and other vvork operations in manufacturing or Service Systems. The use of technologies in manufacturing and business environment has facilitated Industry 4.0 (Wiengarten & Longoni, 2015). This digitalized global concept encompasses high level of Connectivity among people, entrusted customers and agile manufacturing Systems. The new revolution is such that supply chain operations are done timely as people are vastly connected with on-time information 24 hours a day and 7 days a week using application Software, supply and delivery platforms and other vital means to access and exchange information timely. The current revolution, in no doubt will help Companies adjust to swiftly ever- changing patterns in supply chain operations, enthralled on the behaviour of consumers and responding to stochastic and deterministic business operations at all levels. 467 Ground-breaking ideas, originality and agility are required to match the new revolution. There is no doubt that this new revolution has aided smart process Organization which has equally set new Standards for effective management of industries (Moeuf et al., 2017). Industry 4.0 is an occupational environment characterised by high-tech innovations which require the use of smart machines for Communications. It must be noted that the more complex the supply chain, the more necessary it becomes to Setup a structure for ground-breaking or innovative ideas for total business and System transformation. Three major causes of complexity in supply chain System have been discussed elsewhere (Handley, 2020). The sophistication of coordinating and synchronizing all interconnecting supply chain System is a serious task which require great attention and there is no doubt that the easy way or Steps to adopt is the implementation of industry 4.0 technologies like artificial intelligence, Big Data Analytics, Internet of Things (IoT) and others (Oberg & Graham, 2016). Autonomous Systems are not left out as one of the incredibly significant and advantageous industry 4.0 enabling technologies (Okwu, 2020). If these technologies are properly integrated, there is guarantee for development and total transformation in all aspect of manufacturing Systems (Uche et al., 2020). Fisk (2020) listed three innovative Companies in the year 2020 based on digitalized System of operations to include Telsa, Microsoft and Snap. This is a testament to the fact that the Industry 4.0 technologies will in no doubt lead to high innovation and performance in manufacturing Systems. Some of the fourth industrial revolution enablers for supply chain sustainability are presented in Table 1. 468 Table 1: Fourth Industrial Revolution Technologies for Supply Chain Sustainability S/N Fourth Description Accessible Literature Industrial Revolution Tech. Enabler(s) 1 Meta- Improving Ghasemian heuristic supply chain Sahebietal.,2017; Okwu analysis of performance by et al. 2018; Machesa et al. barriers in digitizing supply 2020; Olayode et al. 2020. Supply Chain chain activities in Activities supply chain sustainability 2 Digitization Technologies of Agrifoglio et al. 2017; Lu, of Supply Industry 4.0 and 2017; Müller & Voigt, Chain applications in 2018; Agrawal, 2019. Activities Supply chain for sustainability. 3 Promoting Supply chain Latif et al.,2017; Knowledge performance and Stoychevaetal.,2018; Management sustainability is Aggarwal et al., 2019. in Supply improved by Chain (SC) practicing knowledge management in SC. 4 Commitment High level Chen et al., 2018b; of Supplier for algorithms for Seuring et al., 2019. Sustainable Sustainable procurement procurement 469 5 Supply Chain Optimization of Moeuf et al., 2017; for SMEs Supply Chain for Schwabetal., 2019. SMEs 6 Business Importance of Banker, 2015; Baur & Process procurement 4.0 Wee, 2015; Garcia-Muina Performance in business et al., 2018; Bag et al., Operation 2020. 7 Smart Factory Technologies of Mishra et al. 2016a. Operations Industry 4.0 can and IoT facilitate process Chen et al. 2018a. Improvement in factories 8 Big data Improvement in Acter et al., 2016; Analytics operations Babiceanu & Seker, 2016; management Addo-Tenkorang & Helo. 2016; Mishra et al. 2016b; Gunasekaran et al.. 2017; Nguyen et al. 2017; Papadopoulos et al., 2017; Wamba, 2017: Choi et al., 2018: Gunasekaran et al., 2018; Olayode et al., 2020. 9 3D Printing Holmstrom & Gutowski. Technology 2017; Feldmann & Pumpee, 2017. 10 Robotics and Path Planning Automation, and Navigation Jazdi, 2014; Ukaegbu, AI and ML. of Autonomous 2020. Vehicles 470 2 Technologies of the Fourth Industrial Revolution This section is focused on the major Industry 4.0 technologies that will help facilitate supply chain in manufacturing operations. Some of the industry 4.0 technologies include: Big data analytics, Cloud computing, 3D printing technology. Machine leaming and Artificial Intelligence, Internet of Things (IoT), Cyber-Physical Systems. Automation and Robotics and others. These are further explained in detail. 2.1 Big Data Analytics Big data analytics is a current global digitalization which involves the extraction of knowledge in form of dataset from Systems thereby facilitating data-driven decision-making. Big data analysis has been recognized in literature as an area of digital technology which is quite elaborate and extremely useful in decision making process. Robust and unprecedented information can be gathered and converted to digital format. This has become extremely useful since past information can be obtained and stored for future use. There is no doubt that big data analytics can provide tremendous opportunity for maximizing the use of capacity, enhancing customer Service, developing new logistics business models and reducing risk in a System. 2.2. Cloud Computing Cloud computing is a global computing technology capable of computing and storing massive amount of data in such a way that organizations have higher chances of expanding and performing effectively at a larger space (Mitra et al.. 2017). Supply chain design and processes can be obtained, computed and stored for future use based on cloud computing technology. Branger & Pang (2015) are of the opinion that cloud manufacturing is anticipated to appear as the next and highly effective model and driver of manufacturing in the fourth industrial revolution. According to Xu et al., (2018), cloud computing can facilitate data sharing and exchange efficiently, thereby promoting complex decision making in manufacturing Systems. 471 2.3. 3D Printing Technology High-tech automatic manufacturing is possible using 3D printing technology. 3D printing or additive manufacturing offers new potential in manufacturing Systems as products can be made available to customers at the right time. 3D printers could be shipped to manufacturing sites where parts can be quickly fabricated on site. Most manufacturing Companies are currently introducing the innovative technology of 3D printing to their production process, taking the next Step towards fully advanced and automatic manufacturing. This process is based on an automatic production process where products are made faster and easier than ever before and which allow consumers get easy access to products made by manufacturers. Inventory buildup is almost impossible since the exact number of products required periodically can be made available. Also, customized models can be made available to customers. The use of 3D printing at different level of supply chain will enhance Service delivery, cut cost and inventory buildup, increase flexibility in manufacturing and product individualization will increase (Feldmann & Pumpe, 2017; Holmstrom & Gutowski, 2017). 2.4. Machine Learning and Artificial Intelligence Machine learning is the study of Computer algorithms and Artificial intelligence is the Simulation of intelligent behaviour of machines (Machesa et al. 2019). Very few Companies are extremely dominant, considering the ground-breaking and ongoing trend towards computerization or automation and sustained advances in the world of computing. Artificial Intelligence (AI) is speedily changing the pattem of Operation of logistics providers. 2.5. Internet of Things (IoT) The Internet of Things (IoT) implies the interconnection of things (physical objects) using the internet for easy communication and sharing 472 of information with other Systems and devices. In a simpler term IoT is the connection between objects and machines using the internet. This is another new wave of technology which can connect practically any useful information to the internet and speed up logistics driven by data. This systematically means that information can easily be sent, received, processed and stored in the form of useful data which can dynamically contribute in event-driven, self-steering, logistics processes. IoT has unlimited capabilities where data can be used from the linked objects to produce actionable insights that drive improvement and innovative ideas to achieve payoffs for logistics providers. Jazdi (2014) concerted his study on the influence of connecting several devices in a System under IoT and the impact of cyber physical Systems in the life of individuals daily. He further argued that the fourth industrial revolution will have huge impact on the advances of new technologies and consumers lifestyle. 2.6. Cyber-Physical Systems Cyber-physical Systems are machines in which mechanisms are monitored, controlled or computed by algorithms. It is the connection of machines to interact. visualize and make decision autonomously. Data collected by smart sensors can help Professionals understand critical situations faster and more accurately while implementing this technology in in-process supply chain System. This will enable Customers to be informed about the pattem of product flow or Services rendered. Autonomous vehicles will be made available in few years as many Companies are currently testing self-driving vehicles on road in different countries of the world. It is certain that most manufacturing Companies are getting ready to launch autonomous ground robots in the form of lorries, buses and vans where vehicle to vehicle can communicate with each other, accidents will be reduced, traffic congestion in unsignalized road intersections will be a thing of the past, new ways of monitoring navigational pattem of vehicles will be established. 473 2.7 Automatic Guided Vehicles (AGV) and L'nmanned Aerial Vchicles (UAV) One of the useful Industry 4.0 technologies that will enhance supply chain is the autonomous robots. It could be ground robot - automatic guided vehicle or flying robot - unmanned aerial vehicles. AGVs for product distribution in manufacturing settings will be of great economic benefit since they are programmed to function autonomously. AGVs can be implemented in factory settings as material handling devices or delivery agents for moving items from one location to another. Unmanned aerial vehicles (UAV) will be particularly useful either for moving raw materials to factories or for delivering ready items to customers at various locations. 3 Importance of 4IR Technologies in Supply Chain and Manufacturing Operations 3.1 Big data analysis - has been recognized in literature as an area of digital technology which is quite elaborate and useful in supply chain Operation. A good example is demonstrated in a research conducted by Simchi-Levi & Wu (2018) which focused on the analysis and application of big data in retail channel. Price optimization model was used for the analysis as retailers strive to grow their revenue. margins and market share. This technology has equally been demonstrated by Nguyen et al.. (2017) as a prevalent technique in transportation and logistics. Other areas where big data analytics has been applied in supply chain management include(s) transportation and logistics Operation, inventory System in warehousing, routing optimization, safety management (Gunasekaran et al.. 2017; Nguyen et al.. 2017; Zhong et al., 2017).There is no doubt that big data will provide tremendous opportunity for maximizing the use of capacity. enhancing customer Service, developing new logistics business models and reducing risk in a System. 3.2. Cloud Computing is a high-level computing technology capable of computing and storing massive amount of data in such a way that 474 organizations will have higher chances of expanding and performing effectively al a larger space (Mitra et ah, 2017). Supply chain design and processes can be obtained, computed and stored for future use based on cloud computing technology. Branger and Pang (2015) are of the opinion that that cloud manufacturing is anticipated to appear as the next and highly effective model and driver of manufacturing in the fourth industrial revolution. According to Xu et ah, (2018) cloud computing can facilitate data sharing and exchange efficiently thereby promoting complex decision making in manufacturing Systems. Successful implementalion of Industry 4.0 is based on intelligent computing of which cloud-based manufacturing is a key driver. The service-orientation in the field of manufacturing is supported and facilitated via cloud computing (Xu ct ah, 2018). 3.2. 3D-Printing in Manufacturing Systems - Difficult to weld components can be remanufactured with ease and delivered to Customers timcly using 3D printing techniques. This technology is quite expensive but offer robust benefits which include: It is faster and more precise than the traditional System; wastage is reduced via 3D printing; Internal object can be buiit unlike traditional machining; complex stochastic structures difficult to produce via conventional method can be produced with ease; 1t uses the same language used by classical machining process; fantastically complex objects can be produced; lighter weight and stronger structures can be made; customization process is quite affordablc; products are delivered timely. In addition, personalized models can be delivered much more easily and quickly to customers as a result of short distance between production and customer. This application is particularly useful in supply chain operations from manufacturing of parts to redesigning of full components for global supply chain production at inbound and outbound level. 3.3. Machine Learning (ML) and Artificial Intelligence (AI) - will make a big difference especially in promoting supply chain processes. Looking at the recent trend in the dynamics and operational performance of Companies, it is a clear indication that Companies like google, 475 Facebook, Uber operate in such a manner that a single Company Controls a very large part of the market. 3.4. Internet of Things (IoT) and Cyber-Physical Systems- Internet of things and cyber-physical Systems work hand in hand. Considering the manufacturing industry, smart machines can work with humans for easy assembly task, they can also operate autonomously and communicate directly with manufacturing Systems, leveraging the capability of the Internet of things, solving complex problems and making decisions independently. This will have an extraordinarily strong impact on the factory of the future. For example, advanced manufacturing process and rapid prototyping will make it very possible for customers to Order any kind of product without significant increase in cost. These technologies will greatly reduce cost and time associated with product design and engineering of the production process while prompting Simulation and virtual testing throughout the product lifecycle. Advanced human machine interaction handling Systems will help increase safety in production plant and reducing physical demand of workers and physical handling of products by man. 3.5. Automatic Guided Vehicles (AGV) and Unmanned Aerial Vehicles (UAV) - Autonomous vehicles offer very specific benefits which include: Safety - Most accidents are caused by human errors. the use of Computer algorithms and automation to drive machines or vehicles offer a perfect solution in terms of Service delivery; effective coordination and navigational endurance; reduced cost of delivery; great economic benefit as autonomous vehicles are programmed to perform task for a very long time with great endurance limit; social exclusion can be removed by autonomous vehicles; they are more transformational, cleaner, affordable, safer and highly efficient. 4 Discussion It is no doubt that a new data architecture and global network has emerged where people and machines can interconnect for effective and continuous interaction. This has led to high Standard of safety and has changed the society and our daily lives. Currently, the traditional 476 approach to the supply chain is exceedingly populär, particularly in developing and emerging nations. The fourth industrial revolution has ushered modern technological advancement and information network infrastructure to facilitate things. A global network has emerged, which allow direct and continuous interaction between man and machine. This is gradually changing the way we think and carry out our daily operations. Different technologies to Support the fourth industrial revolution has been discussed which include big data analytics; 3D printing technology. Internet of things, artificial intelligence and robotics. These technologies are useful to facilitate supply chain operations. There is no doubt that the technologies of the fourth industrial revolution will greatly enhance supply chain design, processes, engineering and management. Considering product delivery aspect, the use of autonomous Systems (aerial and ground robots) will facilitate delivery process timely inbound and outbound operations. 4.1. Challenges of the Industry 4.0 Technologies in Supply Chain Operations According to Elon Mosk, artificial intelligence is considered the biggest existential threat to humanity (Guardian, 2014). While many workers fear losing their jobs, some see AI as a terminator that will wipe out all humans from the surface of the earth. It is important to focus on the impact of the current revolution in our society especially in the manufacturing and Service industries. These new technologies will no doubt, significantly transform our System, workforce and path planning process. In the physical world, it is important to take safety into consideration before deploying Industry 4.0 technologies. There is a huge disconnect between using a traditional or non-autonomous vehicle for conveyance and transportation of materials and using a self-driving vehicle. Synchronization of autonomous Systems which are key players in the scene of activities is a complex task which requires systematic and Strategie approach for effective coordination. With the ever-growing demand of data in every industry, the need to safeguard and manage sensitive data has increased dramatically. Many countries are already implementing strict regulations, a trend that likely 477 to continue into a conceivable future. ML and AI are required hamess and secure data for Company use. One of the major challenges with this new technology is the issue of security. However, in the coming years there is tendency of increase in decentralized technology for data security, integrity and privacy especially for machine to machine interaction. In manufacturing and supply chain operations where machine agents and Als are the key players, the instructions given to AI must be tested and confirmed satisfactory before using the technologies to avoid any form of disaster. Deploying the technologies could be so complex with multifaceted operational constraints. Setups need to be dynamically routed through a network and other machine agents; such networks are highly unpredictable and much volatile. Considering the current Industry 4.0 technologies already discussed in this study, there are still lot and more technologies evolving, but very often most of the technologies may not scale through real-life or real- world applications. Some may end up as useful techniques in teaching space or research for solving numerical or quantitative problem solving and not really techniques that can drive innovations. Looking closely at the new technologies discussed in this context, artificial intelligence, robotics and machine leaming tend to scale perfectly in supply chain operations if well implemented. There is a great advantage of the new Industry 4.0 technologies over the classical techniques in supply chain management and manufacturing operations. 4.2. Benefits of the Industry 4.0 Technologies in Supply Chain Operations Fully integrated digital supply chain requires dynamically adjustable and synchronized network. Artificial Intelligence (AI). Machine learning (ML) and Robotics are particularly useful technologies in the current revolution especially in supply chain operations. There is no doubl that they will greatly Support intelligent machine agents for product monitoring and fast delivery in manufacturing Systems. ML will be 478 fundamental to optimizing production processes and reducing lead time. Some benefits of Industry 4.0 technologies include: (i) Already available infrastructures can be reused in supply chain operations especially where the methods are well implemented by strategists and managers of manufacturing Companies managing the setup. Systems that are in place can integrate with already existing AI infrastructure to facilitale the network system. Many of the machines learning type of approaches can perfectly fit in. A good example is dynamic routing as a new technology, experts can make good use of already existing routing in place in a manufacturing Company add the python script to execute task effectively. same is applicable using reinforcement learning and olher innovative Industry 4.0 technologies for supply chain operations. (ii) Faster return on investment - At every point in time, product and service-based organizations currently springing up globally. require network of product or Service interaction either at in-bound, in-process or out-bound operations. Some produce similar products where competition abounds. Standing tall and making a difference is a function of strategies implemented in the new era. As already discussed, technologies of the fourth industrial revolulion will goa long way to facilitate supply chain network which remain particularly useful in manufacturing Companies with great possibility of achieving faster return on investment. (iii) Work perfonnance can be easily measured- In a manufacturing Company or establish, workers are employed to facilitate work operations for efficiency, effectiveness. productivity and profitability. There is no doubt that performance of task could be overly complex and diverse since contextual and environmental factors are considered. It is therefore extremely hard to make a fair assessment of perfonnance of workers in the system. Knowing the rate of 479 performance and strength of workers in a chain System of work Operation is important to rate the efficiency, fulfilment or task accomplishment rate of the Company. This will equally help assign the right person to the right task. The traditional approach of using the time study -method study and work measurement is time wasting. Machine leaming based approaches like extra trees, deep leaming algorithm and others can help achieve work performance as they have the capacity and capability to train and view the task by focusing on the history of workers to give a very good prediction of the duration of the task and possible expectation of workers in a complex supply chain network and manufacturing operations. (iv) Inventory management is equally important aspect of supply chain and the traditional approach often used in manufacturing organizations is time wasting and fundamentally based on assumptions regarding demand distribution which has never guaranteed optimality in terms of replenishment strategy. In the era of fourth industrial revolution, it is important to implement the AI technology focused on deep reinforcement leaming for perfect inventory control where leaming process is automatic, the process is fast, and no assumptions are required. Thoug'n there may be possibility of slow convergence. (v) Cyber physical Systems and machine to machine communication will all work together to share data from the shop floor in order to reduce idle time. Intelligent drones can be used to supply or deliver products timely and analyze vast demand of data’s in seconds. Companies like Uber and Google are extremely strong in the machine leaming space when it comes to autonomous vehicles. The method adopted by über which require building retrofit kits, autonomous sensors, and high-level Software technologies has made the Company stand tall among many other corporate organizations. The interesting part is that the already 480 established knowledge can be reused for developing vehicles and making them autonomous. 5 Conclusion Industry 4.0 is the major trend in global manufacturing. Organizations need to follow digital transformation to stay competitive and equally achieve sustainability. This ensures gaining environmental, social and economic advantages. This study is focused on exposition of industry 4.0 technologies and the benefits of integrating the technologies into supply chain operations. There are numerous technologies springing up, but the vital few has been discussed. 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(2015). “A Nuanced View on Supply Chain Integration: A Coordinative and Collaborative Approach to Operational and Sustainability Performance Improvement.” Supply Chain Management: An International Journal 20 (2): 139— 150. doi: 10.1108/SCM-04-2014-0120. Xu F., Feng L. (2019). The influence of big data System for used product agreement on manufacturing- remanufacturing operations. Journal of Clean Production. 209. Zhong, R. Y„ C. Xu, C. Chen, and G. Q. Huang.(2öi7).“Big Data Analytics for Physical Intemet-based Intelligent Manufacturing ShopFloors."International Journal of Production Research55 (9): 2610-2621. 492 CHAPTER 21 Computer Aided Design (CAD) of a Vertical Transportation System in High-rise Building: Case of Ivory Tower, University of Ibadan Ibadan Odunfa, K.M1; Taiwo, O. I1, Odunfa V.O2., Abu, R1 ‘Mechanical Engineering Department, University of Ibadan, Ibadan, Nigeria 2Department of Estate Management, The Polytechnics, Ibadan, Ibadan, Nigeria Abstract In compliance with the global building regulations, building with at least three floors and above must have lift. The Ivory Tower building in the University of Ibadan, Ibadan, Nigeria, for decades has been underutilized due to lack of convenient and less stressful vertical movement of the people within the building. The need therefore arise for the lift design System for the building. Analytical work involves in the design of lift System in building is often time consuming, laborious, rigorous and tedious. This work therefore aims at design and specifies lift System for the Ivory tower building using Computer Aided Design (CAD) approach. Standard Equation based on the lift System design was adopted in the study. Data were collected from the building site which includes the floor to floor distances and floor dimensions. The population in the I0-Storey Ivory tower building coupled with the 4 Storey Administrative building attached to it was determined using the Chartered Institute of Building Services Engineers (CIBSE) design guide (Peters R D Green 1995 and CIBSE 1991). Lift performance analysis for the building was then carried out using FORTRAN IV programming language. Appropriate and suitable lift and its specifications was then selected for the building. The maximum capacity. number of passengers, velocity. Round Trip Time, Handling Capacity, Interval, and number of lift cars of the selected lift System based on the quality of Service are 450kg, 6 passengers, 2.0 m/s, 80.3seconds, 86 passengers, 17.54 seconds and 4 cars, respectively. The 493 lift System therefore selected based on the required quality of Services is four numbers 450kg-6passengers machine room less geared traction type. The lift shaft was successfully designed and the number of lift specified using the developed source code; hence the code can be used to design lift System for any building. Keywords: Handling Capacity, Round trip time, Interval. Word count: 295 words1 Nomenclature C d Car Interval Depth (mm) C w Car Interval Width (mm) E h Car Opening Height (mm) L Lift Travel (m) N Number of People or Car Capacity Ph Pit Depth (mm) R a Machine Room Access (mm) R d Machine Room Depth (mm) Rw Machine Room Width (mm) S Maximum Number of Stops s, Probable Number of Stops Sh Headroom (mm) Td Downward Joumey Time(s) To Door Opening Time (s) TP Passenger Transfer Time (s) T u Upward Joumey Time (s) V Car Speed (m/s) V d Door Speed (m/s) w Door Width (mm) W d Well Depth (mm) W w Well Width (mm) 1. Introduction 494 Vertical Transport Systems in buildings are the Systems that are used to move people and goods from one level of a building to another. (Ramesh Nayaka. 2014). These majorly include lifts and escalators. A lift is a type of vertical tränsport equipment that efficiently moves people or goods between floors (Ievels, decks) of a building, vessel. or other structure. An elevator (lift) is a permanent lifting installation serving two or more defined landing leveis, comprising an enclosed space, or car, whose dimensions and means of construction clearly permit the access of people, and which runs between rigid vertical guides. Elevators are driven directly by an electric motor (electric lifts) or indirectly through the movement of a liquid under pressure generated by a pump driven by an electric motor (hydraulic lifts). Electric lifts are almost exclusively driven by traction machines, geared or gearless, depending on car speed. Hydraulic lifts have become widely used since 1970s for the transportation of goods and passengers, usually for a height not exceeding six floors. Because of wheelchair access laws, elevators are often a legal requirement in new multistory buildings, especially where wheelchair ramps would be impractical. Type of elevators include Direct plunger Hydraulic elevators, Holeless Hydraulic elevators, Roped Hydraulic elevators, Geared Electric Traction elevators, gearless Electric Traction elevators. Vertical transportation of goods and people has its origin in the depths of history, where simple rope and pulley block Systems were used. In 1991, Elisha Graves Otis successfully pioneer vertical transportation Systems that still bear his name tili today. (Otis elevator PLC 1991). By 1850, steam and hydraulic elevators has been introduced, but it was in 1852 that Elisha Graves Otis successfully put a safety device into a lifting mechanism making possible the first passenger elevator.. Some of the very early passenger lifts installed before 1900 were operated from hydraulic water power and in recent years, the use of hydraulic power has been reintroduced but using oil as the pumping medium with pressure supplied by a motor driven pump. Apart from hydraulic lifts/elevators all earlier types of elevator machines were of driving drum type. In 1903, Otis introduced the design that becomes the backbone of the elevator industry and this is the gearless traction electric elevator. Electric lifts are 495 now more commonly used compared to the hydraulic types. They have a greater performance efficiency, provide speeds up to 7m/s and can travel over fifteen floors unlike hydraulic lifts that cannot travel more than 5 floors and provide speeds up to 0.75m/s. In order to prevent accidents, elevator doors were being equipped with electrical inter locks in the late 1920s, hoist ways and elevator cars were being solidly enclosed and solid car doors were becoming Standard. The concept of fireman's lift developed during the 1920’s and 1930’s, as the need for rapid emergency access responded to the growth in number of tall buildings. By the late 1940s, freight elevator hoist way, gates and gate lockirig and contact devices were being required, and the days of the worker opening a gate and falling into a hoist way were on the way out. Prior to 1950, there were few or no locks and people feil in regularly. The elevator industry started to apply microprocessors in 1980 and since then a new generation of the most sophisticated Controls has become available representing new and highly advanced technology. The inverter (VVVF - Variable Voltage, Variable Frequency) control is replacing the traditional ward - Lionard or thyristor - leonard for high speed elevator and primary voltage control of induction motors for medium or low speed elevators. Another important change is the use of the helical reduction gear for high speed AC elevators which is competing with the highly satisfactory 100 years application of the d.c. gearless machine. The first variable voltage and frequency elevator drive System was developed in the United States and put into Service at the beginning of 1983. Since then, more than a thousand have been built and put into Service in the United States. Other countries, in particular Japan, have active variable voltage and frequency elevator development programmes and several elevators of these types have been installed. (KONE 2020). In 2000, the first vacuum elevator was offered commercially in Argentina (KONE Lift. 2000). Otis Elevator Company is working on a new double-deck elevator design that will travel the world’s tallest buildings. The Company used a similar double-deck elevator car design for the Burj Khalifa, which was finished in 2010, OTIS Lift. (2018). 496 2. Fundamental bases of lift traffic analysis and performance evaluation The sizing of the lift Systems to serve the demands of a building’s population has interested the lift community since the 1920s. The methods being used were somewhat rough. However, by the 1970s a recognized method of calculation had evolved for up-peak traffic sizing based on the mathematical determination of the N, S and P (average highest reversal floor, average number of stops and average number of passengers), Bamey et al. (1985). In the 1970s digital Computer Simulation techniques evolved which allowed specific traffic and lift installations to be examined. The traffic sizing of lift System is conventionally carried out by determining the Round Trip Time (RTT), Graver et al. (1971) of a single lift car serving an up-peak traffic condition. Methods for Traffic Analysis and Performance Evaluation (Jones, Basset (1923) UPPINT = RTT/N UPPHC = 300 x 0.8 x c.c UPPINT % POP = UPPHC x 100% POPULATION Where N = No of lift cars UPPINT _ Up Peak interval cc _ Contract Capacity RTT _ Round Trip Time UPPHC — Up-peak handling capacity over a five-minute period. The UPPHC is calculated assuming cars fill with passengers (p) to 80% of the contract capacity. 497 Governing Gquations for the lift design ((Alexandris (1986) (i) A simple expression developed for RTT is RTT = 2Htv + (S + 1) ts + 2 + 2Plp Where s = means number of stops made above the ground floor P = average number of passengers carried in each trip tp = time to transfer p passengers into the lift car ts = time associated with each stop tv = time taken to travel between two floors at contract speed. tu = time to transfer P passengers out of the lift car. tv = df v ts = t f t l ) + tc + t o - t v tp — tp + tu 2 P is taken as 80% of contract capacity (Alexandris (1986.) tr is a single floor jump time to is the time to open the car doors (s + l)times tc is the time to close the car doors (s + 1) times d f i s a Sta nd a rd in t e r f lo o r h e ig h t V is the contract speed. (ii).Another equations based expression developed for RTT (Jones, Basset (1923)) is RTT = Tu + Td + Tp + To Si = S - S (S - l)n 1 s Where S = Maximum number of stops N = Number of people (usually assumed as 80% of the contract capacity). Si = probable number of stops 498 Tu = Si (L_ + 2v) 2 SV Where Tu = Upward Joumey Time L = Lift travel V = Car speed Td L_ + 2v 3 V Td = downward joumey time TP 2n or Tp = 3n depending on the depth of the car A TP — Passenger transfer time To = 2(Si + 1)W v d 5 To = Door Opening Time Vd — Door Speed w = Door Width Passenger’s arrival process Observation is the only procedure that can be employed in obtaining data on the arrival pattem of passengers approaching a lift System at the main terminal of a high--rise building. Observation can be made, either over a consecutive number of days or on the same day for a consecutive a rectangular probability distribution function. 3. Computer-Aided Traffic Analysis of Lift Systems Computer aided design (CAD) enables engineers and designers to use Computers to assist in the decision of complex engineering problems. CAD involves three phases; input, computation and output. In the case of CAD for lift Systems these phases comprise: Input Phase: Enter: building data, lift System data, passenger data. 499 Computation Phase: Perform a discrete digital Simulation of the lift System (time consuming). Output Phase: Examine graphical output; spatial plots; carload; car interval: passenger waiting time: percentiles of waiting time. Examine: numerical tables. 3.1 Computer Analysis and Performance Evaluation based on Lift governing equation The flow diagram that shows the computation of various lift parameter is shown below in Figure 2(a b) while figure 1 is the Ivory Tower building. Case Study: Ivory Tower, University of Ibadan, Ibadan Building Characteristics Fig 1. Ivory Tower, University of Ibadan, Nigeria Number of floors = 10 Floor to floor distances 500 Ground floor 3.3m First floor 3.1m Second floor 3.1m Third floor 3.1m Fourth floor 3.1m Fifth floor 3.1m Sixth floor 3.1m Seventh floor 3.1m Eight floor 3.1m Ninth floor 3.1m Tenth floor 3.3m Lift travel 27.9m (without considering the ground floor) Location of the building - University of Ibadan The building is for unified occupancy. Population of the Building Population in tower Width=l lm Length=6m Height to Height floor= 3.1m Floor Area of tower=66m Using lOOsf/person (9.29m2), Population= =66.77 persons Approximately 67 persons Population in admin building Width=68.8m Length=9.2m Height to Height floor= 3.1m Floor Area of tower=632.96m2 Population= no of floors x Floor area Net Area Using lOOsf/person, 9.29 501 Approximately 204 persons Total population=Population in tower + population in admin building = 67+204 =271 persons Using a safety net of 25%, ---1--0-0- --= 338.75 prersons Approximately 339 persons Key design parameters The following were determined in order to arrive at a suitable lift System for the building. Average round trip time (RTT) Interval (I) Handling capacity (HC) Preliminary Selections From Standard tables, suitable speeds for the lift are 0.63m/s 1.0m/s and 1.6m/s and 2.0m/s. Calculations were done for cars of various sizes / loads (320kg- 5persons,450kg-6persons, 630kg-8persons, 800kg-lOpersons etc.) until a suitable car size is determined. Design Calculations The required handling capacity per 5 minutes to handle a 25% of population flow rate. 25 339 = 84.75 = 85 persons per 5 minutes Minimum handling capacity (MHC) = 85 people. 502 Computc the round trip time (RTT) 1 Computc the nnltlng intcrvnl(I) < 5 503 © Figure 2a: Algorithm of FORTRAN IV programming for the lift performance analysis 504 4. Results and Sclection The summary of the resuit for the Iift performance analysis is in here presented in Table 1 below w No Vcl Prob N Ro Handli Actu Interv Remarks ei of ocit able 0 un ng al al gh Pass y noof of d Capaeil hand l enge (m/ slops lif Tri y ling rs s) t p (%) Capa Ti city me 32 5 0.63 3 6 88. 26.0 81.7 14.68 Imerval doesn'l fall 0 1 wilhin ränge 1.0 5 69. 24.5 86.7 13.8 " 2 1.6 4 60. 26.6 79.9 15.01 Interval is exeellent 1 Handling capacily is good 2.0 4 58. 25.9 81.9 14.65 Inierval doesn'l fall 6 wilhin ränge 45 6 0.63 9 6 10 23.7 89.8 16.71 lnterval is exeellent 0 0 .Handling capacily is exeellent 1.0 5 80. 22.8 93.4 16.06 3 1.6 4 71. 25.2 84.3 17.8 Inierval is exeellent 2 .Handling capacily is good 2.0 4 70. 24. K 85.5 17.54 Inierval is exeellent 2 .Handling capacily is exeellent 63 8 0.63 5 5 11 22.9 91.7 22.89 Interval is exeellent, 0 4 Handling capacity is exeellent 1.0 4 93. 23.4 89.9 23.35 " 4 1.6 3 84. 28.1 74.7 28.11 Interval is good. 3 Handling capacity is good 2.0 3 83. 27.9 75.3 27.9 7 80 10 0.63 5 4 11 25.7 82.4 29.11 0 6 505 1.0 3 95. 28.2 75.5 31.8 Interval is fair, 4 Handling capacity is good 1.6 3 86. 25.5 83.4 28.78 Interval is good. 3 Handling capacity is good 2.0 3 85. 25.3 84.0 28.57 7 Selection For excellent Services (Technically and economically) 4Nos. öpassengers lift are in here selected for the building. Selected and lift specifications From the lift Service comparison table, the 450kg-6 passengers Machine room less traction lift at 2.0m/s is suitable for the building. Lift Specifications No of elevators - 4 Nos. Arrangement - Side by Side Load - 450kg - 6 passenger Speed - 2.0m/s Total Travel - 27.9m Serving - 9Stops, 9 Openings Machine - Machine Room Less Geared traction type Operation (Control System)- Full collective group with independent Service key switch Drive/Control System Variable frequency drive with microprocessor based control 506 Power Supply - A single speed, AC - 3 phase gearless motor, especially made to compromise the VVVF drive control System at: 400 volts and 50 Hz. -Insulation dass " F - Protection IP 21 Lift well size - 1750mm x 1900- mm between finished walls per lift Car (inside size) - 1150mm widex 1080mm deep with side and rear panels in skin plate from a Standard ränge to approve colour. Car fagade - Brush stainless Steel finish Car ceiling - Carved false ceiling finished in white Car Flooring - Hard rubber Car options included - Digital position and direction o Indicators Illuminating car buttons Overload safety device Light ray door protection device (photocell) Hand rails (stainless Steel free Standing) Ventilation fan Alarm bell Skirting for Car - Stainless Steel Car doors - Power Operated centre opening door constructed in Steel 800mm x 2000mm clear openings Finish-brushed stainless Steel Rope arrangement - 2:1 single wrap 507 Entrance Surround - Small trims construction in Steel. Finish - prime Coat. Safety Gear _ Governor Operated gradual type _ noise and thermal protection - Earth leakage protection _ Voltage drop protection - Over speed protection . Phase failure and phase reversal protection Buffers - Terminal buffers for Car and Counter weight Other items includes - Digital hall Position indicator and Entrance fire Service Intercommunicatio n between car and lobby Machine beam supplied and positioned by lift contractor for final fitting by others. 5. Conclusion The traffic analysis and performance evaluation established 4Nos. 450kg, 6 passenger machine room less traction elevator at 2.0m/s are the most suitable lift System for the Ivory Tower University of Ibadan. This lift 508 System will go a long way in mitigating the movement problems encountered by people in the building. It satisfies the condition of safety devices such as safety gear, buffers, light ray protection device, electric contacts and interlocks are installed in the lift System. The handling capacity of the lift System is found to be generally okay for the building. Manual computations for the design could be more laborious, rigorous and tedious. hence use of Computer techniques to obtain Optimum Solutions is recommended. References Alexandris N A (1986). Mean highest reversal floor and expected number of stops in lift-stairs Service Systems of multi-level buildings Applied Mathematical Modeling 10 139-143. Bamey G C and dos Santos S M (1985) Elevator Traffic Analysis Design and Control 2nd edition. (London: Peter Peregrinus). CIBSE (1994). The Chartered Institution of Building Services Engineers Graver, D.P. and Powell B.A. (1971). “Variability in round trip times for an elevator car during up-peak, transportation” Res, Vol. 5, No. 4, Pp. 301 - 307. Jones, Basset (1923). “The probable number of stops made by an elevator” GE Rev., Vol. 26, No. 8, Pp. 583 - 587. KONE lifts (2000). Kone lift for residential building Catalogue on ArchiExpo. 2000. pp. 1-10 KONE (2020) Kone Corporation’s Annual Reviews 2019 Otis elevator PLC (1991). Otis passenger lift planning guide. OTIS Lift (2018). Otis Elevator Company Catalogue Peters R D Green (1995). Proceedings of CIBSE National Conference Ramesh Nayaka (2014) Vertical Transportation Systems in Buildings 509 CHAPTER 22 A Synopsis of Major Classical Inventory Management Models O. Ibidapo-Obe1, F. O. Ogunwolu2* and O. F. Odeyinka3 Department of Systems Engineering, University of Lagos, Lagos. Nigeria. oveibidapoobe@ieloud.com1, fogunwolu@unilag.edu.ng2, oodevinka@unilag.edu.ng3 *Corresponding Author 1. INTRODUCTION 1.1 INVENTORY AND INVENTORY MANAGEMENT COMPONENTS AND FEATURES 1.1.1 Inventory Inventory or stock or work-in-progress in the most general terms refer to physical assets or goods of a venture kept in stock as raw materials/information, semi-finished assets and or finished or processed assets prior to, during or after processing to forestall stock-out or shortage at any stage of processing where they are needed in anticipation of demand. In materials management perspective, inventory is defined as a useable though idle resource with economic value kept for use or circulation. In general manufacturing setup it refers to products-in-process, raw materials, and completely finished products before sale and their departure from the manufacturing System. In service Systems, inventory is all work done prior to sale or offering of service, including partially processed information. Much as keeping inventory is desirable and a productive safe-guard against shortfalls, keeping too much or keeping too little for too long or too short a period of time in an instance of its need might be counter­ productive and uneconomical. The inventory paradox is thus that of a needed asset which may as well tum counter-productive if not well 510 managed. Two paramount questions that inventory acquisition seeks to answer are (1) How much is needed? and (2) when is it needed? On top of the knowledge of the need is the need to optimaily manage the needed inventory in time, quantity and space to forestall shortfalls and gluts, Capital tie-down and uneconomical purchases as well as wasteful utilization of inventory infrastructure. This is where effective Inventory Management comes in. 1.1.2 Types of Inventory Inventory can be seen in different perspectives and thereby the various types involved. Based on a venture’s stage of production or processing three types of inventory can be identified. i. Raw materials: unprocessed basic ingredients of production or Service ii. Works-in-process: unfinished product or Service item in the making iii. Finished goods or Service product Based on the purpose or position an inventory item serves within a venture, there can be: i. Cycle stock - inventories for meeting predicted demand between cycles of replenishments. ii. In-transit inventories / pipeline stock - These are products that are on the way transiting from one location to another. Although they may not be available for sale or shipment until getting to their ultimate destination, they may be considered part of the cycle stock. iii. Safety or buffer stock - items held in excess of the normal cycle stock in anticipation of uncertainty in demand or in lead time).Quantity held is influenced among other factors by lead time of replenishment, fluctuation of demand and the availability level planned for customers. They usually constitute the majority of inventory in typical production or logistic System. 511 iv. Speculative stock - items held in stock in anticipation some future occurrence other than for meeting demand. Such anticipated events may include forecasted price fluctuation, materials shortage, quantity discounts and stock need to cushion effects of possible natural disaster or workforce strikes. Products may also be manufactured in periods when they are not in demand for production economic reasons. These also may constitute speculative Stocks. v. Seasonal stock - these are accumulation of speculative stock held in advance of or during a seasonal period. vi. Dead stock - items which have not been in demand for a specified period of time. They include obsolete products and products which are not in demand in the current season. 1.1.3 Effective Inventory Management Requiremcnts Essentially, a comprehensive System for Inventory Management comprises of two complementary sub-systems: one to keep track of inventory items and the other toenable management take decisions about inventory size and when to order. For effectiveness, a good Inventory Management must incorporate the following features (Vrat, 2014; Ogunwolu et al., 2012):1 1. Ability to keep track of inventory in stock and ordered inventory. 2. Incorporation of dependable demand forecast robust enough to accommodate possible error in forecast. 3. Possess the knowledge of lead times and its variability. 4. Incorporation of reasonable estimates of inventory holding costs, ordering costs, setup costs and shortage costs. 5. An appropriate and effective inventory policy 6. A built-in sub-system for inventory Classification 7. Skill in utilization of appropriate models to determine order point, lead time and reorder points. These inventory components must be well integrated to make inventory management effective, efficient and seamless. 512 1.2 Inventory Models Inventory models can be classified according to one or more of the following modes of Classification (Vrat. 2014):. Number of inventory items Single Item: This type of model recognizes one type of product at a time. If the demand rate changes from period to period, then the problem becomes that of a dynamic lot-sizing problem Multi Item: This type of model considers a number of products simultaneously. These products must have at least one interrelating or binding factor such as budget or capacity constraint or a common setup Stocking Point Single Echelon: Only one stocking location is considered Multi-Echelon: More than one interconnected stocking locations are considered Frequency of Review Frequency of review is the frequency of assessment of the current stock Position of the System and the implementation of the ordering decision. Periodic: Placement of Orders is done at discrete points in time, with a given periodicity Continuous: Order placement can occur at any time. Order Quantity Fixed - Order quantity: Order quantity is fixed to the same amount each time Variable - Order quantity: Order quantity can be variable 513 Planning Horizon Finite Horizon: Demands are recognized over a limited number of periods. Infinite Horizon: Demands are recognized over an unlimited number of periods Nature of Demand Deterministic: Demands are known with certainty over the planning horizon (a) Static demand rate: Demand rate is constant over every period (b) Dynamic demand rate: Demand rate is not necessarily constant. It changes in magnitude from period to period. Stochastic (Probabilistic): Demand is random and may follow Standard probability distributions Fuzzv Demand: Demand is imprecise or ambiguous. Capacity: Capacitated: There are capacity restrictions on the amount produced or ordered Un-capacitated: Capacity is assumed to be unlimited Unsatisfied Demand Not allowed: demand is met and no shortages are allowed Allowed: Demand not satisfied in a particular period. It may be retained and satisfied in a future period (backlogging), partial ly retained and partially lost or completely lost (no backlogging) 514 2. DETERMINISTIC CLASSICAL INVENTORY MODELS 2.1 BASIC ECONOMIC ORDER QUANTITY MODEL (EOQ) AND ITS VARIANTS 2.1.1 THE BASIC EOQ MODEL (Taha, 2017) The most rudimentary inventory model by used industrial and Service delivery practitioners, which caters for replenishment of depleting inventory over time is the economic Order Quantity (EOQ) model (or Economic Lot-Size model). For this model and its variants, demand is assumed known and constant over the inventory management horizon. The primary concem is to minimize the Total Inventory Cost per unit. This cost is made up of Ordering cost, Setup Cost and holding or carrying cost well as shortage cost where shortage is permitted. Generally, for the Economic Order Quantity (EOQ) and its variants, the following Symbols are adopted for the model parameters and variables Model Parameters K = Setup cost of inventory (per ordering cycle) c = cost of purchase of inventory (per unit quantity, per time unit) H = holding or carrying cost per unit time held in inventory D = demand rate for inventory item per unit time Model Variables The major decision variables of the EOQ model and its variants are the Order Quantity (Q) and the Shortage (S) for the single item inventory. Equivalently, for multi-item inventory, the decision variables are Qt and Sj respectively for items i = 1, 2,. . .n Other variables of note are, t c = inventory procurement time or cycle L 515 = inventory lead tim e (tim e allowance between ordering and delivery of ordered item) These model parameter and variable Symbols are used in the EOQ model presented here from its basic form propounded by in to varieties of the variants of the model that emerged thereafter. BASIC ECONOMIC ORDER QUANTITY MODEL (WITHOUT SHORTAGE) (Taha, 2017) For this case depicted graphically as in Figure 1, the Total Inventory cost function is given by, CT = Total Cost = Purchasing Cost + Holding Cost + Setup Cost Purchasing and Setup Costs For inventory quantity (Q), at c cost per unit, the Ordering Cost is. Ordering Cost/ cycle = C0 = K + cQ Fig. 1: Inventory Pattem, Reorder Points and Replenishment Points in Basic EOQ 516 Holding cost Average inventory utilized per cycle = | With H cost per unit per unit time, the cost per unit time is ^ H. Given the demand rate D units, the Cycle duration for consumption of Q i. nventory uni. ts .i s -o Thus the average holding cost per cycle, Ch, is given by, C„ = ^Q H x Q^ = Qf -2H H 2 D 2D The Total Cost per cycle is, CT = C0 + CH = K + c Q + jQ^2H For each unit of inventory, over cycle length the Total Cost per unit, Ctu is, D Q2 D K HQ Ctu — 77 K + cQ + — H — + D c + ~ The Optimum cost that minimizes the Total Cos per unit, CTU , is obtained by finding the first derivative of CTU with respect to the variable Q and setting the derivative to be equal to zero. dCru _ _ £ £ , » _ o dQ Q2 2 From this, the optimal value of Q is obtained as, 517 The corresponding optimal cycle time, t j , is given by fc It is easy to show that CTU at = 0 above is a minimum solution since, d2CTU _ 2DK dQ2 ~ Q3 D > 0, K > 0 and H > 0 implies (?* > 0 thus Hence the derivative of the Total Cost per unit inventory with respect to Q set to zero yields a minimum point. Model Sensitivity and Practical implications Changes in EOQ inventory model parameters K, D and H results in model fesponses of change in the optimal values Q‘ and t'c with practical implications. This is illustrated in Table below (using (+) for increment and (-) for decrement. Table 1: Sensitivity Analysis of EOQ Model with no Shcrtages Parametric Change Optimal Variable Practical Implications Responses K+ t r Smaller Inventory 518 Inventorv Lead Time A lead time L may be required as the time required between the time of Order and the actual time the order is delivered. This is practicable to define the reorder point in time before the exhaustion of the inventory in use. Thus with a lead time of L and inventory demand rate D, the reorder point is when the inventory drops to LD units. Assuming that L < t'c, the effective lead time is defined as, L e = L - nt'c The parameter n represents the largest integer value not exceeding £ . Thus the effective reorder point is when the inventory drops to LeD (Taha, 2017) 2.1. 2 EOQ (WITH SHORTAGES) (Hillier and Lieberman, 2001) Shortages may be planned for in inventory management to forestall stock-out, a case where there are no products to deliver or seil to Customers which more often than ought may lead to loss of goodwill from customers. Though with a guarantee of safety stock planning for shortages will also mean incurring shortage costs. Thus, a good model that allows for shortages must guarantee an optimal trade-off between safety stock and the extra cost incurred. As in the Basic EOQ, the Setup and purchasing costs is made up as Ordering cost, C0 Ordering Cost/ cycle = C0 = K + cQ The quantity ordered, Q is now made up of the normal purchase, N and the shortage, S = Q - N allowed. Within normal inventory cycle, the inventory level remains positive for a period ̂ with an average inventory level of ̂ units. With a holding cost 519 of H per unit per time unit, the holding cost for this period is — per unit time. The normal inventory holding cost per cycle, CN is thus given by, N NH N2H C n~ D * T ~ ~2D~ The remainder of the period caters for the shortfall allowed with an average inventory level of and corresponding cost of (Q ~ - p- per z z unit_ t im( e. Thus the ̂ s(hortage) cos(t per cycle, Cs is given by,Q - N ) p Q - N Q - N ) 2p s 2 D 2 D In all, the Total Cost of inventory per cycle is given by, N2H (Q - N)2p CT = C0 + CN + CS = K + cQ + — + w F The corresponding Total Cost per unit inventory time is, D N2H ( Q ~ N ) 2p Ctu — 77 K + cQ+ 2 D + 2 D DK HN2 + (Q - N)2p = y +Dc+ 2 Q 2 Q Optimal decision needs to be found for the Total Order quantity, Q and the normal order, N. This obtained by partially differentiating CTU with respect to Q and N, setting each derivative to zero to obtain respective optimal CTu decision point and solving the two resultant equations simultaneously to obtain the optimal values Q' and N *. dCTU _ DK__ HN2 | CQ ~ N)p CQ ~ N)2p dQ Q2 2 Q2 Q 2 Q2 dCTU HN CQ~N)p dN ~ Q Q " ° 520 The simultaneous solution of these equations in Q and N yields, the optimal values of the variables. The optimal cycle time, t ’c is, The maximum shortage, S" is The time point when normal inventory is depleted is. The fraction of the optimal cycle time, t'c for which no shortage occurs is given by. tjL = _ P _ t'c P + W From this relationship, which is independent of setup time, K, the sensitivity of (he model when the holding cost, H and the shortage cost, p are made substantially Iarger than each other can be investigated. The sensitivity analysis is summed up in the table below. 521 Table 2: Sensitivity Analysis of EOQ Model with Shortages Costs relationship Optimal Variable Practical Implications Responses p -> co , H constant 5* = Q* - N * As shortage cost (shortage cost -» 0 dominates holding cost, it is not desirable dominates holding to accommodate cost) shortages H -* co , p constant AT -* 0 As holding cost dominates shortage (holding cost cost, it becomes dominates shortage uneconomical to have cost) normal inventory. Orders deiivered are used solely to settle shortages. 2.1.3 EOQ WITH PURCHASING PRICE BREAKS (Taha. 2017) In the previous EOQ models, the optimal inventory policies obtained are not dependent on the cost of purchase. In reality, however, different price regimes, allowing for discounts, may be applicable for purchases depcnding on the quantity. If this is accommodated in the EOQ model, the optimal inventory policy will be dependent on costs too. Assuming a single price break, if Q < q c = f Cl' vc2, i f O > ~ forc N Co As result of this cost break and since order per unit time is — , then the purchasing cost per unit time, Cp is 522 f = Wo = C' D * * * Cp = Eil - E il - r n v T - W - C2° ;Q > q Aggregating all relevant costs, the Total Cost per unit time CTU as a function of order quantity Q is given by, r KD HO Ctu (Q)i - ct D H — I — ;Q < q Ctu (Q) = „ KD hq Ctu (Q)2 - c2D + — + — ; Q > q The values of the functions CTU (Q')1 and CTU (Q)2 differ only by a constant value, (ci - c2)D so their minima are the same and is equivalent to the Basic EOQ minima, The graphs of the two functions are as in figure bclow Fig. 2: Inventory Cost functions with Price Break Zones and Optimal Solutions The optimal Order quantity Q* depends on the location of price break point q out of the three possible Regions I. II and III representing quantity ranges (0, Qm), ( Qm,P ) and (P, co) respectively. For P > Qm can be determined from the equation, C-ru OO2 = Ctu (Qm)l That is, K D H P , C2D + — + — - CTU (Qm)l This results in a quadratic equation in P p 2 + / 2 (c2D - C TU (Qm) i ) \ p + 2KD _ Q \ H / H The optimal quantity Q* is determined as (Qm i f q i s i n z on e l o r l l Q - f q if q is in zone II The following Steps can be used to determine Q‘ Step 1: Determine Qm = J12—KD . If q is in zone 1, then Q* = Qm . Otherwise GO TO Step 2 Step 2: Determine P (> Qm) from the equation. P2 + / 2(c2D - Ctu (Q m )i)H With the value of P known, define the zones II and III as the ranges ( Qmi P) ar,d (P. °°) respectively. 524 If q is in zone II, then Q* = q . Otherwise, q is in zone III and Q* = 2.1.4 EOQ WITH UNIFORM RATE OF REPLENISHMENT OR REORDER Instead of instant replenishment (or reordcr) assumed in the Basic EOQ model, a uniform rate of reorder or replenishment of inventory r units per unit time can be assumed where r is greater than the rate of inventory consumption (demand), D ((r > D). For this case, the maximum inventory is not Q. but Q - ° Q = The Total Cost per unit, CTU is The EOQ is, ; r > D 2.1.5 MULTI-ITEM EOQ WITH STORAGE LIMITATION On a general basis, when there are more than one items of inventory, with known demand and no allowance for shortage, the model which minimizes the grand total of the individual Total Cost per unit of each item can be written a constrained Non-Linear Mathematical Programme. The objective function is constrained by Sum of the storage space utilized 525 by individual inventory item which cannot exceed the total storage space available. (Stevenson, 2005) Using the following notations for inventory items i = 1,2,. . . ,n, Di = Demand rate for item I Ki = Set up cost Hi = Unit holding cost per unit time Qi = Order quantity Oj = storage area required for per unit of item i A = Maximum available storage space for all n items The resulting Mathematical Programme is, V» (KiDi Hi Qi\ Minimize CTU (Qlt Q2 , . . Qn) = £ { -q ^ + ciDi + “ y ) subject to: n ^ a i Q i < A i=1 Qi > 0 ; f o r i = 1,2................. n Several approaches can be used to solve this programme: 1. Reduction of the problem to an unconstrained problem (by stepping down the constraints) and determining the solution as the EOQ value, Qi = > f o r each i = 1 ,2 ,. . . ,n If the solution satisfies the constraint, the QjS are adopted as the optimal solution Ql for each item i. 526 On the contrary if the constraint is not satisfied, then it is binding and another method of solution must be sought. Other methods of solution include: 2. Lagrangean algorithm for constrained programmes. 3. Solution as Non-Linear Programme using many proprietär)' optimization Software available such as AMPL, MATLAB and, Excel Solver. 3. Use of evolutionary algorithms such as Genetic Algorithm and Ant Colony Optimization algorithm. 2.2 DYNAMIC DETERMINISTIC INVENTORY MODELS In this dass of inventory management models, the demand per period is both deterministic and varies from one period to another. The inventory level is also reviewed periodically over a finite number of equal periods. A number of inventory models are in this dass. They include; 1. Periodic Review EOQ Model with No Setup Time 2. Periodic Review EOQ with Setup 3. The Silver-Meal Heuristics 4. Wagner-Whitin Algorithm These models will be b.icfly discussed and characterized in this section. 2.2.1 PERIODIC REVIEW EOQ WITH NO SETUP (Taha, 2017) The basic assumptions of this model are: 1. Setup cost is not involved during any period 2. No shortage is allowed. 3. The periodic unit production cost function is either constant or taken as increasing (convex) marginal costs 527 4. Constant unit holding cost is incurred in during any period Since no shortage is allowed, delayed production in future period cannot fill the demand in a current period. As a result of this assumption, the cumulative production capacity from the starting period to a particular period i is taken as the cumulative demand for the same periods. The model is formulated as transportation model with n periods each period consisting of k levels of production (such as regulär time and overtime). The supply end of the model is equated to the kn production levels as sources while the demand values are specified by the n periods of demand. The unit transportation cost from a source m to a destination n is taken as the sum of the production and holding costs per unit. The objective of the model will then be to determine the production level per source m that minimizes production cost. By reason of the assumption of no shortage and convex production cost, it is possible to solve the transportation model without using the comprehensive transportation technique procedure. It suffices only that for each period’s demand, starting from the first, the minimum cost allocation satisfying the supply and demand at each cell simultaneously are met and updated first before moving to the next demand period This procedure is encapsulated in the algorithm presented below with reference to the generalized kn by n transportation model. (Johnson, 1957) Let m = rj; r = 1 ,2 ,. . . . ,n; j = 1 , 2 , . . . , k for n periods and k production levels and Sm = Srj = S n , . . . . , Sjki S21, S22- • • >S2k» • • • 1 Sni» S„2»• • • *Snk Sm = Srj = Supply amount a t period r and the j th production level o f that period Cmi - Crj.i = ic i + Hi = un it transportation cost fr o m production 528 source m to demand destination i Di = Demand a t period i D = Dummy destination demand S = Dummy source supply (production) demand In this model, transportation from a previous cell Tm_pi = T'r-pj.i ; p = 1,2, . . .;p < r toa current cell, Tm i = Trj- t o i s n o t allowed because shortage is not allowed, hence those cells are blocked. Table 3: Abridged Transportation Scheme for Solution of Periodic EOQ with No Setup Cost Source Subscript DEMAND (DESTINATION) (i) Supply Symbols I R Ij 1 2 . . . N Dummy 1 11 • • • Sn 2 12 • • • Sl2 1 ; l • * • • • J : k lk • • • Sik k + 1 21 S21 k + 2 22! S222 •• i • • I 2k 2k • • H • • • • * I (m - m 1 Sml l)k + 1 529 COrg M (m - m 2 Sm2 l)k + 2 ; • 5 l : mk Mk Smk Dummy Source s D Demand Dn Dd Step 0: Initialize 1 = 0 General Step G: Step G 1: For all unblocked and uncrossed cel 1 in Demand coluinn i, select the cell with the least cost (break des arbitrarily). Allocate as much production units to satisfy the balance of demand, D| andsupply Sr;-; i ,r = 1 ,2 ,, , , , n ; j = 1 ,2 ,..............k, Step G2: Adjust and update demand Dj and supply S rj\ i,r = 1,2, . . . , n ; j = 1,2............,k corresponding to the cell at which allocation is made. Cross out any of the row or cnlumn that run down to zero (break ties arbitrarily). Step G3: If updated Dt = 0, and i * n, then make i = i + 1 and GO TO Gl Step G4: If updated D; * 0, and i * n GO TO Gl Step G5: If updated D* = 0, and i = n STOP. The allocations made to the cells are the optimal allocation depicting the production units required for relevant periods and production levels. 530 2.2.2 PERIODIC REVIEW EOQ WITH SETUP In the case when setup cost is incurred each time a new production lot is started, several periodic review model variants are used. In this section, two of such are discussed. 2.2.3 WAGNER-WHITIN The Within Wagner Algorithm (Wagner and Whitin, 1958) was designed to find the optimal policy for lot-sizing decisions by means of a forward recursive algorithm which first solves a one period problem and then sequentially solves sub problems until the Overall N periods problem solution is found. Let Di, Ki Hi and Qi be the demand, setup cost per order and holding (or carrying) cost per unit per order for period and quantity to order at period i, i = 1,2, . . . , n, respectively. The inventory function can be represented as: i - 1 i - l i = I0+ ^ Q j - ^ D j > o i=i )=i The minimum inventory cost function can be represented as, t (/) = fliyj [Ht. i / + F m ^ + /t+1 o + Q i - D o ] 1+QiZDi F( ) is the Heaviside Step function. The following theorems were proved to Support the WW algorithm (Badiru, 2007): Theorem 1: For any period, I, Ij Q, = 0 ,. This implies that since stockout is not allowed, Inventory from previous period cannot be brought into period i as Ij. Thus if Ij > 0 exists, no order is placed hence Qi = 0 and vice versa. 531 Theorem 2: For some k where i < k < n, an optional policy exists such that Qi = 0 or Qt = Yj)=i Dj for all >• This implies that the quantity ordered in period i is either zero or equal to the total demand of some or all of the future periods. Theorem 3: There exists an optimal policy such that if the demand, Di+j is satisfied by QJ, then demands Dj, Dj+1 , Di+Z , , Dj+t_! are also satisfied by Qj. Theorem 4: Suppose there exists known optimal policy for the first k periods of an n-period inventory plan in which Ij = 0 , i < k . Then it is possible to determine the optimal plan for the periods k + 1 through to period n. Theorem 5: Suppose there exists known optimal policy for the first k periods of an n-period inventory plan, in which Q( > 0 , i < k . Then, it is not necessary to consider periods 1 through k - 1 in formulating optimal policy for the rest of n - k periods. The implication, when this is the case is that, the problem will only be re-initialized to Start at period k and proceed forward. Wagner and Whitin (1958) gave the following algorithm for finding the optimal policy for the inventory problem Initialize the procedure at i* = 1 1. Consider the policies of ordering at periods i**, i** = 1,2, . . . , i * and filling demands Dit i = + 1,, , , , i ' using this order. 2. Add F(Qi-)Ki•• + //;•• to the costs of acting optimally for periods i** — 1 determined in the previous iteration of the algorithm. 3. From these i’ alternatives, select the minimum cost policy for periods 1 through i* 4. Proceed to i* + 1 or STOP if i* = n 532 2.2.4 SILVER-MEAL HEURISTIC (Badiru, 1996) The Silver-Meal heuristic (Silver and Meal. 1973) is a forward method recommended for items that have significantly variable demand pattem. The heuristics involves determining the average cost per period as a function of the number of periods the current Order is to span. The heuristic stops when the function first increases. The objective of the Silver-Meal Heuristic is tominimize Total Inventory Cost per unit time for the cycle of replenishment. Given the ordering cost C0 and the holding cost per unit of demand, H the Total relevant Cost is, CT = Ordering cost + Holding cost = K + C0 = K + HD Defining Cx (T) as the average holding and setup cost per period, and let the current Order spans the next T periods. If the demands are Dj, i = 1,2, . . . , n over n periods. To satisfy the demand for period 1, CT (1) = K For the second period, CT (2) = if CT (2) < CT (1) pause and produce or Order Qr = Dx, Reinitialize process at period 2 Otherwise, compute Cx (3) CT (3) = 22J22S2 if CT (3) < CT (2) pause and produce or Order = Dx + D2, Reinitialize process at period 3. Otherwise, compute CT (4) Thus generally to satisfy the demand for period i, „ W + ( i - 1 )HD2) 533 General ly, if Cx (i) < CT (i - 1) pause and produce or order Qr = £>! + D2 + . . . + Dj-x, Reinitialize process at period i. If i n, compute CT (i + 1). If i = n, Stop. 3. 0 STOCHASTIC CLASSICAL MODELS Just as in the case of deterministic models, Stochastic Inventory Models can be 1. Continuous review Models as typified by Stochastic EOQ models 2. Periodic review Models as typified by Single Period with or without setup cost as well as myriads of multi-period models (Hillier and Lieberman, 2001). In this section some of these models are examined while a more comprehensive undertaking of summary of features of notable stochastic models is later exhibited. STOCHASTIC CONTINUOUS REVIEW MODELS 3.1 STOCHASTIC EOQ MODELS One key family of continuous review stochastic inventory models is the Stochastic EOQ Models. The inventory prediction capabilities of the deterministic EOQ models can be extended to cases where the demand is random and can be fitted to particular probability distributions. Records of demand data which may qualify to be treated this way will normally exhibit very high coefficient of Variation (a ratio of Standard deviation to mean of the data). (Bartmann and Beckmann, 1992) Two approaches are can be used to incorporate random demand into the EOQ models. 1. By treating the effective inventory lead time, Le and the attendant possible shortage during this period in the deterministic EOQ model as stochastic (the Probabilitized EOQ). 534 2. By developing a stochastic model from the inventory variables and Parameters from first principles. (the Probabilistic EOQ) 3.1.1The Probabilistic EOQ Model The cost components of the stochastic EOQ model as in the deterministic case are setup cost, expected holding cost and expected shortage cost per unit time. These variables are obtained as follows. Given K as setup cost per order, D as the expected demand per unit time and an average inventory of the setup cost per unit time is approximated as ^ Similarly, given R as the remnant inventory at the reorder point and H, the cost per inventory unit per unit time, the expected inventory level, I, given y as the demand during the lead time is , f . « + W - y } + W - y ) ) = fl _ B(y) L. The expected holding cost per unit time is thus, HI, where I is obtained as the average of the sum of the expected starting inventory E{R - y) and ending inventory Q + E{R - y}, ignoring the case where R - E{y} < 0. The expected shortage per cycle where y > R is given by, 5 = COJ ( y - R ) / ( y ) d y H The shortage cost, p, per unit inventory item is assumed proportional to the shortage quantity and hence the expected shortage cost is pS. The cycle time is ^ and hence the shortage cost per unit time is, = £££. 535 The Total Cost per unit time function is given by, c T (q , r) = y + H (§ + R “ e w ) + ^ + /00 (y - R) f(y) dy R To obtain the optimal values Q’ and R* the partial derivatives of CT (Q, R) with respect to Q and R are found, equated to zero and the resulting equations solved. 3Ct (Q,R) H pDS _ n dQ \Q 2/ 2 Q2 ^ = H - ( f ) / f W d y = 0 Solving the two equations yields, |2 D (K + pS) Q . The least value oft?* is J ^ which occurs at S = 0. The steps of the Hadley and Whitin algorithm are: Step 0: Use the optimal solution, Qt Q ' = and let R0 = 0. Set i = 1, and go to Step i. Step i: Use to determine Rj from equation (2). If Rt « R t-i, stop; the optimal solution of Q’ = and R* = R(. Otherwise, use R( in Equation (1) to compute Qt. Set i = i + 1, and repeat Step i. 3.2 STOCHASTIC PERIODIC MODELS SINGLE PERIOD STOCHASTIC MODELS The Stochastic Single Period Models are models inventory decision is made in a single time period. This implies that whatever inventory items remaining are disposed of. Furthermore demand within this single period are random characterized by continuous or discrete probability distributions. The single period stochastic models can be divided into two groups of models (1) without setup cost and (2) with Setup cost (Hillier and Lieberman, 2001). 3.2.1 THE STOCHASTIC SINGLE PERIOD MODEL WITH NO SETUP TIME (The Perishable Goods Model) This model usually characterizes the inventory problem of perishable or short life cycle inventories such as periodicals like newspaper, flowers being sold by florist, seasonal clothing among others, which if any is left over at the end of the sales period becomes stale and can only be disposed of. 537 The model is characterized by i. Variable uncertain demand occurring instantaneously at the Start of the period immediately following receiving of Order ii. No setup cost Using the usual notation of Q and D for order quantity and demand within the period, /(D ), the probability distribution function, p, the unit cost of shortage and H the holding cost per unit for the period, it follows that for the problem two cases ensues in relation to inventory and shortages. When Q > D, then the periods inventory is Q - D for which holding cost H per unit will be incurred and when Q < D, shortages of D — Q occurs for which a shortage cost of p per unit will be incurred. Fig. 3: Illustration of (i) Holding (ii) Shortage Inventory in a Single Period Model The demand probability function can either be a continuous distribution or discrete mass function/(D).The expected cost for the period, E{Ct ((?)} can thus be expressed i. When demand distribution function is continuous as, Q OO E{CTm = h J ( Q - D) f (D)dD + p J ( D - Q)f (D)dD 0 Q 538 ii. When demand function is discrete as, x w £ { C t W ) } = h D£ =(0Q - D ) / ( D ) + p XD =Q +1 For either of these cases, the optimal inventory policy can be obtained. For the continuous model case, the first derivative with respect to Q and setting it to zero yields, -d ^ T = H Io m d D - p J “ f(D )dD = 0 This is equivalent to, dCT(Q) dQ = HP{D < Q } ~ p[ 1 - P{D <(?}] = 0 P{D s. If the amount of available inventory prior to placement of order is y, the question this model answers is that under this condition, how much inventory should be ordered? The answer to the question can be tackled for the three different quantity order regimes stated above. Case 1 (when y > s), Since y is already on hand, its expected cost is E{CT(y)} From the figure, if any additional quantity Q - y is ordered for, the expected cost of y is, mmE{CT(S)}= E{Ct(S)} < E{CT(y)} The implication of this is that the optimal inventory policy is to order S - y inventory units. Case 2 (when s < y < S) In this case, referring to the figure above, E{CT(y)} S) From the figure, if Q > y, E{CT(y)} < E{Ct(Q)} As in case 2, it is not also advantageous to order in this case as again, Q ‘ = y In summary, the optimal inventory policy for the Stochastic Single period Model with Setup cost.incurred, otherwise known as the s - S policy is: 541 (s — S)Policy = ! If inventory on hand, y < s, then order S — y units to level up to S If Inventory on hand, y > s, do not order VARIATIONS OF THE SINGLE PERIOD NO SETUP COST MODEL There variations of the stochastic single period model. Two important ones among such variations are: (Nahmias, 2005) 1. The Single Period Model (No Setup Cost) with Initial Stock Level 2. The Single Period Model (No Setup Cost) with Non-Linear Cost In the case of the Variation with initial stock level,y, if the policy decision to be made is to determine the value of inventory, Q after replenishment, Q — y has been made. The expected inventory cost can be written as, Q CO E{Ct(Q)} = c(Q - y ) + H f (Q - D)f(D)dD + p J ( D - Q)f(D)dD 0 Q 3.2.3 STOCHASTIC TWO-PERIOD MODEL WITH NO SETUP COST A method of dealing with multi-period stochastic inventory model which can only yield approximate Solutions is when the single-period stochastic model is used to plan ahead one period at a time. This will not yield optimal solution even for just two periods. The Optimum solution can however be guaranteed when the probabilistic distribution of the demand for each of a multi-period problem is known using probabilistic dynamic programming approach. Obviously since dimension of the problem will make the problem difficult to solve using probabilistic dynamic programming. For a two-period model, however, the problem of dimension can relatively be easier to surmount. A number of assumptions can be made to develop the two-period model. These are that: 542 1. Only one type of inventory units are under consideration. 2. Unsatisfied demand of period 1 can be back-logged to be met in period 2 but that of period 2 cannot be back-logged. 3. The probability distributions of the demands in periods 1 and 2 (Dx and Dx) are both independent and identically distributed random variables with specifiable probability density function f ( D) and cumulative distribution function, 0 ) . 5. The decision required is to determine the inventory levels, Qx and Q2 to reach by replenishment (if any) at the beginning of periods 1 and 2 respectively. 6. The expected sum of total costs for the two periods is to be minimized. In developing the model, using the normal Symbols in previous deductions, c, H and p represent the purchasing or producing cost per unit, the holding cost per unit remaining at the end of each period and the shortage cost per unit of unsatisfied demand at the end of each period. These parameters are assumed the same for each period. However, in reality, they may differ in the two periods. Let E{C1(y1)} (E{C2(y2)}) be the expected total costs for both periods (period 2 only) at an optimal policy given that yx (y2) is inventory level prior to replenishment at the beginning of period 1 (period 2). The dynamic Programme approach first solves for E{C2(y2)} and Q2 with q, balance of one period thereafter. The result is then used to solve for E{Ca(yi)} and Q{. Using the result of the single-period model with no setup cost earlier found, the optimal quantity for period 2, Q2 can be obtained by solving, p ' d s « > = h T ? 543 Since y2 is given, the resulting optimal policy is given by, Period 2, Policy = (Order Q*z - y2 ify2 < Q2 ( to bring inventory up to Q2) 2(Do not Order ify2 ^ Q2The corresponding cost of this optimal policy isc (y2) . ( S(yx) ify2 > Q2 1c(Q2 - y2) ify2 < Q2 Where S(z) is the expected shortage cost plus holding cost for a single period when the inventory level after replenishment is z. This cost is expressed as S(z) = E{Ct(Q)} = c«? - y) + H JQz(z - D)f(D)dD + p / “ (D - z)f(D)dD For period 1, using the dynamic programme approach, the cost incurred sum of the ordering cost c(Qx - yx), the expected shortage plus holding cost C(Qi) and the cost associated with an optimal policy during the second period. Thus the expected cost following the optimal policy for the two periods is E{Cx{y 1)} = min [c«2x - yx) + 5«?x) + £{C2(y2)} ] Q i = yi Since yx = Qx — Dx is a random variable at the beginning of period 1, then £{C2(y2)} can be obtained from, C2(y2) — C2(Qi — Dx) fS«?! - Dx) i f Q i~ Dx > Qi U W 2 - Q i + Dx) + L«?2*) i f Q l - Dx < Qi This also shows that C2(y2) is also a random variable. Its expected value can be obtained from 544 E{C2(y2)} = f C2(Qi — D )f( D )d D o Qi-Qi = I L(Qi - D) f(D)dD 0 co + f [c«?2 - Q x + D ) + U Q D f m d D ] Qi-Qi Hence, £{Ci(yi)} = minQizyi c(Q i - y O + U Q i) Qi-Qi + f L{QX - D) /(D )dD 0 00 + f [c(Q; - Qi + D ) + L(Q2)f(D)dD] Qi-Qi E{Ci(yi)}has a unique minimum and it can be shown that, Ql , the o- pPtim+ a l( vpa+lu ef of)f/ Q(tO sait)i+sf ie(sC th-e equation,p ) f i . Q { - Q l ) Qi-Qi + CP+W) | / « ? ! - D) f ( D) dD = 0 o The optimal policy for period 1 is thus, 545 Period 1, Policy [Order Ql - yi ifyi < Ql ( to bring inventory up to Qj) ~~ 1 Do not Order i fyx > Qj 3.2.4 STOCHASTIC MULTI-PERIOD MODEL WITH NO SETUP COST The two-period model can be extended to n periods (n > 2) with the same assumptions as used earlier. In order to calculated the expected total cost for the n periods, a discount factor a , 0 < a < 1 will be used. Giving that inventory levely,-, i = 1,2,. . . ,n as level of inventory entering a period i, prior to replenishment, the optimal policy can be generally specified as, Period i, Policy r Order QJ - y( ifyi < QJ to level up to QJ) l Do not order in period i ify( > QJ In addition, Qn < Qn-1 ^ Qn-2 < • ■ • < Q*2 < Q*x For the infinite period case (ie = co ), all critical optimal Q values are equal, Q- = Q ^= Qn-l = Q ; - 2 = • • •= Q*2= Qi It can be shown that Q* satisfies, p - c ( l - a) F m = p + H 3.2.5 STOCHASTIC MULTI-PERIOD MODEL WITH SETUP COST This case is also identical to the single period case with setup cost. In the single period case, also referred to as the (s, S) policy model, s dictates when to order (when the inventory level is less that s) and how much to 546 order to bring inventory level to S level. In the multi-period case, these values may differ from period to period. For the multi-period case, let critical quantity cuts be represented as s4 and for each period i, i = 1 ,2 ,. . . , n while y t is the inventory level at beginning of period i before replenishment. The optimal policy is, Period i, Policy = (Order — y( i f y t < St (to bring inventory up to S [Do no t order in period i i f y t > St Conclusion An exhaustive coverage of all known Inventory Management Models cannot be treated in a chapter of a book. Attempts have been made in this chapter to cover the basic and seminal models of inventory management. The classical inventory models may not account for many practical considerations of the inventory challenges like competitions and the ever changing industry dynamics that Contemporary industries face, in the sense that they were formulated at the product level and not the firm level. However, insights and guides gleaned from the understanding of these basics can greatly enhance the understanding of the basic and rudimentary parts of inventory concems that make the whole and hence contribute to gaining understanding of the dynamics of the entire industry. Interestingly, inventory practitioners and researchers in the field still bend back to the basics to gamer understanding for the basis of the robust models and Systems they work on. Hence, an understanding of these seminal models prepares a practitioner, Student or researcher for the bedrock of inventory issues. Referenccs Badiru, A. B. (1996). Project management in manufacturing and high technology operations. John Wiley & Sons. 547 Badiru, A., Badiru, A., & Badiru. A. (2007). Industrial project management: Concepts, tools, and techniques. CRC Press. Bartmann, D., & Beckmann, M. J. (1992). Inventory control (models and methods). Lecture notes in economics and mathematical Systems. Hillier, F., & Lieberman, G. (2001). Introduction to Operations Research, McGraw-Hill Higher Education ISBN 0072461217. Johnson, S. M. (1957). Sequential production planning over time at minimum cost. Management Science, 5(4), 435-437. Nahmias, S., Production and Operations Analysis (2005). 5lh ed., Irwin, Homewood, EL. Ogunwolu, L., Alli, O. A„ Onyedikam, C., & Sosimi, A. A. (2012). Multi-Item Multi-Period Dynamic Capacity-Constrained Lot- Sizing Model with Parallel Machines and Fuzzy Demand. In Advanced Materials Research (Vol. 367, pp. 627-638). Trans Tech Publications Ltd. Taha, H. A. (2017). Operations Research: An Introduction. © Pearson Education Limited 2017. Silver, E. A., & Meal, H. C. (1973). Production and Inventory Management. Stevenson, W. J. (2005). Operations management. Tata McGraw-hill Vrat, P. (2014). Introduction to Integrated Systems Approach to Materials Management. In Materials Management (pp. 1-19). Springer, New Delhi. Wagner, H. M., & Whitin, T. M. (1958). Dynamic version of the economic lot size model. Management Science, 5(1), 89-96. 548 CHAPTER 23 Redesign of Organisational Structure of a Manufacturing Firm ‘Anyaeche C. O*. and 2Akindele J. O. 1,2 Department of Industrial and Production Engineering University of Ibadan, Ibadan, Nigeria losita.anvaeche@ui.edu.ng. osyanya@yahoo.com 2iiheritage()l @ vahoo.com ’Corresponding Author Abstract The business of managing human resource in an Organization has continued to task the managers’ ability on how to be efficient and effective often done by focusing on the three components of organizational structure involving organisational design, Job and People. This has evolved through theory building of various concepts to the development of structures. Yet the changes in the marketplace suggest the most current approaches lack proven principles and acceptable criteria. This has posed challenges for managers who wish to propose a new structure or determine the level of performance of an existing one. This study is an attempt to adopt a mathematically rigorous approach to redesign an organisational structure of a manufacturing firm using the Operations Research paradigm. The amount of work content was determined using work sampling technique while the number of lowest level personnel (No) computed using the man-hours/available work-hours function. Personnel utilization (H) objective function was formulated in terms of subordinate-superior Consulting rate (X), superior-subordinate attending rate (p) and daily working hours (A) as parameters while span of control (K), number of supervisors/managers (Ni) and number of management levels as design variables were adapted from the literature. The values of X, p were 549 determined using queuing theory and data on A collected from the firm’s records. A management structure design problem was then defined and solved by systematically selecting Ki, Ni and M to maximize H using optimisation approach, and a new structure was proposed. The newly proposed structure was then compared to the existing using t- statistics (a < 0.05). The firm’s operating labour man-hours were 414336; the associated No is 166; the objective function H(A, X, p, Ni, M, Ki) was nonlinear while span of control, number of Supervisors, number of lowest, middle and topmost level managers and the number of management levels were the structure design variables. It was a nonlinear constrained maximization problem. The number of floor personnel (166), Supervisors (34), lowest level managers (9), middle (3), topmost (1), Spans of control {5, 4, 3, 3} and management levels (4) with a maximum personnel utilization (95.29%) were significantly better than the existing (180, 36, 10,4, 1; {5, 4, 3,4}). N22, 103,900, the monthly personnel management running cost favourably compared with the existing 23,903,000 (N I,799,100 being savings per month). It was concluded that the quantitative approach to Organization design is feasible for designing an optimal management structure for a tobacco Processing firm. It is a useful tool for cost reduction and productivity improvement. SECTION 1: INTRODUCTION 1.1 OverView of Organisation Design The business of managing human resource in an Organization has evolved through theory building of various concepts to the development of structures. The changing Organization environment in the marketplace is also tasking the managers’ ability on how to use and manage people, material and time by focusing on the three components of Organization structure i.e. Organisation, Job (tasks/activities) and People. 550 Organisation can refer to an Organised group of people with a particular purpose, such as business or govemment. It also refers to the framework of many interrelated activities taking place in order to achieve set goals, while Jobs are the activities performed in an Organization and are achieved through the functional departments. People, often referred to as the personnel or the manpower have different skills, which are very vital in building an organisational structure. According to Charles-Owaba (2002), personnel has three components: the muscle (source of energy for physical work), brain (essential for decision making, creativity solving difficult problems) and the will power i.e. ability to endure odd circumstances; be resolute on previously accepted principles and decisions). However, despite the will to choose one’s actions, man must be subject to control and management by others, to get the right mix, type, quality and quantity of human power essential for good operations and results. Design is a plan or specification for the construction of an object or System or for the implementation of an activity or process and the result of that plan or specification in the form of a prototype, product or process, (Wikipedia, 2020). A business organizationis an entity formed to carry on commercial enterprise, by providing goods or Services, to meet the needs of the customers. Such an Organization could have different types and forms including Service, merchandising, manufacturing(Lamarco, 2018). The structure of ownership of a business may be a sole proprietorship, partnership, limited liability, Corporation, non-profit Corporation, or cooperative. According to Anyaeche and Oluwanimifie (2011), ownership structure affects not only how businesses are run, but also the organisational structure, the productivity and the reporting relationships among the personnel and their activities. Burton (2013) opine that organisational design addresses two issues i.e. how to divide the organisation's work into small units and how to reassemble those parts into a whole, these may lead to complexity and 551 interdependence. There are engineering approaches for designing of human work environments; however, Information is sparse on similar procedures for organisational structure design Stewart,(1993);Charles- Owaba, (2002); Alberts, (2012); Burton (2020). Kulik and Baker (2008) suggest that a proposed model should be not be limited to the characteristics of the type of Organisation for which development is pursued but also to the influence of extemal factors like the business environment. Business Organisational Structure is chosen mostly through evolution and contingency theories (Charles-Owaba, 2002). The focus of the former is that business evolves naturally, but the latter are contingently designed. Over the years, the evolution theory has dominated the process of organisational structure design, because, it allows a benchmarking approach which enables the business owners to imitate a structure working in one establishment with the hope that it will work in others. Hax and Majiluf (1981) explained that this proposition has appeal because most organisations are too soft and mostly lack a qualitative approach to Organization structure design that would lend itself to mathematical modelling and optimization. However, the business environments’ complexity, dynamism, and ever-changing complicated consumers' characteristics have made a simple selection of structure unappealing. Also, mass customization, global competition, cheap foreign labour, and free trade agreements require dynamic, but consistent organisational transformation (Roberts, 2004) An Organization structure is the accepted working relationship of employees towards the achievement of the primary goals of the establishment (Charles-Owaba, 2002). The structure may be a framework for decision making and the network for transmitting such decisions to the point where they are translated to action. Since Organization structure involves a grouping of related activities into Strategie positions, the number of such positions, their levels, skills-mix, together with prescribed working relationships among positions specify the structure. 552 Literature is sparse on the quantitative framework for developing the Organization structure for Optimum performance Charles-Owaba (2002), Ofiabulu, et eil., (2013a) 1.2 Statement of the Problem With the drive to achieve and retain leadership in business as well as the recent global pandemic, Companies would wish to right size rather than just downsize by reducing their workforce. They need to apply reengineering, job enlargement, and synchronizing roles in developing new ways of doing work, work culture, online work, more virtual work, including mass customization which invariably increases the pressure to satisfy all customers. However, the tools to achieve optimality in these challenges appear sparse, and not readily available.Some scholars Hax and Majiluf (1981), Ofiabuluef ai, (2013b,c), have adopted the quantitative method of organisational design in all their approaches, whereby Organisation variables like personnel utilisations, redundancy, productivity, etc are used as determinantsfor the Organization structuredesign and shapeprove more effective, however, using a quantitative framework to design organizations that will help in addressing these challenges is the thrust of this work. 1.3Study Objectives The main objective of this study is the Redesigning of the OrganizationStructure of a manufacturing firm, which hopefully will be achieved by pursuing the following sub-objectives: (a) Observe the existing organisational structure of a manufacturing firm. (b) Redesign the OrganisationalStructure of a manufacturing firm, addressing the observed gaps, to improve the System. (c) Compare the redesigned and existing organisational structures of themanufacturing firm. 1.4 Scope and Limitations of the Study This study is limited to the re-design of the Organization structure of the production department in a manufacturing Company. Itdoes not include 553 departments like Human Resources, Finance Supply Chain etc. Although Organization structure could take many forms including Hierarchical, matrix, circular, flat, network, team-based, etc._only theorganization structure where subordinates report to and get feedback from their bosses and there may be delay leading to queue formation, is considered. 1.5 Definitions of Terms Here we present some of the terms used in this work. Design: Creation of a plan or convention for the construction of an object, System or measurable human interaction. The six basic elements of organisational structure are departmentalisation, chain of command, the span of control, centralisation, decentralisation, work specialisation, and the degree of formalisation. Departmentalisation (or departmentalisation) refers to the process of grouping activities into departments. Chain of Command is how tasks are delegated and work is approved. In other words, it shows who teils whom to do what, as well as how are issues, proposals, requests are communicated down (instruction) that the ladder and up the ladder (feedback). If a bottleneck appears, a queue is formed and avoidable costs and other consequences. Span of Control indicates who falls under a manager's unit and which tasks fall under a department's responsibility. Centralization involves bringing together as many decision units as possible. A business Organization can lean toward centralised structure, where final decisions are made by just one or two entities; or decentralized, where final decisions are made within the team or department that will implement the decisions. Work specialisation, sometimes called division of labour, refers to the degree to which an Organization divides individual tasks into separate jobs. It involves breaking down complex tasks into smaller, more 554 precise tasks that individual workers can complete and the degree of formalization. The degree of formalization is the extent that roles are independent of specific personal attributes of individuals occupying the roles. Formalization tries to standardize and regulate behaviour. It also is an attempt to make the structure of relationships more visible and explicit (Scott, 1981) SECTION 2: ORGANIZATIONAL DESIGN CONCEPTS 2.1 OrganizationalStructure Design 2.1.1 Mechanistic and Organic Structure Design Organisational structures can be mechanistic or organic. The mechanistic structure represents the traditional, top-down approach, whereas the organic structure represents a more collaborative, flexible approach as shown in figs 2.1 and 2.2. Mechanistic structure Organic structure Fig. 2.1 and 2.2: Mechanistic and Organic Structure Design Source As a Company gets bigger, its organizational structure can also help know who manages what processes and how work flows. This is usually 555 represented by organisational structure diagrams referred to as organogram or Organisation chart. An organisational chart depicts the diagrammatic representation of the people in an Organisation showing their subdivision in various specialisation, departments, or sections as well as the internal lines of authority, Communications, and responsibilities. An organisational structure usually has decision-making centres, Operation centres, and Communication lines as the basic elements. 2.1.2Types of Organization Structures Simple Structure: A simple structure is a design with low departmentalisation, wide spans of control, centralised authority and little formalisation. It is more common in small businesscs with fewer employees. Often employees work in all aspects of the business and just do not focus on one job-creating little, if any departmentalisation. Functional Structure is designed as a cluster of similar or related occupational specialists together. It is the functional approach to departmentalisation established throughout the Organisation. Divisional structure is made up of separate semi-autonomous units or divisions. Within one establishment, there may be many divisions with each division having its own specific goals to achieve. A manager oversees the division and he is responsible for the success or otherwise of it. This enables the manager to direct his energy more on getting results as he is held accountable for his division. The hierarchical structure is a pyramid-shaped Organization chart. It is the most common type of organisational structure—the chain of command goes from the top (manager) down (e.g., entry-level and low- level employees) and each employee has a Supervisor. Hierarchical Organization Structurebetter defines levels of authority and responsibility and shows who each person reports to or who to talk to 556 about specific projects. However, it can slow down innovation or important changes due to increased bureaucracy as well as cause employees to act in the interest of the department instead of the Company. A boundaryless Organisation is not designed by or limited to boundaries and can be horizontal, vertical or extemally imposed by a predesigned structure(Harvard Business Review 2011). It is an unstructured design and flexible because there are no boundaries like a chain of command, departmentalization. Organisation hierarchy to deal with. instead of the department, the Organisation uses a team approach. Galbraith et al., (1978) introduced the matrix type of Organization structure in which a person may report to one or more Supervisors in line with business process Re-engineering (BPR) Organisation structure. This they define as the fundamental rethinking and radical design of business process to achieve dramatic improvement in critical measures of performance such as cost, product quality or develop timely Service delivery. An organisationthat has the capacity to develop and continuously leam, adapt. and change is referred to as a Leaming Organisation. A leaming Organization is skilledatcreating, acquiring and transforming knowledge and at modifying it behaviour to reflect new knowledgeand insights. Some of its characteristics are Systems thinking, personal mastery, mental models, shared vision, and team leaming. Hax and Majiluf, (1981) investigated the possibility of using Operations Research approach for organisational design and opine that the existing theories are lacking in quantitative approach that would lend itself to mathematical modelling. We can therefore infer from the foregoing review that the manager-subordinate ratio and other structural inferences on production deserve more attention than they receive as there has not been a one fit for all model to the Organization structure designs using the concept of span of control. 557 2.2Theories of Organizational Management Theories of Organizational Management include Classical theory, Human relations, organizational and decision making, contingency, Projectized (Babcock and Morse, 2005). The Classical theory States that for good performance, the design of an Organisation structure may have to follow certain universal management principles. The exponents of this theory are the scientific management school of Taylor (1911), Bureaucratic model of Taylor (1911). Given the copious volume of materials on these, readers are referred to Taylor (1911), Charles -Owaba, (2002), Babcock and Morse (2002), for detailed Information 2.3 Attributes and Criteria of Organization structure Drucker (1973) called for systematic approaches to organisational design, while Hax and Majluf, (1981) called for an investigation into the possibility of using the "Operation Research paradigm of theory, for organizational design. The Organization structure design has also been viewed from the standpoint of "fixed workload principle" that is every person in the organization is assigned to aworkload, which is neither overload nor an underload). Although at variance with the concept of small group approach and the Business Process Re-engineering (BPR) concept of Hammer and Champy (1993). Charles-Owaba (2002) shared the view that there is a remarkable difference in the requirement for organisational design and organisational management. In managing an Organisation, jobs may be assigned to group (BPR requirement) instead of individuals as in the division of labour. However, in the design of organisational structure, the designer needs to know the exact number of personnel to run the structure. Even in the Situation of small or large group management approach, there is still the need to know thenumber of personnel per group. This information is required to determine the number of groups to work in the Organisation. Once the exact number to run the structure is known, management may group and train them as deemed fit. Thus the designer 558 may use ergonomics, physics, and mathematical principles to determine the appropriate Standard workload per worker for anorganization, thus by combining such information with the concept of Standard workload per personnel, the correct number of personnel may be easily determined. For more detailed information on Classical principles, attributes, and criteria readers may consult Fayol (1949), Samuel (1996) and Charles- Owaba (1989, 2002). From the above, a very clear contextual framework to define the organisational structure through a mathematical modelling can be proposed 2.4 Queuing Theory Waiting for Service occurs in restaurants, Stores, and post Offices. Jobs wait to be processed on a machine, planes for permission to land, and cars stop at traffic lights. These may form queues and the measures of performance include average queue length, average waiting time in queue, and average facility utilization (Taha, 2007;Hillier and Lieberman, 2007;Anyaeche, et a/2015). Queueing theory is the study of waiting. Not providing enough Service capacity results in excessive waiting and costs. The models enable finding an appropriate balance between the cost of Service and the amount of waiting Queuing and Simulation deal with the study of waiting lines, they are not optimizationtechniques; rather, they determine measures of performance of the waiting lines. Queuing models utilize probability and stochastic models to analyse waiting lines, and Simulation (is flexible and can be used to analyse practically any queuing Situation) estimates the measures of performance by imitating the behaviour of the real System. The main difference is that queuing modelsare purely mathematical. For on this see Taha (2007), Hillier and Lieberman 2007, Anyaeche, et al 2015. To study public establishment is often structurally complex because the number of hierarchical management levels is usually numerous and 559 sometimes difficult to specify and results in low personnel utilisation, high level of ineffectiveness, and inefficiency. Charles-Owaba (1998, 2002) observed that the number of management (decision) levels may be a major factor that determines the Organisation performance (Ofiabulu, 2013d). We use queuing theory instead of Simulation because of our interest. There are different nomenclature and discipline in queuing theory, generally given by the following format: (a/b/c): (d/e/0 where a = Arrivals distribution b = Departures (Service time) distribution c = Number of parallel Servers (= 1,2..... oo ) d = Queue discipline e = Maximum number (finite or infinite) allowed in the System (in- queue plus in-service) / = Size of the calling source (finite or infinite) For this work we use Kendall’s notation with one channel queuing model (Taha 1976, 2007); m/m/l:(FCFS//fi;/K,y) as the corresponding factors. 3.0 THEORETICAL CONSIDERATIONS AND METHOD OF STUDY 3.1 Some elements of organisational structurc a) Decision centre: A position (head of a section) for decision making in an Organisation with the authority and responsibility to make policies, give instruction or prepare procedures for subordinates. b) Operation Centre: These are work centres at the bottom of an organisational structure where the decision taken at decision centres are carried out. c) Superior: One in Charge of a decision centre Interested readers may consult Charles-Owaba (2007) for more detailed information 560 3.2 Organisational Design Charles-Owaba (2002) appliedOperationsResearch techniques to organisational design. He argued that the present-day Organisation could be represented by a quantitative structure that can lead themselves to mathematical modelling for optimal performance. This appears novel. Because of the copious volume of Information on this (Charles-Owaba. 2002), only a summary is presented here. This formulation is adopted in this work for our analysis. 3.2.1 Definition of Symbols Lij Average number of arrivals for Supervisor or manager’s attention in a day at decision or management level i, decision position j. Wjj Average waiting time of subordinates at decision level i, position j Pij Probability of having no one attended to by Supervisor at the decision centre (i,j). A: Available working hours per period for each subordinate and superior. Ky: Number of subordinates reporting to centre j at the ilh level. H y: Human resource utilisation function at decision level i, position j. Lq: Average daily man-hours spent working by a subordinate who left their Workstation to seek information from the superior. Lw: Daily man-hours spent by a subordinate who had no reason to seek information from the boss’ L/,: Daily man-hours actually spent working by the head of unit / superior at decision centre (i ,i). L;: Daily man-hours scheduled for work by both subordinate and superior. H: Human utilization for the entire Organization. N0: Number of Operation positions that perform terminal activities Note: i = 1,2...........M j - 1.2...........N, 561 Xij: Rate at which subordinates at centre j of level i consult the boss at decision centre(ij). IMj'. Rate at which superior’s spent with subordinates at decision centre (y). Pij: Utilisation factor: traffic intensity for system j^j M: Total number of decision levels (hierarchy) Ni: Number of decisions, position at level Position Ni: Number of supervisory positions at level 1 N2: Number of purely decisions or management positions at management level 2. Nm: =1: Chief Executive Position M,Ni,Kjj, Nm: Organisation structure variables N0,A,Xij,/iij: Organisation structure Parameters The total number of hours available for work at a decision centre is the combination of hours of the superior and the subordinates. This work has assumed that the call source is finite and the Queuing discipline of FirstCome, First Served(FCFS)discipline holds 3.2.2 Computation of Human utilization Human utilization (Hy) is defined as the proportion of man-hours actually spent on useful work to the total establishment man-hours provided for work. Mathematically human utilisation is defined as: ^ _ M a n — h o u r s a c t u a l ly sp e n t f o r u s e f u lw o r k i; T o ta le s t a b l is h m e n t ' s m a n — h o u r s p r o v id e d f o r w o r k Man-hours spent for useful work is given by: Lq + Lw + Lj, Total establishment’s man-hours provided for work is given as L z Hence 3.1 but L g = L y ( i 4 y - W i j) 3.2 562 Lw - (Kij ~ Lij)Aij 3.3 Lb = (1 - Pij)Aij 3.4 L z = A g K t j + A (j = A t j f a + 1 ) 3.5 Combining expressions 3.2, 3.3, 3.4, and3.5 into 3.1 17 _ L ij(,A i j - w i j ) + ( K i j - Li i ) A i j + ( 1 - p i j ) A i j A l j (K i j +1 ) 3 JS By mathematical manipulation, expression 2.6 becomes: H, _ 1 lyWij Puij Alj{KU+l) Kii+1 3.7 By Kendall’s notation with one channel queuing model (Taha 1976); m/m/l:(FCFS!/Ky//ftj-), (Taha, 2007, Hillier and Lieberman,2007) L i j = L i j + 1 - P ij 3.8 L u + l-P 3.9 Pij = ( l + l . n l X lJ 3.10 7 _ E*i'2(n-l)c"'n!ej} 3.11 Where e = — na 3.12 Combing expressions 3.8, 3.9, 3.10, 3.11, and 3.12 into 3.7 563 Hu = 1 - Kij + 1 Expressing Htj in terms of decision centre j parameters i and the variables. Hij(KljlA, fi ljXij) = l - Klj+l 3.14 ln expression 3.14, the span of control Ki;- is the only variable since it is the human utilisation in one decision position. The daily work hours A, rate of at which the boss at decision centre (i, j) attends to the subordinate Hij and the rate at which subordinate arrives for consultation Ai;are the Parameters of the organisational structure at decision centre (i, j). For the design of the entire organisational structure which is a combination of all decision position j and decision level i, the human utilisation; 3.15 Where 0h = (A, N0) 3.16 564 The Organisation variables are therefore /Cy, N^andM while the Parameters are 0h(A, Ay, py, N0). The purpose of this study, therefore, is to determine experimental ly in the workplace or establishment the values of Ky, Ay,/iy, andN0 (A is Standard; 8 hours) so that variables Kjj N j and M will be selected to give the maximum possible value of H (Ky, Ni M; (A, Ai j ,H i j ,N 0). This can be stated in the Standard operations research form as: Maximize H(Kij, N j M j ; A Aij, Hi j ,N 0). Subject to Ni i=l Nm = 1 Kij. N„ M > 0 Design Parameters The work sampling techniques, widely applied to monitor the performance of workers, was used in this study basically to find the Parameter values of the Operation position No, and human dynamic Parameter Ay and p y at the decision positions/management level. The sampling method for determining the Operation position No differs from that of the human dynamic parameter Ay and p y for the management level, hence the experiments to determine both parameters were carried out in two phases. Phase one uses the work sampling or activity sampling technique for estimating the work content of each of the existing Operation positions. This method requires fewer man-hours and cost less, than using the other alternatives such as the continuous-time study (Barnes, 1968). Its accuracy depends on the number of observations and randomness. In this study, only the aspect of dealing with the determination of the amount of work content available in Operation positions in the firm was presented. 565 The second phase is to determine experimentally, the values of the human dynamic interaction parameters A[;the rate at which subordinates arrive to consult the boss for instruction, etc; and the rate at which superior attends to the subordinates and ß i j . The parameter personnel interactions or information flow. Relative high values of Ay may mean inexperienced personnel who would want to see the boss frequently for more clarifications, a complex job Situation while low values of Ai;- may mean experienced personnel who may have only a few cases for the attention of the boss. High values of p y might mean an experienced boss who is naturally fast or also be that the problems taken to the boss for Solutions are relatively simple. Low values of piy- might mean supervising personnel with complex tasks, experienced personnel with complex tasks, an inexperienced or lazy boss who takes a longer period per subordinate who reports to him. To solve the problem of redesigning of the organisational structure using the quantitative approach of work sampling technique, the procedure includes the following: i Determination of the amount of annual work available at Operation positions by using the expression below; N o . o f S t a f f ( o p s p o s i t i o n ) G r a n d t o t a l S t a n d a r d m a n - h o u r p e r a n n u a l - ( C h a r l e s A v a i l a b l e h o u r s x u s e f a c t o r — O w a b a 2002) ii Determination of Parameter set d2 = C41( Ap n{) iii Optimal span of control iv Analysis of optimal personnel utilization, size, and shape 3.4 Procedure for determining the number of Operation positions .(No) The following steps were used for phase 1 of the study to collect and analyse the data for the Operation position No. 566 Step 1 All the Operation positions of the production departments of the manufacturing firm taken from available records. The respective positions were visited and a route was mapped out for taking an Observation of workers to ascertain the busy or not busy Status of each Operation position. Step 2 The data collection form was designed to reflect the departments and sections where the study was carried out. Step 3 The preliminary number of observations to determine the study Parameter, P, the proportion of time an observed staff was found busy on the paid job was carried out. At this preliminary number of observations, only few of the positions were randomly picked and twenty observations were carried out for each Operation position to determine P. The value of the study parameter was then determined by the expression. p _ Number o f tim es s t a f f were fo u n d busy ^ 2 j Total num ber o f observations fo r all o b se rve d sta ff Step 4 At this stage, the number of observations N for the actual study was computed using a desired accuracy or level of confidence (A). The number of observations N was modelled as follows: Let; N = Number of observations A = Desired relative accuracy K = number of Standard deviations away from the mean Hence, Ip ( i - p ) N _ k H i - p ) A2P 3.22 For most purposes, Bames (1968) observed that with K=2, A=5% a confidence limit of 95% is adequate. In this case expression, 3.22 becomes: N = 4 [!z£l = 1600(1—p) (0.05)2 L P J P 3.23 567 The recording form was filled in the appropriate space, for date, department or section, the Start time and names of positions to be observed. At each position, the foilowing was noted and recorded as soon as each observation was concluded: • Busy or not busy mode • Performance rating of the individual At the end of each study day, the number of busy modes for each position was counted; the total number of observations and end of study time was also recorded. Also determined was the average performance rating for each position. Step 5 The data analysis in the information conducted in Step 5 was carried out at this stage and the foilowing quantities were computed: • Utilisation factor (/i,) for each position i • Estimated Annual Man-Hours E A M t • Estimated Basic Man-Hours, (EßM,) • Estimated Standard Man-Hours (ESM*) The expressions that follow were then used to compute the Total Annual Standard Man-hours (TAM). N u m b e r o f o b s e r v e d b u s y m o d e f o r p o s it io n i1 1 to ta l n u m b e r o f o b se r v a t io n s E A M ( = U ix A v a ila b le h o u r s o f w o r k in the y e a r P erform ance Rating in Positions i E B M i - b A M i X ----------------------------------------------- — E S M , = E B M iX 3.25 where PAi is percentage allowance for each type of job done in position i T A M = J % s l E S M l 3.26 The number of Operation position No is thus; ^ _ Total S tandard m a n -h o u rs per annum 0 available hours x use fa c to r 3.27 568 3.3Investigation of organisational structure of the selected firm: Case Study The selected Organisation for this study manufacturers and sales Tobacco in Nigeria. This Company has an investment of $150million in2001 through foreign direct investment agreement. The investment is an integrative activity that impacts on all aspects of the tobacco business from leaf growing, through manufacturing to the distribution of tobacco products.The Company has two factories in different locations in Nigeria and its stable arethe populär brands and many more products. Scope and Limitation of Study This study was carried out to redesign the Organization structure of production department of a Tobacco in Nigeria, this study would not include other departments in the Organization like Human Resources, Finance Supply Chain etc and henceit is focused on production, so the Service sector like education institutions, Consulting firms or construction firms are not included. An investigation carried out showed that the existing structure is made up of four; decision levels; supervisory positions (36); lsl level managers (10); middle-level manager (4); Top-level executive (1); and the Operation positions (180). The existing Organization structure isas in figure 3.1. The following categories of workers can be identified Manufacturing Manager (MM) Pry Manufacturing Department (PMD) Secondary Manufacturing Department (SMD) Cell Manager (CM) Shift supervisor/Tech Support (SS) Technician (TECH) Operators (OPS) 569 The first phase of the study was carried out to determine the number of Operation position No, which is one of the parameters of Organisation structure. The Operation positions are labelled Pi to Piso. Other information about the Company include the following: The annually available man-hours were deduced as follows: The Organisation runs through the year, but the personnel work an average of 48hrs per week running 3 shifts per day and work 52 weeks per annum including public holiday. Hence, the available Man hour per annum = (48x52) = 2496 hours per annum 1. The Organisation works through the year running 24hours daily. 2. The personnel work in a shift with variant schedules, for instance, some work 12hrs daily running 2 shifts, others work 3 shifts with shift schedule 7-7-1 Ohrs. However, each personnel work average of 48hrs per week and 52 weeks in a year. 3. The percentage allowance. PA=0.15 4. The factory utilisation factor, Ui=0.8= 80% 5. Hence, the available Hour = 48x52= 2496 Man hours. Since the use factor = 0.8 , then K= 2496 X0.8 The data to determine the number of Operation positions N0, was gathered for 5 days at 10 trips per day for each identified Operation position. The total observations were 50 observations. The Organisation operating parameters such as described above, was applied to the work sampling expression 3.4, 3.5, 3.6 and 3.7. An excel application package was used to perform the computation for Operation position 1 to position 180, that is Pi to P180- The outcome of the analysis is presented in Table 4.1 570 Note: Although, there are three shifts, some workers work two shifts while other work three shifts. In order to have a fair engagement, every worker works for 48 hours a week. Also, it is assumed that Weekends, public holidays, leave must apply. To account for this the Company allows a 15% personnel allowance. Furthermore, a fair structure should allow every boss to have same number of subordinates. This work also assumes a fair structure. These are the applicable Situation in this firm. Other organisations may have different arrangements and theirs would apply in the design and analysis. It is enough that the structure is fair and the work content properly captures and distributed. FIGURE 3.1: EXISTING ORGANOGRAM E3 S ^ . a p wmm föfre si ® m m na m m - ■ffrP'W ' ^rP'■P'— -iw» H w» 1 S S t 571 O 3.4 Re-design of Procedure organisational structure understudy 3.4.1 Determining the human dynamic parameter (Ay and /ly) In the second phase of the study, the human dynamic interaction Parameters Ay and /iy were determined using the following steps as depicted below: Step 1 The study period was picked to cover low, moderate and peak levels of activities. Step 2 The time study commenced at each decision position j , level i was noted and recorded. Step 3 As each subordinate arrived to consult the Supervisor, it was noted whether the subordinates waited and received attention from the boss. The total number of cases at position j of level t, was taken as TNCy . The Observation taken was either an immediate boss to a subordinate interaction or a subordinate to a boss interaction. Step 4 The amount of time the personnel occupying position j , level i spent attending to each case was noted and recorded. Let the time for case a be tjja . Step 5 The completed cases were counted within the study period and labelledTCCy (Total completed cases). Step 6 The total working time (hours) spent observing the activities at the decision position of interest was recorded and this was taken as 7TSy (Total time of the study). Step 7 The values of Ay and /iy are then calculated thus, T n tn l rtiim hpr n f the* rnce* n t nnci'fi’nn ( i H _ T■N C( ji ij ~ TTStj Time(,hours) spent to trea t all com pleted cases 3.29 For a fair organisational structure where the span of control is assumed to equal for each decision position at the same level, let /q be the case 572 completion rate at level i and Ay ; the arrival rate. These values may be estimated at the mean values of /iy and Ay respectively. Hence, Hi = S r = iuO/Ni and Aj = ^7 With A/0, A,- , jq and A known, the variable M, Ni and Kij can now be picked from the human utilization Table (Charles-Owaba 2002) for the design of the organisational structure. SECTION 4: APPLICATIONS, RESULTS, AND DISCUSSION The first phase of the study was carried out to determine the number of Operation positions No, which is one of the parameters of Organisational structure. The Operation positions are labelled Pi to Piso. Vital information about the Company operating System was collected and included the following: 6. The Organisation works through the year running 24hours daily. 7. The personnel work in a shift with variant schedules, for instance, some work 12hrs daily running 2 shifts, others work 3 shifts with shift schedule 7-7-10hrs. However, each person works average of 48hrs per week and 52 weeks in a year. 8. The percentage allowance PA=0.15 9. The factory utilisation factor, Ui=0.8= 80% 10. Hence, the available Hour = 48x52= 2496 Man hours. The data to determine the number of Operation positions N0 werecollected for 5 days at 10 trips per day for each identified Operation Position. The total observations were 50 observations. The Organisation operating parameters described above were applied to the work sampling expressions3.24, 3.25, 3.26, and 3.27to compute for Operation positions 1 to 180, which is Pi to Pigo. The total man-hour per annum, being the Summation of required man-hour for each identified Operation position was 333,025.6hrs. 573 4.1 The number of Operation position No. Two scenarios are considered here at 80 % and 100% utilization use factor respectively as shown as it Table 4.1 From expression 3.7. we have that —__T_o_t_al_ _S_ta_n_d_a_r_d_ m__a_n_ h_o_u_r p__e_r _a_n_n_u_m_ _ 0 Annual available man hour x use factor For P , . N0 = 1840 + 1932 + 2185 + 1584.125 + 2021.125 + 1474.875 + 2021.125 + ________________ 1911.875 + 2021.125 + 1584.125________________ 2496 x 0.8 = 9.3026 By fractional man principle and agreement between the management and the in-house onion, >0.5 is taken as 1.0, while <0.5 is rounded off to 0.0. Hence, Wi_io = 9 personnel at 80% use factor. For 100% the value is 7. The above procedure of computation of Operation position in 4.1 was repeated for other Operation positions fromP11_180as well as for both 100% and table 4.1 was deduced. Table 4.1: Proposed Operation positions No. Poi I(Not) «=iat 80% Z(No») u a t 100% 1 Pl-10 9 7 2 Pl 1-20 9 7 3 P2I-30 9 7 4 P31-46 14 11 5 P47-67 19 15 6 P68-90 21 17 574 7 P9 1 - 1 2 2 28 23 8 P|23-I38 15 12 9 Pl39-I60 21 17 10 Pl6M80 21 17 TOTAL 166 133 The total Operation positions Top80% = £"=1(/Voi) =9+9+9+14+19+21+28+15+21+21=166 The total Operation positions Topl00% = Ey=i(^oi) =7+7+7+11+15+17+23+12+17+17= 133 The implication is that the Company can operate at either 80% or 100% use factor. 4.2 Determination of Äü and f i t t at Supervisory level and Managers The study for determination of both Aü and Hu was carried out in 3 days for each decision level. A total of 9, 10, 11 and 11 hrs respectively were used as study hours. while 6.4,5.2,5.06 and 6.28 hours respectively were observed as consultation hours. Total number of cases who arrived for consultation was 45 while only 40, 32,33 and 33 cases actually consulted at each level. The data computed and analysed and the result presented in the Table 4.2 The summary of analyses of human dynamic interaction at the supervisory. Ist level management, the middle level and Top-level management is shown in the table 4.2a: 575 Table 4.2a: TheHuman dynamic interaction at decision levels Criteria Supervisor l 5* level Middle Level Topmost level Manager Manager X 5.0 4.5 4.09 4.09 M 6.25 6.06 6.5 5.25 Ki* 4 4 4 4 Hi* 0.9621 0.9612 0.9633 0.9565 Table 4.2b: The Human dynamic interaction at decision levels Criteria Supervisor l s* level Middle Level Topmost level Manager Manager X 5.0 4.5 4.09 4.09 ß 6.25 6.06 6.5 5.25 Ki* 5 5 5 5 Hi* 0.9621 0.9612 0.9633 0.9565 4.3 Span of Control at decision levels The first phase of the study gave the total number of proposed Operation positions for the new organisational structure as 166. The span of control at the supervisory Ki* as shown in the Table 4.2a.is Ki*= 4. Hence, the required number of Supervisors, Ni* to oversee the N * 1 166operation positions is N f = -7 = — = 33.2 = 34 Ki 5 The number of First Level Manager required to direct the affairs of the Supervisors with value of N f =34 and Span of Control K2*=4 is deduced as follows: 576 N: 34 Wz = kJ = T = 8,5 “ 9 Hence, 9 first level managers are to oversee the 34 Supervisors. The number of middle level manager to oversee the first level managers with span of control Kj=3 is thus n ; 9 N ; - r r 5 = 3 Therefore, 3 middle level managers would oversee the affairs of 9 first level managers. The Top executive position N4 with span of control K%=3 is thus; n ; 3 " : = f r 3 = 1 4.4 Computation of proposed Personnel Utilisation Personnel utilization, H* is calculated from expression 3.15 as H'(K N m 0 Where 0n = (A.jjj, m, N0). Thus, from expression 3.16 W * W,*(K;.A.Ai,u1) + (W2-x H-20C2,A ,\2. il2) + (N I x H2(K’3,A.X3, n3) H. = _________________ +(n; x h 'a(k; ,a,A4,h4)_________________ N, + N2 + N3 + N< 34(0.9513) + 9(0.9612) + 3(0.9467) + 1(0.9512) 38.5584 34 + 9 + 3 + 1 “ 41 = 94.04% 34(0.9513) + 9(0.9612) + 3(0.9467) + 1(0.9512) 38.5584 34 + 9 + 3 + 1 “ 41 = 94.04% Now, the size and shape of the Organisation is computed as follow, while the proposed Operation positions stood at 166, the required Supervisors were computed as 34. The Ist level manager to oversee the 577 Supervisors would be 9, even though computed at 8.5, but a fractional man principle applies here, so the required Ist level manager was taken at 9. The middle level management is 3 as the span of control for each manager was taken at 3 for optimal performance. Finally, the top-level management requirement is 1 as his span of control was 3. From the above, the size and shape of the Organisation is as follows; S*(size) = N0 + A/j + N2 + N3 + A/4 = 166 + 34 + 9 + 3 + 1 = 213 The height of the Organisation M* = 4 The width of the Organisation, Z = (Ni + N2 + N3 + N4)/M* 34 + 9 + 3 + 1 “ 4 = 11.75 = 12 (to the nearest whole num ber) The organisational structure is thus given as G= (5 M*Z) G= (213.4,12) This in matrix is given as: r4 l i 3 3 2 9 1 34 LO 166-1 This is the proposed organisational structure for the firm 4.5 A comparative analysis of Existing and proposed Structure A comparative analysis of existing and proposed personnel utilization at the decision levels was carried out to know the impact of the redesign of the organization.The personnel utilization and respective human dynamic interaction were computed for both existing and proposed Organization structures and results presented in the Table 4.3. 578 Table 4 3 showing a comparison of Existing and Proposed structure Criteria Existing Proposed structure Structure Operation Position 180 166 Supervisor (span of control) 36(5) 34(5) l a Level Managerfspan of 10(4) 9(4) control) Middle Level Managerfspan 4(3) 3(3) of control) Top Level Manager (span of 1(4) 1(3) control) Human Utilization Factor 0.9529 0.9404 4.5.1 Grouping of Operation positions into Supervisory tasks The Operation positions have been reduced from 180 to 166 personnel and consist of both Machine operators. Mechanical technicians and Electrical technicians; and they are to be superviscd by 34 Supervisors from the existing 36 Supervisors. Hence, the grouping of Operation position into supervisory tasks is as shown in the table below: Table 4.4: Grouping of Personnel into Supervisory tasks. S/N S u p erv iso rs N o o f O p e ra to rs N o o f T echnicians 1 Mech 1 3 2 2 Mech 2 3 2 30 Mech 2 3 2 31 Elect 1 4 579 34 Elect I 4 TOTAL 34 90 76 The proposed organisational structure is shown in figure 4.1. All positions are represented in the proposed Organogram 580 FIO 4.1PROPOSEO ORGANOGRAM KEY: 1 581 4.5.2 Grouping of Supervisors into the Is t level management tasks 34 Supervisors are being proposed for the new organisational structure and 9 first-level managers are to oversee their activities. It should be noted that the existing Ist level managers were 10 personnel while 9 was being proposed. Hence, their grouping follows this trend as shown in Table 4.5 below: Table 4.5: Showing Supervisory personnel grouping S/N Ist Level Manager No of Supervisors 1 Electro Tech 14 2 Mechanical 2 4 9 9 2 TOTAL 9 34 4.5.2 Grouping of Ist Level Manager into Middle-Level Managerial Tasks In the existing organisational structure, 4 middle-level managers oversee the activities of 10 Ist level managers. This is a case of underloading of personnel and this will affect their productivity. However, in the proposed structure, the middle-level manager was computed to be 3 personnel to oversee the activities of the 9 first-level managers. Each middle-level Manager oversees the activities of 3 first-level managers. 582 4.5.3 Grouping of Middle-Level Managers into Topmost Executive There is only one existing topmost manager and in the proposed Organization structure. the number was retained. Hence, one topmost manager is to oversee the activities of the 3 middle level managers. Table 4.7 Comparison of Cost Implications of Rcdesigning the Organization Structure Position Existing Structure Cost (N) Total Proposed Structure Cost Total Diffcrencc (Desired Rcduction) Ops Position 180 95000 17100000 166 95000 15770000 14 Supervisors 36 122000 4392000 34 122000 4148000 2 Ist level Manager 10 205000 2050000 9 205000 1845000 1 Middle-Ievel Manager4 285000 1140000 3 285000 855000 1 Topmost Manager I 310000 310000 1 310000 310000 0 Total24.992.000 22.992,000 22,928.000 2,064,000/month From the above cost analysis table. in 12month, N (2064000) x 12 N24768000 would be saved. Meanwhile, if the allowances and other emoluments were considered, more money would be saved by the newly proposed organisational structure, implying more profits for the business as the recurrent expenses would decline substantially. 4.6 Discussion of Results The data gamered from the work sampling on the shop floor indicated that there should be changes in the number of operations in the proposed structure. Also, the values of the human dynamic interaction deduced at the hierarchy of the Organization as shown in Tables 4.2 and 4.3 showed disparity in the span of control of the supervision even though, the span of control of Supervisor at the existing structure was 5, but the scope of work did not justify the number of Operation position. Hence, the span of 583 control for Supervisor, Kl still remain at 5, while the number of Supervisors is reduced to 34. The Ist level manager position was also reduced from 10 to 9, with a span of control K2=3 retained. The middle-level manager in the existing structure seemed to be underloaded, while 4 of them managing 10 lower level managers-, 2 of these managers were underloaded. However, this has been corrected in the new structure with the number of middle-level managers reduced to 3 and a span of control of K3=3. The topmost manager was overloaded in the existing structure with a span of control of 4, but the new structure would afford the topmost manager to supervise only 3 middle-level managers. In all, the human utilization of the proposed structure is almost in tandem with the existing, but with a lower headcount and consequently, cost implications. The benefits of this redesigning are more pronounced in the logical arrangement of the personnel and the monetary value of about 724,768,000 per annum this is excluding another emolument like allowances and estacode.Finally, in the proposed structure 18 personnel were redundant and the rest working with an ideal span of control. SECTION 5: CONCLUSION AND RECOMMENDATION 5.1: CONCLUSION The feasibility of applying a quantitative approach to redesign a tobacco Processing firm was demonstrated. The firm's annual work content was observed and the number of lowest-level personnel determined. Personnel utilization mathematical expression was given in terms of Organization design variables and parameters and applied as the design 584 objective function. The firm's organizational design problem was then defined and solved using the Operations Research paradigm. The redesigned proposed structure compared favourably to the existing Organization structure. Based on this, the following conclusions were drawn: The existing Organization structure has four management/supervision levels, thirty-six Supervisors, ten first line and four middle and one higher manager with a monthly running cost of N23,903,000 The firm's mathematical model of an operating Organisational structure indicating personnel utilization (H), human dynamic parameters (?, ?), daily working hours (A), number of manual workers (NO), number of Supervisors (NI), number of managers (Nij) per level, their respective span of control (Ki) and number of management levels (M) was established. The optimal Organization structure showing N0=166; NI =34; N2=9; N3=3; and N4=l; H=96% with N22,103,900 monthly running cost was derived. The redesigned outperformed the existing Organization structure. 5.2 RECOMMENDATION The personnel utilization function, the complement of personnel redundancy, were taken as organisational design performance measures. 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New York Wikipedia (Sept 22, 2020) https://www.google.com/url7sa 589 CHAPTER 24 Anthropometric Evaluation of Bus Drivers And Their Workstations S. O. Ismaila1*, S.A Odunlami2, S.I Kuye3, A. I. Musa4, T. M. A. Olayanju5, A. P. Azodo6 O. A. Adeaga7 1'Department of Mechanical Engineering, Federal University of Agriculture Abeokuta, Nigeria 2Department of Mechanical Engineering, Federal Polytechnic, Ilaro, Nigeria 3Department of Mechanical Engineering, Federal University of Agriculture Abeokuta, Nigeria 4Department of Mechanical Engineering, Moshood Abiola Polytechnic, Abeokuta, Nigeria 5Department of Agricultural and Bio-Resources Engineering, Federal University of Agriculture, Abeokuta, Nigeria 6DepartmentofMechanical Engineering, Federal University of Agriculture, Abeokuta, Nigeria 7Department of Mechanical Engineering, First Technical University, Ibadan, Nigeria *Corresponding author: ismailaso@funaab.edu.ng Abstract This study conducted an anthropometric evaluation of bus drivers and their Workstations in Southwest Nigeria. Thirty (30) anthropometric measurements were obtained from one hundred and fifty (150) commercial bus drivers. The assessment of the structural dimensions of their workstation was from two categories of buses, mini-buses, and midi-buses from ten different models of buses predominantly used for public transport in seven urban centers in three Southwestem States of Nigeria. The data collection instruments for this study were a stadiometer, digital Vernier caliper, a 3.5m stainless Steel retractable 590 tape, and a universal bevel protractor. Analysis of the anthropometric variable of the drivers showed that human body characteristics varied across different tribes, locality, and nation. The results of the analysis showed that drivers’ Workstations in the commercial urban buses used in South-Western Nigeria did not ergonomically fit the urban bus drivers in the region. This study concluded that there were mismatches between the drivers’ anthropometric variables and the design measurements of the present driver workstation. There is a need to consider the human body anthropometric variables of the drivers in the nation at the design stage of the vehicles for safe occupational health, work efficiency and performance. Keywords: anthropometry, ergonomics, workstation, drivers, buses, Nigeria 1.0 Introduction Realyväsq seeuez-Vargas et al. (2020) described workstation design as a strategy to increase human factor performance and productivity. Inadequate workstation designs in automobiles represent an occupational risk factor of drivers (Realyväsquez-Vargas et al., 2020; Samuel et al., 2016). The workstation design determines the adoption of work posture, the concentration, work performance, and well-being of the drivers (Kushwaha and Kane, 2016). Studies revealed that poor design of workstations results in fatigue, loss of concentration, increases probability of mistakes, affects comfortable work postures, imposes musculoskeletal disorders, and consequently, affects work performance and well-being of workers (Kushwaha and Kane, 2016; Yeow et al., 2014). Accumulated risk of chronic injuries, discomfort, and muscle movement disorders development in Professional drivers from their work ■Station negatively influences their personal and Professional lives (Okunribido et al., 2006; Sadri, 2002; Bemard and Putz-Anderson, 1997). The impact of physical pressure from the work conditions on the musculoskeletal System of drivers depends on the driving hours and the working conditions (Jensen et al., 2008; Okunribido et a l, 2006). The design, features, and manufacture of automobile operator’s workstation 591 determine the level of comfort, safety, and performance of a driver in the workspace envelope (Samuel et al., 2016; Onawumi and Lucas, 2012). The human factor and vehicular performance requirements misfit in the workstation of the drivers can lead to fatal accidents, resulting in loss of life, motor vehicle, and properties contained in it (Igboanugo et al., 2002). Phillips (2000) opined that the human biological System is significant in vehicle-related road accidents. One of the ergonomic risks and the peculiar challenge to drivers in Nigeria is in the drivers' workstation. Studies revealed that the design of these vehicles was without the anthropometric data of Nigerians (Onawumi and Lucas, 2012; Ismaila et al., 2010; Igboanugo et al., 2002). The use of these vehicles deprives the vehicle users in the nation the user-friendliness of vehicle, forces people to be fitted into the non-fitting technological Systems that are available in the market (Onawumi and Lucas, 2012; Igboanugo et al., 2002). Studies revealed that the mismatch between the vehicle drivers and the Workstations of the vehicles imported and used in Nigeria is a potential contributor to health risks experienced by the drivers (Onawumi and Lucas, 2012; Igboanugo et al., 2002). Ismaila et al. (2010) added that the Workstations in these vehicles, especially, the seats are designed or redesigned locally based on the assuinptions of the local manufacturers, often without consideration to the users' safety and comfort. This challenge was buttressed by Lucas and Onawumi (2013), who observed poor design and mismatches between the anthropometric characteristics of the drivers and in-vehicle requirements of automobiles imported into Nigeria. The integration of anthropometric design in the Standardization of Workstations facilitates the sustainable development of a workplace (Realyväsquez-Vargas etal., 2020). The consideration of anthropometric variables at the onset design of the workstation accounts for the measurement and the characterization of the human body (Lee and Krause, 2002). Anthropometry in workstation design establishes the physical geometry, mass properties, and strength capabilities of the human body for the development of Standards and evolving of specific demands associated with the product manufactured, product usability 592 enhancement, and suitability for the user population (Samuel et al., 2016; Agrawal et al., 2010; Del Prado-Lu, 2007; Muzammil and Rizvi, 2007; Caragliu, 2006). The application of human anthropometry in the design of a workplace is through evaluation of work postures, making of a detailed specification of the relationship between the control point and the workstation. and analysis of forces and torque of the human Operation at work (Hertzberg, 1972; Pheasant, 1986; Del Prado-Lu, 2007). Samuel et al. (2016) opined that the least expectation from an ergonomically designed workplace is an accommodation of a large ränge of users typically between the 5th and the 95th percentiles of females, and males. The design or redesign of any workstation by considering anthropometric variables of the workers improves the body posture and reduces the risk of WMSD (Colim et al., 2019). Other studies added physical suitability of workplace design and enhanced sustainability as benefits of anthropometric variables in workstation design (Kim et al., 2017; Nadadur and Parkinson, 2013). Considering the variability among people of a different race, tribes, and nations, correct use of anthropometry in workstation redesign influences the postures and improves the well- being, health, comfort, and safety of operators (Realyväsquez-Vargas et al., 2020; Hitka et al., 2018; Gaudez et al., 2016). Tailoring the anthropometric database towards the implementation of design for drivers’ Workstations should involve a defined representation of the drivers, researchers, information scientists, and manufacturers (Samuel et al., 2016). Studies affirmed that anthropometric variables of a specific population is necessary for an ergonomic suitability determination of a product and a workplace (Ismaila et al., 2010; Agrawal et al., 2010). In this way, the mismatches between drivers’ anthropometric characteristics and the workstation requirement observed by Lucas and Onawumi (2013) become addressed. Anthropometric variables and ergonomics principle in the design of a workstation, in the light of global industrialization, guarantee a reduction of human error in System performance, minimization of workers hazards in the work environment, a decline in the adverse occupational health effects on workers, and an enhanced System efficiency (Anema et al., 2004). Evaluation of the workplace health and safety through match analysis 593 between the anthropometric variables of workers and Workstation is essential for the reduction of work-related illnesses and injuries incidence (Del Prado-Lu, 2007). The anthropometric evaluation of drivers and their Workstations in Nigeria demands an ergonomics approach in the design of automobile used in the nation, serve as a survey for the manufacturers on the health and work issues on their product, the legislation regarding the importation of vehicles into the country, and for an enhanced Workstation and performance of commercial drivers (Nishint and Apurava, 2015; Onawumi and Lucas, 2012; Del Prado-Lu, 2007). The above factors are the terms governing the concept of this study as it evaluated anthropometric variables of Nigerian bus drivers and their Workstations in South-Westem Nigeria. 2.0 MATERIALS AND METHOD 2.1 Data collection Instruments for the study The instruments used for data collection include Stadiometer, (model PD300DHR, Cardinal scale manufacturing Company, UK) (Fig 1) is a digital height and weight measurement device. It also calculates the body mass index. It has maximum capacity of 220 kg with an accuracy of 0.1 kg. Digital Vemier Caliper (model Mitutoyo 500-506-10, Mitutoyo Corporation, Japan) (Fig 2) is digital precision device for linear measurement of inside and outside diameters, depth, and step of items of objects. it has a measurement ränge of 0 to 600mm, resolution of 0.0005" (0.01mm), and an accuracy of ± 0.05mm. A 3.5m stainless Steel retractable tape (Model TU-3516, Komelon, U.K) (Fig 3) is linear measuring device made of stainless Steel. It has a measuring ränge of 0 - 3.5m A universal bevel protractor (model Mitutoyo 187-906, Mitutoyo Corporation, Japan) (Fig 4) is an angle and linear dimension measuring device. It has a 12 inches vemier scale for resolution of 5 minutes. The angle measurement can either be in clockwise and counterclockwise directions, with a measuring ränge of 3 x 90 degrees. 594 Fig 1. Stadiometer Fig 2. Digital vemier caliper Fig 3. Stainless Steel Fig 4. Universal bevel protractor retractable tape 2.2 Collection of anthropometric and Workstation variables The data collection for analysis in this study involved human anthropometric variables of Professional drivers and the design specifics of their Workstations. Thirty (30) anthropometric variables were collected 595 frotn one hundred and fifty (150) Professional male drivers in seven urban centers (Abeokuta, Ilaro, Sagamu, Ijebu-ode, Oshodi, Yaba, Ibadan, and Oyo) in three South-West States (Lagos, Ogun and Oyo States) of Nigeria. The data Collection was carried using a random sampling technique. The details of the anthropometric variables assessed are presented in Table 1. The drivers’ workstation assessment was carried out on fifty (50) buses used for urban transportation in the study area. The workstation assessment was based on the use of the dimensions of the Workstations relevant to the body anthropometry of the drivers. The buses considered and assessed were in two categories. Category ‘A’ comprises of six vehicle models of urban mini-buses. The models were Mitsubishi, Toyota- coaster, Mazda, Honda odyssey, and Nissan-Urvan. Models of buses assessed in Category ‘B’ were midi-buses from four different models Foton, Ashok, Tata, and Comil. The selection criteria for the buses were that they were predominantly used for both inter- and intra-city transportation in the urban centers in South-Westem Nigeria. Measurement of the workstation parameters and the seat dimensions in all selected buses were done. Table 1: Anthropometric parameters of urban bus drivers and their relevance S/N Human body variables Relevance drivers’ workstation part Pi Stature Cabinet total height P2 Sitting height Seat backrest height P3 Eye to floor Seat pan height from cabin floor P4 Shoulder width Seat backrest (thoracic level) width P5 Shoulder height Seat backrest height P6 Shoulder to elbow Armrest placement height P7 Knee height Steering wheel height from floor P8 Popliteal height Seat height and pedal placement P9 Foot length Pedal placement from SRP P10 Foot width Pedal width P li Hand length Steering wheel rim thickness 596 P12 Hand breath Armrest surface width P13 Chest width Steering wheel diameter P14 Elbow angle with Steering wheel distance from SRP steering P15 Elbow angle with gear Gear-lever distance from SRP P16 Popliteal angle (leg on Placement of pedal floor) P17 Foot angle (leg on Placement of pedal pedal) P18 Back angle (sitting) Placement of steering wheel P19 Hip width Backrest width P20 Stomach depth Steering wheel placement P21 Knee length Seat distance from steering rack P22 Head width Headrest width P23 Head height Headrest height P24 Stomach to steering Steering rack placement P25 Popliteal length Seat depth P26 Elbow to wrist Steering wheel placement/armrest P27 Chest to steering wheel Steering wheel placement P28 Knee to dashboard Placement of seat from dashboard P29 Knee to steering rack Placement of seat P30 Arm length Placement of steering wheel 2.3 Procedure for Statistical Data Analysis The dimensions of the interior compartment of drivers' Workstation of category A (mini-buses) and category B (midi-buses) were analyzed using Microsoft Excel Starter 2010 and SPSS 20.0 to obtain the mean values, Standard deviations, 5th, 50th, 75th, and 95th percentiles. Independent sample t-test analysis was used to determine the mean difference of the anthropometric variables and dimensions of the interior compartment of drivers' workstation of the category A (mini-buses) and category B (midi-buses) at a confidence level of 0.05 for significance. 597 3.0 RESULTS AND DISCUSSIONS 3.1 Human body anthropometry analysis of the bus drivers Table 1 presents the anthropometric variables of the urban bus drivers and their relevance. The summary of the anthropometric variables of the one hundred and fifty urban bus drivers assessed in this study is presented in Table 2. The anthropometric variables guide the physical geometry, mass properties, and strength capabilities of the human body for the establishment of the Standards and the specific demands for the commercial bus drivers' workstation design. The evaluation carried out in this study was with respect to the work postures which will guide in providing a detailed specification of the drivers' control point in the workstation. Table 2 shows that the mean stature of the drivers was 173.15 cm (SD = 3.32) while the average mean of their sitting height was 83.18cm (SD = 4.52). The 5th and the 95th percentiles represented the minimum and maximum expectations from an ergonomically designed drivers’ workstation (Samuel et al., 2016). The extreme statures of the drivers that the buses accommodated using the 5th and the 95th percentiles were 168.8 and 179.1 cm respectively. The extreme sitting height of the drivers was 76.9cm for the 5th percentile and 90.0cm for the 95th percentile. The anthropometric variables in this study were within the average ränge of the anthropometric variables obtained by Samuel et al. (2016). The sitting height determines how high the head of the driver is from the sitting position. Studies showed that inadequate space for sitting height of the driver's workstation contributed to neck pain through awkward bending of the neck (Funakoshi et al., 2004; Okuribido et al., 2007). Table 2: Summary of the anthropometric variables of Nigerian male urban bus drivers (N = 150)___________________________________ S/N Variable Mean SD Min. Max. Percentile 5th 50th 75lh 95th PI Stature 173.15 3.32 166.00 180.00 168.80 173.00 175.50 179.10 P2 Sitting height 83.18 4.52 74.00 91.00 76.90 83.00 86.25 90.00 P3 Eye-Floor height 73.40 5.23 50.00 88.00 60.00 77.00 81.00 83.15 598 P4 Shoulder width 44.50 3.25 39.00 51.00 40.00 44.00 46.20 50.00 P5 Shoulder height 55.40 1.97 53.00 62.00 53.00 55.00 56.00 58.15 P6 Shoulder- elböw length 34.61 1.91 31.00 38.00 31.48 35.00 36.00 37.05 P7 Knee height 59.25 1.48 55.00 62.00 56.95 59.00 60.00 61.05 P8 Elbow- wrist length 30.29 1.35 28.00 33.00 28.00 30.00 31.00 33.00 P9 Knee length 60.71 1.68 57.00 63.00 57.95 61.00 62.00 63.00 PIO Popliteal length 48.75 1.45 45.00 51.00 49.95 49.00 50.00 50.00 P l i Hip breadth 37.02 1.98 32.40 41.00 34.70 37.00 38.00 40.15 P12 Tommy depth 20.33 3.06 11.70 25.00 14.93 21.00 22.40 25.00 P13 Poplitcal- height 47.46 1.22 45.50 50.00 46.00 47.50 48.00 50.00 P14 Foot length 26.53 0.83 25.00 28.00 25.00 26.40 27.10 28.00 P15 Foot breadth 9.52 0.74 8.20 11.20 8.40 9.70 10.00 10525 P16 Hand length 20.06 0.70 18.80 21.00 19.00 20.00 20.63 21.00 P17 Hand breadth 9.75 0.57 8.70 11.00 8.99 10.00 10.00 10.51 PI8 Shoulder -wrist length 64.8 2.93 60.00 70.00 60.48 65.00 67.00 70.00 P19 Head breadth 14.98 0.73 13.80 16.10 13.90 14.95 15.53 16.00 P20 Head length 20.21 0.99 19.00 22.00 19.00 19.90 21.00 22.00 P21 Tommy - steering 19.70 3.19 15.00 26.00 15.95 19.50 22.00 24.10 P22 C hest- steering distance 32.20 2.95 26.00 38.00 27.00 33.00 34.00 36.00 P23 Right knee dash board distance 12.45 2.26 9.00 16.00 9.00 12.00 15.00 16.00 599 P24 Left knee -dash board distance 12.95 2.34 10.00 17.00 10.00 12.00 15.00 16.05 P25 Knee- steering rack distance 8.28 1.88 5.50 11.00 5.50 8.00 10.00 11.00 P26 Elbow angle, with steering 144.19 3.88 139.50 162.00 140.00 144.25 146.00 147.15 P27 Elbow angle with gear 165.30 3.38 158.00 171.00 160.00 166.00 168.00 171.00 P28 Knee angle foot on floor 123.08 1.92 120.00 130.00 120.95 123.00 123.25 126.03 P29 Ankle angle foot on pedal 95.68 4.75 91.00 110.00 91.00 94.00 98.00 104.25 P30 Back angle sitting 100.98 4.02 96.00 112.00 96.00 101.00 102.25 111.05 3.2 Analysis of the drivers’ Workstation The Information in Tables 3 and 4 is the Statistical analysis (mean, Standard deviation, and percentiles) of the data obtained during the fieldwork for the seat reference point used for the placement of the Controls for two categories of buses: mini-buses and midi-buses. The total number of drivers’ Workstation variables for the two bus categories were 38 for mini-buses and 37 for midi-buses. The Variation observed in the Workstation variables in the two bus categories was from the absence of armrest in the midi-buses. 600 Table 3: Summary of data obtained from mini-bus Workstations (Category A) (N = 30)________________________________________ S/N Variable Mean SD .Percentile 5th 50th 75lh 95th 1 Cabin height 142.17 13.39 142.17 122.00 148.00 149.50 2 Cabin widlh 92.67 6.53 92.67 90.00 90.00 90.00 3 Cabin lenglli 90.17 2.32 90.17 87.25 90.50 91.75 4 Seal io door dist. 5.33 3.44 5.33 3.00 4.00 5.50 5 Cabin floor to road 59.00 16.54 59.00 36.50 61.50 67.50 6 Pedal io scm 42.83 4.49 42.83 38.50 41.50 45.25 7 Steering io floor 66.83 4.12 66.83 61.00 68.50 70.00 8 Dashboard-backrest 77.50 10.65 77.50 62.50 79.50 81.50 9 Steering io backrest 45.00 3.58 45.00 40.50 45.50 46.75 10 dashboard widlh 92.67 6.53 92.67 90.00 90.00 90.00 11 Dashboard height 41.67 7.34 41.67 32.00 42.50 44.50 12 Steering whccl Dia. 40.50 4.72 40.50 38.00 38.50 39.75 13 Steering rim thickness 3.58 0.92 3.58 2.63 3.50 4.00 14 Pedal angle 46.67 2.58 46.67 45.00 45.00 48.75 15 Steering rack angle 64.00 2.00 64.00 61.00 65.00 65.00 16 Door widlh 113.33 9.29 113.33 101.25 116.00 120.00 17 Door height 134.83 5.78 134.83 127.00 135.00 139.00 18 Dashboard to scat 26.33 8.14 26.33 14.50 29.00 30.00 19 Gear lever to seat 16.00 5.33 16.00 10.00 16.50 19.50 20 Bus total height 194.17 30.06 194.17 162.00 190.00 197.50 21 Steering rack to scat 23.33 13.60 23.33 9.50 21.50 24.25 23 SRP to steering (horizontal) 50.67 5.79 50.67 42.50 51.50 54.50 24 SRP to steering (vertical) 32.00 2.45 32.00 30.00 31.00 34.25 25 SRP to pedal (horizontal) 91.67 3.33 91.67 87.25 93.00 93.75 26 SRP to pedal (vertical) 27.17 2.32 27.17 25.00 26.50 29.25 27 Floor to scat height 32.67 6.09 25.50 33.50 34.75 40.25 28 Seat front width 50.33 1.97 48.50 50.00 50.00 53.00 29 Seat pan back width 41.00 2.76 38.00 41.00 43.50 44.00 30 Seat pan depth 49.67 0.52 49.00 50.00 50.00 50.00 31 Backrest width (lumbar levcl) 49.00 2.00 47.00 49.00 50.00 51.50 32 Backrest width (thoracic level) 44.50 2.26 42.25 44.00 45.75 47.50 33 Backrest height 53.67 3.14 50.00 54.50 55.00 57.25 34 Headrest widlh 26.50 4.09 22.00 25.50 28.25 32.00 35 Headrest height 23.00 8.44 16.00 22.00 22.75 35.00 36 Armrest length 30.00 0.00 30.00 30.00 30.00 30.00 37 Armrest width 7.00 0.00 7.00 7.00 7.00 7.00 38 Armrest thickness 8.00 0.00 8.00 8.00 —L °° 8.00 601 Table 4: Summary of data obtained from midi-buses Workstations (category B) (N = 20)_________________________________________ S/N Variable Mean SD Percentile 5th 50th 75th 95th 1 Cabin height 198.75 23.39 192.60 199.50 203.25 203.85 2 Cabin width 104.50 10.63 80.25 105.00 120.25 128.05 3 Cabin Icnglh 122.75 8.81 109.85 127.00 128.50 129.70 4 Seal lo door dislance 17.25 8.02 10.15 15.00 21.50 27.50 5 Cabin floor to ground 103.75 7.33 94.10 106.50 107.75 109.55 6 Pedal lo seat distance 30.50 3.32 23.60 29.50 34.00 38.80 7 Stcering to floor 72.50 12.53 70.00 71.50 74.00 76.40 S Dashboard to backrest. 81.75 6.53 69.60 82.50 92.25 92.85 9 Stcering to backrest distance 42.00 9.80 35.20 42.00 44.00 48.80 10 Stcering wheel diameter 54.70 1.37 49.49 50.00 54.85 66.49 11 Stcering rim thickness 3.53 7.47 2.48 3.10 3.85 5.17 12 Pedal angle 133.13 2.95 124.38 135.00 136.25 139.25 13 Stcering rack angle 76.13 0.71 73.30 75.75 77.38 79.48 14 Door width 79.50 12.73 79.05 79.50 79.75 79.95 15 Door height 165.00 2.83 156.90 165.00 169.50 173.10 16 Dashboard to seat distance 28.00 10.79 24.60 29.00 30.00 30.00 17 Gear lever to seat distance 20.50 0.00 8.25 22.00 25.25 30.65 18 Total height from ground 310.00 14.84 310.00 310.00 310.00 310.00 19 Stcering rack to seat dist. 30.50 21.00 13.95 33.50 42.25 42.85 20 Pedal to seat distance 50.50 2.06 28.10 54.00 68.00 68.00 21 SRP to steering (horizontal) 54.75 2.22 52.45 55.00 55.50 56.70 22 SRP to steering (vertical) 23.75 4.92 22.15 23.00 24,00 26.40 23 SRP to pcdal (horizontal) 88.25 2.99 82.35 90.00 90.50 91.70 24 SRP to pedal (vertical) 42.75 23.39 40.30 42.00 43.25 46.25 25 Floor to seat height 41.25 2.06 39.15 41.50 43.00 43.00 26 Scat pan thickness 11.75 2.36 10.00 11.00 12.75 14.55 27 Seat pan back width 41.50 4.36 38.00 40.50 44.00 46.40 28 Backrest angle 102.50 7.37 95.20 102.00 104.50 110.50 29 Backrest thickness 10.25 2.63 8.00 10.00 12.25 12.85 30 Backrest width (lumbar level) 48.67 3.86 45.73 47.50 50.25 53.25 31 Backrest width (thoracic level) 39.47 4.39 34.60 40.00 42.47 43.59 32 Headrest Angle 127.33 28.31 110.20 112.00 136.00 155.20 33 Hcadrcst width 27.79 1.92 26.57 26.82 28.41 29.68 34 Headrest height (with stand) 37.00 1.73 35.30 38.00 38.00 38.00 35 Headrest height (no stand) 22.00 2.00 20.20 22.00 23.00 23.80 36 Seal pan depth 47.50 5.00 41.50 50.00 50.00 50.00 37 Backrest height 44.25 5.06 38.75 44.50 47.00 49.40 3.3 Analysis of the drivers' Workstation dimensions for categories 'A' and ’B' and the drivers’ anthropometric variables Studies highlighted the mismatch betwcen the anthropometry variables of drivers and their Workstation when the seat height was > 95% or < 88% of the popliteal height (Parcells e t a l ., 1999) when the seat length and buttock - popliteal length differed by > 95% or < 80% (Ismaila e t 602 al., 2010). The mean seat height of 68.8% (< 88%) to the mean popliteal height observed in this study was a mismatch between the drivers’ popliteal height and seat height (Table 4) for the mini-bus category. The seat height dimension implied that the seats were too low for the popliteal height of the drivers. Hence, there is tendency for discomfort for the drivers as the driver must bend while driving. This posture may result in low back pain and sprain of the thigh, as well as hitting the knees against the steering wheel. The mean seat length/depth was 101.8% (> 95%) of the buttock to popliteal length. The Variation in the seat length/depth of the buttock to popliteal length was a mismatch for the user as the seat was longer than the popliteal length of the user. The discomfort associated with this was that the legs of the drivers do not touch the Workstation floor, or the driver had to shift forward so that his leg could touch the Workstation floor. To do this, the driver may have to lose contact with the backrest. As such, the driver is subjected to the risk of leg, back, and shoulder pains. Also, there was a mismatch between the seat width and the hip-width.The seat width was 110.8% (> 95%) of the hip-width. Similarly, for category B, the mean seat height was 86.8% (< 88%) of the mean of the popliteal height having the same effects of being slightly low for the comfort of the Nigerian bus drivers (Table 4). The side effects may include back pain, spraining an ankle, hitting the steering wheel with the thigh, and the dashboard with the knees. The mean seat length/depth here was 97.4% (> 95%) of the mean buttock to popliteal length. The seat length/depth of the mean buttock to the popliteal length relation observed in this study was also a mismatch for the drivers, as suggested by Parcells et al. (1999). In the same manner, the results from this study showed that the mean seat width of the driver seat was 41.00 cm for 37.02 cm mean hip width of the midi-bus drivers (97.43 (> 95%) of the hip-width implying a mismatch for the users and leading to back pain and discomfort when in use. Parcells et al. (1999) suggested that seat height should not be < 88% or > 95% of the popliteal height. It then follows that the mean seat height for a mean popliteal height of 47.46cm should be between 41.76 and 45.09cm, rather than 25.50 to 40.25cm; and 39.15 to 43.00cm representing the 5th and 95th percentiles obtained from mini- 603 buses (A) and midi-buses (B) respectively. Similarly, for the seat depth/length, Parcells etal. (1999) suggested that good seat depth should not be <80% or >95% of the buttock - the popliteal length. Therefore, ergonomic driver’s seat depth for a mean buttock - the popliteal length of 48.75cm, should ränge between 39.00 and 46.71cm rather than 49 to 50cm and 41.5 to 50 cm representing the 5th and 95th percentiles in the mini-buses (A) and midi-buses (B) respectively. Ismaila e t a l. (2010) quoted Molebrook et al. (2003) that the seat width should be equivalent to 99 percentile of the hip value plus 15%. With this, the ergonomic seat width ränge should be 41 to 47.15 cm and not 38 to 44cm and 38 to 46.4 cm representing the 5th and 95th percentiles for category A (mini-buses) and category A (midi-buses), respectively. This study also noted a mismatch between the anthropometric data of the drivers and the dimensions of the backrest. Some of the seats have a square or rectangle shape with short heights. While in some, the lower parts dimension was larger than the upper parts of the backrest. This shape of the backrest affects the comfort of the drivers and may lead to neck and shoulder pains. This study suggests that the ergonomic driver's seats should have 95th percentile of the shoulder height as the backrest height, 95th percentile of the shoulder width as the dimension of the upper part, and the seat width dimension for the low back level. The seat should have the following dimensions: 58.15cm height, upper shoulder level width of 50cm, and the low back/hip level width of 47.15cm rather than the mean of the height upper width, low back width of 53.66, 49, 41.5; and 44.25, 48.67, 39.47cm in that order for the category A (mini-buses) and category B (midi-buses) respectively 604 Table 4. Comparative analysis of the drivers' seat dimensions for categories 'A' and ’B’ and the relevant drivers’ anthropometric variables in this study________________________________________ Drivers' workstation dimensions Drivers’ Anthropometric Data Seat Parameters Category A Category B (midi- Relevant human Dimensions (minibuses) buses) body variables Mean SD Mean SD Mean SD Floor io scal heighl 32.67 6.09 41.30 2.06 Popliteal height 47.46 1.22 Seat pan depth 49.62 0.52 47.50 5.00 Buttock - popliteal 48.75 1.45 Seat pan back width 41.00 2.76 41.50 4.60 Hip width 37.02 1.98 Backrest height 53.67 3.14 44.25 5.06 Shoulder height 55.40 1.97 Backrest width (lumbar level) 49.00 2.00 48.67 3.86 Shoulder breadth 44.50 3.25 Backrest width (thoracic level) 44.50 2.26 39.50 4.39 Hip width 37.02 1.98 Headrest heighl 23.00 8.44 22.00 2.00 Shoulder height 27.78 N/A Headrest width 26.50 4.09 27.79 1.92 Shoulder breadth 44.56 3.25 Armrest length (right Elbow to wrist hand only) 30.00 0.00 N/A N/A length 30.29 1.35 Armrest width (right hand only) 7.00 0.00 N/A N/A Hand breadth 9.75 0.57 3.4 Relationship between drivers' Workstation dimensions for categorics ’A' and ’B’ and the drivers’ anthropometric variables The dimensions of the driver's workstation interior compartment of category A (mini-buses) and category B (midi-buses) were analyzed using an independent sample t-test to determine whether there was a difference between their means. The mini-buses represented in category A buses had a lower mean value of 45.00 cm (SD = 26.12) compared to category B buses (midi-buses) that had 52.08 cm (SD = 31.87), t(23) = - 1.181, p = 0.250 (Table 5). The means of category A and B buses were not significantly different as the value was greater than 0.05. The p-value obtained indicated that the parameters for the structural dimensions of the anterior compartment of the driver workstation for the mini-buses and midi-buses fit a particular population. It also implies that the same set of drivers can operate mini-buses and midi-buses drivers’ workstation. 605 Table 5. Independent sample t-test for interior compartment of drivers’ Workstation in the buses between Category A (mini-buses) and Category B (midi-buses)__________________________________ Descriptive slatislics_______________________________________ t-test for Equalily of Mcans Commercial buses N Mean SD SEM T df p-value Category A (mini-buses) 24 45.00 26.12 5.33 -1 181 23 0 250 Category B (midi-buses) 24 52.08 31.87 6.50 Relevant design dimensions of the driver’s workstation compartment from the six mini-bus models were compared with relevant anthropometric variables of the drivers to obtain useful inferences on the relationship between the drivers and the Workstations. Independent sample t-test carried out showed that the anthropometry data of the drivers had a higher mean value (mean = 55.43 cm, SD = 4.75) as compared to the mean driver’s workstation compartment dimension of category A (mini-buses) (mean = 40.16 cm, SD = 18.73) (Table 6). The difference between the means of the anthropometry data variable and the drivers’ workstation parameters was significant (p-value = 0.00). The obtained p-value was an indication that the mismatch between the anthropometric variables of the drivers and the mini-bus model Workstations was significant. Table 6. Independent sample t-test for interior compartment of drivers’ workstation in the buses between Category A (mini-buses) and Category B (midi-buses) Descriptive statistics t-test for cquality of means Assessed variables N Mean SD SEM T Df p-value Category A (mini-buses) 18 40.16 18.73 4.41 Anthropometry data 18 55.43 20.16 4.75 -3.46 17 0.00 The independent-samples t-test results between the relevant anthropometric variables of the drivers and the relevant dimensions of the driver workstation compartment of the midi-bus models showed that the mean value of the category B (midi-buses) dimensions of driver's workstation compartment had a lower mean value (mean = 46.57 cm, SD = 29.53) compared to the mean value of anthropometry data of the drivers (mean = 55.43 cm, SD = 4.75) (Table 7). However, the difference in their 606 mean values was not significant since the p-value obtained was greater than 0.05. Table 7. Independent sample t-test for interior compartment of drivers’ Workstation in the buses between Category A (mini-buses) and Category B (midi-buses)__________________________________ Descriplive staiistics t-test for equality of means Commercial buses N Mean SD SEM T Df p-value Category B (midi-buses) 18 46.57 29.53 6.96 Anthropometry data 18 55.43 20.16 4,75 -1.86 17 0.08 4.0 CONCLUSIONS The analysis of results showed that there were mismatches between the drivers’ anthropometric variables and the dimensions of the present driver's workstation. The drivers’ Workstations in the commercial urban buses used in South-Western Nigeria did not ergonomically fit the urban bus drivers in the region. The observed ergonomics challenge was due to the non-consideration of anthropometric variables of the Nigerian male bus drivers in the design phase of the buses. There is need for the enhancement of the drivers workstation for efficiency and availability of urban bus drivers. 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Journal o f Applied Sciences, 14(24), 3464-3471. 611 Advancing Industrial Engineering in Nigeria through Teaching, Research and Innovation is a twenty-four- chapter book written by the former students and colleagues of Professor Oliver Charles-Owaba, a Professor of Industrial Engineering. Professor Charles- Owaba who has all his degrees in Industrial Engineering retired from the University of Ibadan, having put in over forty years in Teaching and Research. The chapters in the book straddle the areas of: P r o d u c t i o n / M a n u f a c t u r i n g E n g i n e e r i n g , Ergonomics/Human Factors Engineering, Systems Engineering, Engineering Management, Operations Research and Policy. They capture challcnges and developments in various aspects o f Industrial Engineering while shining light on how they can be mitigated in Creative and innovative ways while meeting societal needs. The Festschrift is in appreciation of the immense contributions of Professor Charles-Owaba to Teaching, Research and Innovation. The editors would like to thank all contributors and alumni of the Department of Industrial and Production Engineering, University of Ibadan for making the publ ication possible.