Mathematical Modelling of Engineering Problems Vol. 10, No. 1, February, 2023, pp. 1-13 Journal homepage: http://iieta.org/journals/mmep Forecast of the Trend in Sales Data of a Confectionery Baking Industry Using Exponential Smoothing and Moving Average Models Rasaq A. Kazeem1,2* , Moses O. Petinrin1 , Peter O. Akhigbe3, Tien Chien Jen2 , Esther T. Akinlabi4 , Stephen A. Akinlabi4 , Omolayo M. Ikumapayi5,6 1 Department of Mechanical Engineering, University of Ibadan, Ibadan 200005, Nigeria 2 Department of Mechanical Engineering Science, University of Johannesburg, Auckland Park, Johannesburg 2006, South Africa Y 3 Department of Industrial and Production Engineering, University of Ibadan, Ibadan 200005, Nigeria 4 Department of Mechanical and Construction Engineering, Faculty of Engineering and Environment, NorthumbrRia University, Newcastle NE7 7XA, United Kingdom 5 Department of Mechanical and Mechatronics Engineering, Afe Babalola University, Ado Ekiti 360101, NiAgeria 6 Department of Mechanical and Industrial Engineering Technology, University of Johannesburg, DFCR 2092, South Africa Corresponding Author Email: ra.kazeem@ui.edu.ng IB https://doi.org/10.18280/mmep.100101 ABSTRACT L Received: 19 July 2022 Starch-containing foods such as bread, pastries, and cakes are usually baked at a Accepted: 3 October 2022 moderately high temperature in an oveNn. When these products are later exposed to room temperature, the associated gelatinized starch begins to harden which causes Keywords: retrogradation and molecuDlar reAalignment. Due to this circumstance, manufacturers forecasting model, moving average model, need to have a fairly accurate estimate of products demand in order to determine the exponential smoothing model, mean absolute precise amount of baAking powder and additives for use in their production so as not to percentage error incur losses in their business arising from the stale and consequentially unsalable products. This rBesearch was therefore focused on selecting the best forecasting model using a promiInent confectionery firm in Abeokuta, Ogun State, Nigeria as a case study. The study was based on 24-week operational period sales data collected from the company. The moving average model and the exponential smoothing model were the two forecasting models considered in this research. The data obtained was thoroughly rOeviewFed and the results of the forecasting models were compared. The most effective model was the exponential smoothing model as it produced the lowest mean absolute percentage error on the average of 3.7347 for the cumulative days of sales under review Y as against the 15.1713 for the moving average model. However, the exponential smoothing model was considered the best forecasting model for minimizing forecasting IT error in this study. 1. INTRODUCTION RS from tests of numerous plausible hypotheses in experiments [5]. Demand is the area where forecasting is most frequently Making decisions reqEuires a great deal of planning, strategy, employed, even though many products are projected. The and information V[1]. Small bits of information have demand projection will directly affect a wide range of business historically impIacted the various segments of the operations. Hugos [6] asserts that for every supplier, producer, manufacturing chain. Daily planning is crucial for or retailer, predicting product demand is essential. The managemenNt to make every significant decision [2]. Planning amounts that should be ordered, produced, and shipped will be might take the form of determining the quantity needed, the determined by forecasts of future demand. Forecasting quantity to be generated, and the storage methods [3]. The demand is required because it takes time for finished items to most cUrucial step we can take to increase the efficacy and get from the suppliers' raw materials to the customers' hands efficiency of the logistics process in many supply chains is to in the fundamental operational process. Most businesses are raise the caliber of the demand forecasts. Using a planned unable to simply wait for demand to materialize before acting marketing strategy and several unpredictable and competitive on it. Instead, they must foresee and prepare for future demand elements, demand forecasting estimates sales for a certain to respond quickly to consumer orders as they come in. future time [4]. How much can be sold given the circumstances, Forecasts give people power because it implies that we can it asks? The scenario considers the state of the general change variables right now to change the future [7]. Higher economic, social, and legal concerns, as well as the productivity is the goal for every food-based sector, especially characteristics of vendors, buyers, and the market. The confectionaries, in terms of lowering production costs, situation also involves the company's, its rivals', and interest increasing product demand, and maintaining competitiveness groups' actions. Demand forecasting knowledge has advanced by lowering the cost of their varied products [8]. in the same way that science always does by accumulating data Even when sufficient care and professionalism are put into 1 the efficient creation of the products in the manufacturing of autoregressive integrated moving average model. This model bread, cakes, and confections, a poor profitability index is utilized auto regression, moving average, or a mix of both. nevertheless seen. Retailers and vendors base their demand for Using evaluation metrics such as RMSE, sum of squared bread on the amount of stock that is currently available as well regression, MAPE, mean absolute deviation (MAD), and as the amount of the prior stock that was sold because bread is maximum absolute error, it is possible to determine how well a perishable product made from flour with a concise shelf life the model performs. The findings demonstrated that the that must be consumed within the first 24 hours of production. accuracy of forecasting using autoregressive integrated The amount of the order cannot be guaranteed since, barring moving average models is 7.6% better than that using neural exceptional circumstances, the merchants must wait until the network methods. Moreover, Jere et al. [14] compared the residual stock levels fall to an average of around 9% of the performance of Holt Winters exponential smoothing models starting stock before placing an accurate order. The bakers (HWES) and auto-regressive integrated moving average. The rarely produce enough goods to meet demand since they are error indicators including MAE, mean percentage error, unsure of how many to order. Most of the time, they either RMSE, mean absolute scaled error, and MAPE demonstrated produce less than what is required or less than what is required, that HWES is a suitable model with adequatYe forecast which results in one of two outcomes: either significant loss accuracy. The HWES has lower error than the autoregressive for bakers and retailers because of underproduction or integrated moving average models. In order toR anticipate how excessive production leading to waste because bread must be changes in temperature would affect the amount of energy consumed within the first 24 hours of production (depreciation produced at a Nigerian Agricultural InsAtitute, Kazeem et al. of product due to staleness). Both the stores and the bakeries [15] used multivariate linear regression (MLR) and artificial ultimately suffer losses because of this. The need to reduce neural network (ANN) models. Of Rthe two models examined excessive manufacturing capacity, which will also reduce in this study, the ANN model performed the best. On train data daily losses and shortages, maximize sales volume and profit and test data, respectively, thIe mBean squared error was reduced margin, grow the client base, maintain high standards of by 42% and 39%, showing that ANNs outperformed the MLR quality, and boost the worth of the product, is essential. As a model. The ANN fa reLd noticeably better than the MLR, result, before production starts, the assurance of the actual according to additional metrics like MAE and MAPE. demand quantity can be made available. Bakeries use their Most of the apNplication of forecasting models in literature judgment on how much bread was sold the day before to are centered on predicting future events in health, estimate the quantity to be manufactured. Reliable projections telecommunAications, energy and agriculture but very little must be made to ensure that the production amount is as close investigators had bothered on their use in confectionery as feasible to the actual demand quantity [9]. Therefore, it is forecasDting. The study, therefore, aims to establish an effective necessary to use forecasting methodologies to forecast the and efficient model that will forecast how much is produced quantity of actual demand, thereby increasing sales and eaAch day in the selected baking and confectionery company. decreasing wastages and losses. BAdditionally, it will show how this approach is used in the Businesses that give quick delivery to their clients tend to I sales and operations of the bakery and confections sector. The compel their market rivals to maintain completed produc t remaining part of this paper, which are in three sections have inventories to offer quick order turnaround times [10]. FAs a the data source, the procedure for data collation and result, almost all organizations involved are required to forecasting models, and the performance statistics index as produce or at the very least order parts following aOn estimate sub-headings in section 2. The results and discussion is of future demand. Accurate demand forecastYing also gives the presented in section 3. The conclusions is presented in section company the chance to reduce costs by balancing 4 of the paper. manufacturing volumes, optimizing transportation, and generally organizing effective logistical oTperations. In general, correct demand projections result iIn operations that are 2. METHODOLOGY efficient and provide high levelsS of customer service, while inaccurate forecasts invariably result in operations that are 2.1 Data source inefficient, expensive, andR/or provide a low standard of customer service. NumeErous studies have examined the use of various forecastingV models in a variety of technical and The data used in this study were obtained from XXX Bakery industrial applicaItions. Liu et al. [11] used the exponential and Confectionery located in Abeokuta, Southwestern, smoothing and seasonal autoregressive integrated moving Nigeria. The company makes several varieties of average models to anticipate the trend in the prevalence of confectionaries and baked items therefore, customers have a acute hUemorNrhagic conjunctivitis in China from 2011 to 2019. wide range of confectionaries to choose from. Confections Consequently, the moving model with the lowest mean include vanilla, chocolate, strawberry, and chicken pizza, absolute percentage error (MAPE) and root mean squared chicken pie sausages, bread, and sponge cakes in flavors. The error (RMSE) was chosen for in-sample modeling. Also, products come in a variety of sizes and shapes and are Rabbani et al. [12] used univariate time series analysis, such primarily divided into six main pricing ranges. However, there as exponential smoothing and seasonal autoregressive is variation in the demand for various products. The data integrated moving average models, to develop temporal derived from sales is transformed into a uniform size for variations to forecast accidents and fatalities in Pakistan. Upon simple data collecting, analysis, and interpretation. To select determining the lowest RMSE, mean absolute error (MAE), an acceptable forecasting model, the generated data will be MAPE, and normalized Bayesian estimation technique, the employed. The data collected was for a period of one hundred results showed that the exponential model fit perfectly on and sixty-eight days (24 weeks). The data was collected accident data than the moving average model. In predicting physically and not from any National Scientific Data Sharing telecommunication data, Nalawade and Pawar [13] utilized an Platform. 2 2.2 Procedure yT+1 T = yT +(1−)yT−1 +(1−) 2 yT−2 + ..., (1) The first step in conducting this study was gathering and critically analyzing the sales and demand data for twenty-four where, 0≤α≤1 is the smoothing parameter. The one-step-ahead weeks, after which appropriate alterations were made to suit forecast for time T+1 is a weighted average of all the the situation at hand. The next step was the application of the observations in the series y1…, yT. The rate at which the forecasting models that were considered when conducting this weights decrease is controlled by the parameter α. Formally, investigation. The forecasting models applied to the data the exponential smoothing equation employed is given in Eq. include (i) The exponential smoothing model and (ii) The (2). moving average model. Each technique used to apply these models to the sales data was closely examined for any errors, y = y + (1−)y T +1 T T (2) T T−1 corrections, and modifications (mathematical, computational, data misevaluation, and formula or figure distortion) during where, yT+1/T=forecast for the next period; yT=observed sales the analysis. The model with the smallest divergence from the value of series in period t; α=smoothing conYstant; and actual sales record was considered the best prediction ?̂?𝑇/𝑇−1=old forecast for period t. approach for the company’s products. R 2.2.2 Moving average model 2.2.1 Exponential smoothing model The simple moving average (SMA) Amethod is used with The most utilized class of techniques for smoothing discrete time-series data to smooth out short-term fluctuations and time series to forecast the near future is exponential smoothing. long-term trends. The simple movinRg average is given by Eq. The objective behind exponential smoothing is to smooth the (3). original series in the same manner that the moving average B I does, then use the smoothed series to forecast future values of Pn−k+1 + Pn−k+2....+ Pn 1 n the variable of interest. However, in exponential smoothing, SMA k = L =  Pi (3) k k we want the more recent values of the series to have a higher i=n−k+1 influence on the forecast of future values than the more distant When calAculatNing the next mean SMAk, next with the same observations. Weighted averages are used to calculate sampling width k the range from n=k+2 to n+1 is considered. forecasts, and as observations are gathered from further in the A newD value Pn+1 comes into the sum and the oldest value past, the weights decline exponentially, with the oldest 𝑃𝑛−𝑘+1 drops out. This simplifies the calculations by reusing observations having the smallest weights (see Eq. (1)): thAe previous mean SMAk, prev shown in Eq. (4).     1 n+1 1 B  SMAk ,next =  Pi = P + Pn−k I+3 + .....+ Pn + Pn+1 + P − Pk n−k+2 n−k+1 n−k+1  (4) i=n−k+2 k  F n+1 0   Pi   O i=n−k+2  2.3 Performance statistic index Y data in Table 1 is better appreciated in the graph provided in T Figure 2. According to sales statistics, the company sold more To compare the predicting capabilIities of the exponential goodies on the weekends and had poor sales during the middle smoothing model and the moving average model, one metric of the week because most customers had free time on the was used: the mean absolute perScentage error (MAPE). The weekends and were extremely busy during the middle of the accuracy of fitting was evaluRated using MAPE [16]. The lower work week. The weekly trend in sales also show a downward the MAPE value, the greater the prediction ability. MAPE is trend in sales. Moreover, an outside factor that influences the expressed as a percentagEe. The mathematical formula is shown company's sales demand is the seasonal effect. Also, the strike in Eq. (5). action of the flour-producing companies in the country was IV said to have affected the supply of flour for production in their  establishment and this invariably caused the fluctuation N y − y1 n t t among some days in the data provided. Another cause of sales (5) MAPE =  100% drops in some of the days was attributed to price increase of U n t=1 yt petroleum products and epileptic power supply which therefore caused price increases of the company's goods. where, yt-actual sales at time t; ?̂?𝑡-predicted sales; n-number Generally, sales are often higher on weekends than on of predictions. weekdays and are at their lowest on Wednesdays. As computed in the last column of the Table 1 for the average weekly sales and the spread of daily sales across the 24 weeks 3. RESULTS AND DISCUSSION shown in Table 1. Figure 1 shows that the trend in the sales data for each day of the study period was not linear, making it The data were collected from the company’s daily sales and impossible to use linear regression [17, 18]. However, it could are represented as shown in Table 1. The model applications be deduced form this figure and as indicated in the last column and analysis are presented in Tables 2-15, and subsequently, of Table 1, that the sales are badly affected from the early the forecasts with the least MAPE for each day were plotted weeks of data collection, and this trend continues till the end against the actual sales values as shown in Figures 1 (a-n). The of the twenty-fourth week. As it was mentioned earlier, the 3 trend in reduced sales was unconnected with hike in the price of petroleum products, which are mostly used in transportation, and production of goods. This reduced production of confections, and there was also low demand from customers arising from market inflation, which reduces the purchasing power of the customers. Y (e) ARR B (a) LI N AD A (f) IB OF (b) Y SI T R (g) E IV (c) UN (h) (d) 4 (l) Y (i) AR IB R L DA N (m) (j) BA I O F TYI (n) RS Figure 1. (a-n): Comparison of forecasting models for weekly sales data E (k) IV Table 1. Daily sales data for twenty-four weeks NWeek Monday Tuesday Wednesday Thursday Friday Saturday Sunday Weekly Average U 1 331200 251400 188750 227580 385500 397500 482500 323490 2 256600 245200 156400 214600 375400 302500 405000 279386 3 305450 224500 156400 224500 360000 325500 385000 283050 4 287500 256000 195000 205000 308000 320000 356000 275357 5 297500 295400 231000 196000 312500 345000 355000 290343 6 302500 287500 158000 213500 333500 389000 402500 298071 7 259500 245600 102300 187000 365000 352000 397000 272629 8 287000 302000 145600 198400 297500 302000 312500 263571 9 297000 187500 90540 121500 312500 264880 298740 224666 10 282500 210330 102300 213000 301230 298700 315000 246151 11 294000 198750 112300 198800 302540 325400 302500 247756 12 245660 189700 132500 223000 298700 265000 278900 233351 13 265000 123000 187900 206500 356400 345600 298700 254729 14 287000 175640 154600 198700 335640 312540 325600 255674 15 185000 187900 177000 214500 397000 345600 287000 256286 5 16 290500 245600 156400 194500 198700 196540 178900 208734 17 320200 231200 213000 245100 225780 325460 298970 265673 18 251000 245800 198000 214500 235460 298750 312000 250787 19 245000 214000 187000 231450 348790 387500 312540 275183 20 265400 165400 145600 224500 332540 356470 314500 257773 21 212000 132540 103200 204500 398700 346500 321500 245563 22 174500 123000 154600 198400 302500 312500 320540 226577 23 147800 198700 135600 197800 287500 365400 287950 231536 24 186500 165020 112300 245600 302540 302540 298750 230464 Table 2. Analysis of Monday data using exponential smoothing method Exponential Smoothing for Monday MAPE Week Monday α= 0.2 α= 0.4 α= 0.6 α= 0.8 0.2 0.4 0.6 0.8 1 331200 2 256600 331200 331200 331200 331200 29.07248636 29.07248636 29.07248636 29.0724863Y6 3 305450 266370 276140 285910 295680 12.79423801 9.595678507 6.397119005 3.198559502 4 287500 301860 298270 294680 291090 4.994782609 3.746086957 2.497391304 1.248R695652 5 297500 289500 291500 293500 295500 2.68907563 2.016806723 1.344537815 0.672268908 6 302500 298500 299500 300500 301500 1.32231405 0.991735537 0.661157025 A0.330578512 7 259500 293900 285300 276700 268100 13.25626204 9.942196532 6.628131021 3.314065511 8 287000 265000 270500 276000 281500 7.665505226 5.74912892 3.8327526R13 1.916376307 9 297000 289000 291000 293000 295000 2.693602694 2.02020202 1.346801347 0.673400673 10 282500 294100 291200 288300 285400 4.10619469 3.079646018 2.0I53B097345 1.026548673 11 294000 284800 287100 289400 291700 3.129251701 2.346938776 1.56462585 0.782312925 12 245660 284332 274664 264996 255328 15.74208255 11.80656191 L7.871041277 3.935520638 13 265000 249528 253396 257264 261132 5.838490566 4.37886792 5 2.919245283 1.459622642 14 287000 269400 273800 278200 282600 6.132404181 4.599303136 3.066202091 1.533101045 15 185000 266600 246200 225800 205400 44.10810811 33.081N08108 22.05405405 11.02702703 16 290500 206100 227200 248300 269400 29.05335628 21.79001721 14.52667814 7.263339071 17 320200 296440 302380 308320 314260 7.420362274 5A.565271705 3.710181137 1.855090568 18 251000 306360 292520 278680 264840 22.05577689 16.54183267 11.02788845 5.513944223 19 245000 249800 248600 247400 246200 1.959A1836D73 1.469387755 0.979591837 0.489795918 20 265400 249080 253160 257240 261320 6.149208742 4.611906556 3.074604371 1.537302185 21 212000 254720 244040 233360 222680 20.1509434 15.11320755 10.0754717 5.037735849 22 174500 204500 197000 189500 182000 17.19197708 12.89398281 8.595988539 4.297994269 23 147800 169160 163820 158480 153140 B14.45196211 10.83897158 7.225981055 3.612990528 24 186500 155540 163280 171020 1F7876 0 I 16.60053619 12.45040214 8.300268097 4.150134048 Sum 288.5781051 223.7017004 158.8252957 93.94889104 OMean 12.54687413 9.726160886 6.90544764 4.084734393 Table 3. Analysis of Tuesday data using exponential smoothing method Exponential Smoothing forY Tuesday MAPE Week Tuesday α= 0.2 α=T 0.4 α= 0.6 α= 0.8 0.2 0.4 0.6 0.8 1 251400 2 245200 25140S0 2I51400 251400 251400 2.528548124 2.528548124 2.528548124 2.528548124 3 224500 241060 236920 232780 228640 7.376391982 5.532293987 3.688195991 1.844097996 4 256000 2R30800 237100 243400 249700 9.84375 7.3828125 4.921875 2.4609375 5 295400 263880 271760 279640 287520 10.67027759 8.002708192 5.335138795 2.667569397 6 287500E 293820 292240 290660 289080 2.19826087 1.648695652 1.099130435 0.549565217 7 245600 279120 270740 262360 253980 13.64820847 10.23615635 6.824104235 3.412052117 8 I3V02000 256880 268160 279440 290720 14.94039735 11.20529801 7.470198675 3.735099338 9 187500 279100 256200 233300 210400 48.85333333 36.64 24.42666667 12.21333333 1N0 210330 192066 196632 201198 205764 8.683497361 6.512623021 4.341748681 2.17087434 11 198750 208014 205698 203382 201066 4.661132075 3.495849057 2.330566038 1.165283019 U12 189700 196940 195130 193320 191510 3.816552451 2.862414338 1.908276226 0.954138113 13 123000 176360 163020 149680 136340 43.38211382 32.53658537 21.69105691 10.84552846 14 175640 133528 144056 154584 165112 23.97631519 17.98223639 11.9881576 5.994078798 15 187900 178092 180544 182996 185448 5.219797765 3.914848324 2.609898882 1.304949441 16 245600 199440 210980 222520 234060 18.79478827 14.09609121 9.397394137 4.698697068 17 231200 242720 239840 236960 234080 4.982698962 3.737024221 2.491349481 1.24567474 18 245800 234120 237040 239960 242880 4.751830757 3.563873068 2.375915378 1.187957689 19 214000 239440 233080 226720 220360 11.88785047 8.91588785 5.943925234 2.971962617 20 165400 204280 194560 184840 175120 23.50665054 17.62998791 11.75332527 5.876662636 21 132540 158828 152256 145684 139112 19.83401237 14.87550928 9.917006187 4.958503093 22 123000 130632 128724 126816 124908 6.204878049 4.653658537 3.102439024 1.551219512 23 198700 138140 153280 168420 183560 30.4781077 22.85858078 15.23905385 7.619526925 24 165020 191964 185228 178492 171756 16.32771785 12.24578839 8.163858926 4.081929463 Sum 336.5671114 253.0574706 169.5478297 86.03818893 Mean 14.63335267 11.00249872 7.371644771 3.740790823 6 Table 4. Analysis of Wednesday data using exponential smoothing method Exponential Smoothing for Wednesday MAPE Week Wednesday α= 0.2 α= 0.4 α= 0.6 α= 0.8 0.2 0.4 0.6 0.8 1 188750 2 154220 188750 188750 188750 188750 22.3900921 22.3900921 22.3900921 22.39009208 3 156400 154656 155092 155528 155964 1.11508951 0.83631714 0.55754476 0.278772379 4 195000 164120 171840 179560 187280 15.8358974 11.8769231 7.91794872 3.958974359 5 231000 202200 209400 216600 223800 12.4675325 9.35064935 6.23376623 3.116883117 6 158000 216400 201800 187200 172600 36.9620253 27.721519 18.4810127 9.240506329 7 102300 146860 135720 124580 113440 43.5581623 32.6686217 21.7790811 10.88954057 8 145600 110960 119620 128280 136940 23.7912088 17.8434066 11.8956044 5.947802198 9 90540 134588 123576 112564 101552 48.6503203 36.4877402 24.3251602 12.16258008 10 102300 92892 95244 97596 99948 9.19648094 6.8973607 4.59824047 2.299120235 11 112300 104300 106300 108300 110300 7.1237756 5.3428317 3.5618878 1.7809439 12 132500 116340 120380 124420 128460 12.1962264 9.14716981 6.09811321 3.04905660Y4 13 187900 143580 154660 165740 176820 23.5870144 17.6902608 11.7935072 5.896753592 14 154600 181240 174580 167920 161260 17.2315653 12.923674 8.61578266 4.307R891332 15 177000 159080 163560 168040 172520 10.1242938 7.59322034 5.06214689 2.531073446 16 156400 172880 168760 164640 160520 10.5370844 7.9028133 5.2685422 A2.6342711 17 213000 167720 179040 190360 201680 21.258216 15.943662 10.629108 5.314553991 18 198000 210000 207000 204000 201000 6.06060606 4.54545455 3.030303R03 1.515151515 19 187000 195800 193600 191400 189200 4.70588235 3.52941176 2.35294118 1.176470588 20 145600 178720 170440 162160 153880 22.7472527 17.0604396 11.3B736264 5.686813187 21 103200 137120 128640 120160 111680 32.8682171 24.6511628 1I6.4341085 8.217054264 22 154600 113480 123760 134040 144320 26.5976714 19.9482536L 13.2988357 6.649417853 23 135600 150800 147000 143200 139400 11.2094395 8.40N7079 65 5.60471976 2.802359882 24 112300 130940 126280 121620 116960 16.5983972 12.4487979 8.29919858 4.149599288 Sum 436.812451 333.206861 229.601272 125.9956819 Mean 18.9918457 A14.4872548 9.98266399 5.478073125 Table 5. Analysis of Thursday data using expoDnential smoothing method Exponential Smoothing for Thursday MAPE Week Thursday α= 0.2 α= 0.4 α= 0.6 αB= 0.8 A 0.2 0.4 0.6 0.8 1 227580 2 214600 227580 227580 227580 I227580 6.048462 6.048462 6.048462 6.048462 3 224500 216580 218560 220F540 222520 3.52784 2.64588 1.76392 0.88196 4 205000 220600 216700 212800 208900 7.609756 5.707317 3.804878 1.902439 5 196000 203200 201400 199600 197800 3.673469 2.755102 1.836735 0.918367 6 213500 199500 203000 206500 210000 6.557377 4.918033 3.278689 1.639344 7 187000 208200 202900O 197600 192300 11.3369 8.502674 5.668449 2.834225 8 198400 189280 19156 0 193840 196120 4.596774 3.447581 2.298387 1.149194 9 121500 183020 Y167640 152260 136880 50.63374 37.97531 25.31687 12.65844 10 213000 13980T0 158100 176400 194700 34.3662 25.77465 17.1831 8.591549 11 198800 210160 207320 204480 201640 5.714286 4.285714 2.857143 1.428571 12 223000 S203I640 208480 213320 218160 8.681614 6.511211 4.340807 2.170404 13 206500 219700 216400 213100 209800 6.392252 4.794189 3.196126 1.598063 14 198700 204940 203380 201820 200260 3.140413 2.35531 1.570206 0.785103 15 214500 201860 205020 208180 211340 5.892774 4.41958 2.946387 1.473193 16 E1945R00 210500 206500 202500 198500 8.226221 6.169666 4.113111 2.056555 17 245100 204620 214740 224860 234980 16.51571 12.38678 8.257854 4.128927 18 214500 238980 232860 226740 220620 11.41259 8.559441 5.706294 2.853147 I19 231450 217890 221280 224670 228060 5.858717 4.394038 2.929358 1.464679 20V 224500 230060 228670 227280 225890 2.476615 1.857461 1.238307 0.619154 N 21 204500 220500 216500 212500 208500 7.823961 5.867971 3.91198 1.95599 22 198400 203280 202060 200840 199620 2.459677 1.844758 1.229839 0.614919 U 23 197800 198280 198160 198040 197920 0.242669 0.182002 0.121335 0.060667 24 245600 207360 216920 226480 236040 15.57003 11.67752 7.785016 3.892508 Sum 228.758 173.0806 117.4033 61.72586 Mean 9.946002 7.525246 5.104489 2.683733 Table 6. Analysis of Friday data using exponential smoothing method Exponential Smoothing for Friday MAPE Week Friday α= 0.2 α= 0.4 α= 0.6 α= 0.8 0.2 0.4 0.6 0.8 1 385500 2 375400 385500 385500 385500 385500 2.690464 2.690463506 2.690463506 2.690463506 3 360000 372320 369240 366160 363080 3.422222 2.566666667 1.711111111 0.855555556 4 308000 349600 339200 328800 318400 13.50649 10.12987013 6.753246753 3.376623377 5 312500 308900 309800 310700 311600 1.152 0.864 0.576 0.288 7 6 333500 316700 320900 325100 329300 5.037481 3.778110945 2.51874063 1.259370315 7 365000 339800 346100 352400 358700 6.90411 5.178082192 3.452054795 1.726027397 8 297500 351500 338000 324500 311000 18.15126 13.61344538 9.075630252 4.537815126 9 312500 300500 303500 306500 309500 3.84 2.88 1.92 0.96 10 301230 310246 307992 305738 303484 2.993062 2.244796335 1.49653089 0.748265445 11 302540 301492 301754 302016 302278 0.3464 0.259800357 0.173200238 0.086600119 12 298700 301772 301004 300236 299468 1.028457 0.771342484 0.514228323 0.257114161 13 356400 310240 321780 333320 344860 12.95174 9.713804714 6.475869809 3.237934905 14 335640 352248 348096 343944 339792 4.948159 3.711119056 2.474079371 1.237039685 15 397000 347912 360184 372456 384728 12.36474 9.273551637 6.182367758 3.091183879 16 198700 357340 317680 278020 238360 79.83895 59.8792149 39.9194766 19.9597383 17 225780 204116 209532 214948 220364 9.595181 7.196385862 4.797590575 2.398795287 18 235460 227716 229652 231588 233524 3.288881 2.466661004 1.644440669 0.822220335 19 348790 258126 280792 303458 326124 25.99386 19.49539838 12.99693225 6.498466126 20 332540 345540 342290 339040 335790 3.909304 2.931978108 1.954652072 0.977326036 21 398700 345772 359004 372236 385468 13.27514 9.956358164 6.637572109 3.318786055 Y 22 302500 379460 360220 340980 321740 25.44132 19.08099174 12.72066116 6.360330579 23 287500 299500 296500 293500 290500 4.173913 3.130434783 2.086956522 1.04347R8261 24 302540 290508 293516 291450 299121 5.122391 2.653425321 3.348750922 1.114736028 Sum 254.8531 191.8124763 128.7718054R 65A.73113445 Mean 11.08057 8.339672884 5.598774147 2.857875411 Table 7. Analysis of Saturday data using exponential smoothing method B Exponential Smoothing for Saturday MAPEI Week Saturday α= 0.2 α= 0.4 α= 0.6 α= 0.8 0.2 0.4 L 0.6 0.8 1 397500 2 302500 397500 397500 397500 397500 31.40496 31.4049N5868 31.40495868 31.40495868 3 325500 307100 311700 316300 320900 5.652842 4.239631336 2.826420891 1.413210445 4 320000 324400 323300 322200 321100 1.375 1.03125 0.6875 0.34375 5 345000 325000 330000 335000 340000 5.797101 4.A347826087 2.898550725 1.449275362 6 389000 353800 362600 371400 380200 9.048843D 6.786632391 4.524421594 2.262210797 7 352000 381600 374200 366800 359400 8.409091 6.306818182 4.204545455 2.102272727 8 302000 342000 332000 322000 312000 13.A24503 9.933774834 6.622516556 3.311258278 9 264880 294576 287152 279728 272304 B11.21111 8.40833585 5.605557233 2.802778617 10 298700 271644 278408 285172 29193I6 9.057918 6.793438232 4.528958822 2.264479411 11 325400 304040 309380 314720 320 060 6.564229 4.923171481 3.282114321 1.64105716 12 265000 313320 301240 289160 F277080 18.23396 13.6754717 9.116981132 4.558490566 13 345600 281120 297240 313360 329480 18.65741 13.99305556 9.328703704 4.664351852 14 312540 338988 332376 325764 319152 8.462277 6.346707621 4.231138414 2.115569207 15 345600 319152 325764 332376 338988 7.652778 5.739583333 3.826388889 1.913194444 16 196540 315788 285976 2 56O164 226352 60.67365 45.50524066 30.33682711 15.16841355 17 325460 222324 24810Y8 273892 299676 31.6893 23.76697597 15.84465065 7.922325324 18 298750 320118 314776 309434 304092 7.152469 5.364351464 3.57623431 1.788117155 19 387500 316500 3T34250 352000 369750 18.32258 13.74193548 9.161290323 4.580645161 20 356470 381294 I375088 368882 362676 6.96384 5.222879906 3.481919937 1.740959969 21 346500 3544S76 352482 350488 348494 2.301876 1.726406926 1.150937951 0.575468975 22 312500 339700 332900 326100 319300 8.704 6.528 4.352 2.176 23 365400 R323080 333660 344240 354820 11.58183 8.6863711 5.790914067 2.895457033 24 302540 352828 340256 327684 315112 16.62193 12.46645072 8.310967145 4.155483572 Sum 318.784 246.9392675 175.0944979 103.2497283 E Mean 13.86018 10.73648989 7.612804257 4.489118621 IV Table 8. Analysis of Sunday data using exponential smoothing method N Exponential Smoothing for Sunday MAPE Week Sunday α= 0.2 α= 0.4 α= 0.6 α= 0.8 0.2 0.4 0.6 0.8 U 1 482500 2 405000 482500 482500 482500 482500 19.1358 19.13580247 19.13580247 19.13580247 3 385000 401000 397000 393000 389000 4.155844 3.116883117 2.077922078 1.038961039 4 356000 379200 373400 367600 361800 6.516854 4.887640449 3.258426966 1.629213483 5 355000 355800 355600 355400 355200 0.225352 0.169014085 0.112676056 0.056338028 6 402500 364500 374000 383500 393000 9.440994 7.080745342 4.720496894 2.360248447 7 397000 401400 400300 399200 398100 1.108312 0.831234257 0.554156171 0.277078086 8 312500 380100 363200 346300 329400 21.632 16.224 10.816 5.408 9 298740 309748 306996 304244 301492 3.68481 2.76360715 1.842404767 0.921202383 10 315000 301992 305244 308496 311748 4.129524 3.097142857 2.064761905 1.032380952 11 302500 312500 310000 307500 305000 3.305785 2.479338843 1.652892562 0.826446281 12 278900 297780 293060 288340 283620 6.769451 5.077088562 3.384725708 1.692362854 13 298700 282860 286820 290780 294740 5.30298 3.977234684 2.651489789 1.325744895 14 325600 304080 309460 314840 320220 6.609337 4.957002457 3.304668305 1.652334152 8 15 287000 317880 310160 302440 294720 10.75958 8.069686411 5.379790941 2.68989547 16 178900 265380 243760 222140 200520 48.33985 36.254891 24.16992733 12.08496367 17 298970 202914 226928 250942 274956 32.12898 24.09673211 16.06448808 8.032244038 18 312000 301576 304182 306788 309394 3.341026 2.505769231 1.670512821 0.83525641 19 312540 312108 312216 312324 312432 0.138222 0.103666731 0.069111154 0.034555577 20 314500 312932 313324 313716 314108 0.498569 0.373926868 0.249284579 0.124642289 21 321500 315900 317300 318700 320100 1.741835 1.306376361 0.870917574 0.435458787 22 320540 321308 321116 320924 320732 0.239596 0.179696762 0.119797841 0.059898921 23 287950 314022 307504 300986 294468 9.05435 6.790762285 4.527174857 2.263587428 24 298750 290110 292270 294430 296590 2.89205 2.169037657 1.446025105 0.723012552 Sum 201.1511 155.6472797 110.143454 64.63962821 Mean 8.7457 6.76727303 4.788845824 2.810418618 Table 9. Moving average analysis for Monday Week Monday 2 week MAPE 3 week MAPE 4 week MAPE 5 week MAPE Y 1 331200 2 256600 R 3 305450 293900 3.781306 4 287500 281025 2.252174 297750 3.565217 A 5 297500 296475 0.344538 283183.3 4.812325 295187.5 0.777311 6 302500 292500 3.305785 296816.7 1.878788 286762.5 5.202479 29565R0 2.264463 7 259500 300000 15.60694 295833.3 14.00128 298237.5 14.92775 I2B89910 11.71869 8 287000 281000 2.090592 286500 0.174216 286750 0.087108 290490 1.216028 9 297000 273250 7.996633 283000 4.713805 286625 3.493266 286800 3.434343 10 282500 292000 3.362832 281166.7 0.471976 286500 1.41 59L29 288700 2.19469 11 294000 289750 1.445578 288833.3 1.75737 281500 N4.251701 285700 2.823129 12 245660 288250 17.33697 291166.7 18.52425 290125 18.10022 284000 15.60694 13 265000 269830 1.822642 274053.3 3.416352 279A790 5.581132 281232 6.125283 14 287000 255330 11.03484 268220 6.543554 271790 5.299652 276832 3.542857 15 185000 276000 49.18919 265886.7 43.72252 272915 47.52162 274832 48.55784 16 290500 236000 18.76076 245666.7 15.43316 245665 15.43373 255332 12.10602 17 320200 237750 25.74953 254166.7 20.62253 D256875 19.7767 254632 20.4772 18 251000 305350 21.65339 265233.3 5.670651 270675 7.838645 269540 7.386454 19 245000 285600 16.57143 287233.3 17.23A81 261675 6.806122 266740 8.873469 20 265400 248000 6.556142 272066.7 2.511932 276675 4.248304 258340 2.660136 21 212000 255200 20.37736 253800 B19.71698 270400 27.54717 274420 29.4434 22 174500 238700 36.79083 240800 I37.99427 243350 39.45559 258720 48.26361 23 147800 193250 30.75101 217300 47.023 224225 51.70839 229580 55.33153 24 186500 161150 13.59249 17F8100 4.504021 199925 7.198391 208940 12.03217 Sum 310.37 3 O 274.2963 286.6712 294.0583 Mean 14.10786 13.06173 14.33356 15.47675 TabYle 10. Moving average analysis for Tuesday Week Tuesday 2 weeIk TMAPE 3 week MAPE 4 week MAPE 5 week MAPE 1 251400 2 245200 S 3 224500 248300 10.60134 4 25600R0 234850 8.261719 240366.7 6.106771 5 2E95400 240250 18.6696 241900 18.11104 244275 17.30704 6 287500 275700 4.104348 258633.3 10.04058 255275 11.2087 254500 11.47826 7 V245600 291450 18.66857 279633.3 13.85722 265850 8.245114 261720 6.563518 8I 302000 266550 11.73841 276166.7 8.554084 271125 10.22351 261800 13.31126 9 187500 273800 46.02667 278366.7 48.46222 282625 50.73333 277300 47.89333 N10 210330 244750 16.36476 245033.3 16.49947 255650 21.54709 263600 25.32687 11 198750 198915 0.083019 233276.7 17.37191 236357.5 18.92201 246586 24.06843 U 12 189700 204540 7.822878 198860 4.828677 224645 18.42119 228836 20.63047 13 123000 194225 57.9065 199593.3 62.271 196570 59.81301 217656 76.9561 14 175640 156350 10.98269 170483.3 2.93593 180445 2.735709 181856 3.539057 15 187900 149320 20.5322 162780 13.36881 171772.5 8.583023 179484 4.478978 16 245600 181770 25.98941 162180 33.9658 169060 31.1645 174998 28.74674 17 231200 216750 6.25 203046.7 12.17705 183035 20.83261 184368 20.25606 18 245800 238400 3.010578 221566.7 9.858964 210085 14.53011 192668 21.61595 19 214000 238500 11.4486 240866.7 12.55452 227625 6.366822 217228 1.508411 20 165400 229900 38.99637 230333.3 39.25836 234150 41.5659 224900 35.9734 21 132540 189700 43.1266 208400 57.23555 214100 61.53614 220400 66.28942 22 123000 148970 21.11382 170646.7 38.73713 189435 54.0122 197788 60.80325 23 198700 127770 35.69703 140313.3 29.38433 158735 20.11324 176148 11.34977 24 165020 160850 2.526966 151413.3 8.245465 154910 6.12653 166728 1.035026 Sum 419.9221 463.8249 483.9878 481.8243 Mean 19.08737 22.0869 24.19939 25.35917 9 Table 11. Moving average analysis for Wednesday Week Wednesday 2 week MAPE 3 week MAPE 4 week MAPE 5 week MAPE 1 188750 2 156400 3 156400 172575 10.34207 4 195000 156400 19.79487 167183.3 14.26496 5 231000 175700 23.93939 169266.7 26.72439 174137.5 24.6158 6 158000 213000 34.81013 194133.3 22.8692 184700 16.89873 185510 17.41139 7 102300 194500 90.12708 194666.7 90.29 185100 80.93842 179360 75.32747 8 145600 130150 10.61126 163766.7 12.47711 171575 17.83997 168540 15.75549 9 90540 123950 36.90082 135300 49.43671 159225 75.8615 166380 83.76408 10 102300 118070 15.41544 112813.3 10.27696 124110 21.31965 145488 42.21701 11 112300 96420 14.14069 112813.3 0.457109 110185 1.883348 119748 6.632235 12 132500 107300 19.01887 101713.3 23.23522 112685 14.95472 110608 16.52226 13 187900 122400 34.85897 115700 38.42469 109410 41.77222 116648 37.92017 Y 14 154600 160200 3.622251 144233.3 6.705476 133750 13.48642 125108 19.07633 15 177000 171250 3.248588 158333.3 10.54614 146825 17.04802 137920 22.07R91 16 156400 165800 6.01023 173166.7 10.72038 163000 4.219949 152860 2.263427 17 213000 166700 21.73709 162666.7 23.63067 168975 20.66901 161680 A24.0939 18 198000 184700 6.717172 182133.3 8.013468 175250 11.4899 177780 10.21212 19 187000 205500 9.893048 189133.3 1.14082 186100 0.481283 1798R00 3.850267 20 145600 192500 32.21154 199333.3 36.90476 188600 29.53297 186280 27.93956 21 103200 166300 61.14341 176866.7 71.38243 185900 80.13566 B180000 74.4186 22 154600 124400 19.53428 145266.7 6.037085 158450 2.49L0298I 169360 9.547219 23 135600 128900 4.941003 134466.7 0.835792 147600 8.849558 157680 16.28319 24 112300 145100 29.20748 131133.3 16.77056 134750 N19.9911 145200 29.29653 Sum 508.2257 481.1439 504.4785 534.6103 Mean 23.10117 22.91162 25.22393 28.13739 Table 12. Moving average analysis for AThursday Week Thursday 2 week MAPE 3 week MAAPE D4 week MAPE 5 week MAPE 1 227580 2 214600 3 224500 221090 1.518931 4 205000 219550 7.097561 222226 .7 IB8.403252 5 196000 214750 9.566327 21F4700 9.540816 217920 11.18367 6 213500 200500 6.088993 208500 2.34192 210025 1.627635 213536 0.016862 7 187000 204750 9.491979 204833.3 9.536542 209750 12.16578 210720 12.68449 8 198400 200250 0.9324 6O 198833.3 0.218414 200375 0.995464 205200 3.427419 9 121500 192700 58.60082 199633.3 64.30727 198725 63.55967 199980 64.59259 10 213000 159950 2Y4.9061 168966.7 20.67293 180100 15.44601 183280 13.95305 11 198800 167250 15.87022 177633.3 10.64722 179975 9.469316 186680 6.096579 12 223000 205900T 7.668161 177766.7 20.28401 182925 17.97085 183740 17.60538 13 206500 210900 2.130751 211600 2.469734 189075 8.438257 190940 7.535109 14 198700 S2147I50 8.077504 209433.3 5.401778 210325 5.850528 192560 3.090086 15 214500 202600 5.547786 209400 2.377622 206750 3.613054 208000 3.030303 16 19450R0 206600 6.22108 206566.7 6.203942 210675 8.316195 208300 7.095116 17 245100 204500 16.56467 202566.7 17.35346 203550 16.95226 207440 15.36516 18 2E14500 219800 2.470862 218033.3 1.647242 213200 0.606061 211860 1.230769 19 231450 229800 0.712897 218033.3 5.796788 217150 6.17844 213460 7.772737 20 V224500 222975 0.679287 230350 2.605791 221387.5 1.386414 220010 2 21I 204500 227975 11.47922 223483.3 9.282804 228887.5 11.92543 222010 8.562347 22 198400 214500 8.114919 220150 10.9627 218737.5 10.25076 224010 12.90827 N23 197800 201450 1.845298 209133.3 5.729693 214712.5 8.550303 214670 8.528817 24 245600 198100 19.34039 200233.3 18.47177 206300 16.00163 211330 13.95358 U Sum 224.9262 234.2557 230.4877 209.4487 Mean 10.22392 11.15503 11.52439 11.02361 Table 13. Moving average analysis for Friday Week Friday 2 week MAPE 3 week MAPE 4 week MAPE 5 week MAPE 1 385500 2 375400 3 360000 380450 5.680556 4 308000 367700 19.38312 373633.3 21.30952 5 312500 334000 6.88 347800 11.296 357225 14.312 6 333500 310250 6.971514 326833.3 1.999 338975 1.641679 348280 4.431784 7 365000 323000 11.50685 318000 12.87671 328500 10 337880 7.430137 8 297500 349250 17.39496 337000 13.27731 329750 10.84034 335800 12.87395 10 9 312500 331250 6 332000 6.24 327125 4.68 323300 3.456 10 301230 305000 1.251535 325000 7.89098 327125 8.596421 324200 7.625403 11 302540 306865 1.429563 303743.3 0.397744 319057.5 5.459609 321946 6.414358 12 298700 301885 1.066287 305423.3 2.250865 303442.5 1.587713 315754 5.709407 13 356400 300620 15.65095 300823.3 15.5939 303742.5 14.77483 302494 15.12514 14 335640 327550 2.410321 319213.3 4.894133 314717.5 6.233613 314274 6.365749 15 397000 346020 12.84131 330246.7 16.81444 323320 18.55919 318902 19.67204 16 198700 366320 84.35833 363013.3 82.69418 346935 74.60242 338056 70.13387 17 225780 297850 31.92045 310446.7 37.49963 321935 42.58792 317288 40.52972 18 235460 212240 9.861548 273826.7 16.29435 289280 22.85739 302704 28.55857 19 348790 230620 33.87999 219980 36.93053 264235 24.24238 278516 20.14794 20 332540 292125 12.15343 270010 18.80375 252182.5 24.16476 281146 15.45498 21 398700 340665 14.55606 305596.7 23.35173 285642.5 28.35653 268254 32.71783 22 302500 365620 20.86612 360010 19.01157 328872.5 8.718182 308254 1.902149 23 287500 350600 21.94783 344580 19.85391 345632.5 20.22 323598 12.55583 24 302540 295000 2.492232 329566.7 8.933254 330310 9.178952 334006 10.40061 Y Sum 340.5029 378.2135 351.6139 321.5055 Mean 15.47741 18.01017 17.5807 16.9213R4 Table 14. Moving average analysis for Saturday A Week Saturday 2 week MAPE 3 week MAPE 4 week MAPE B5 weeRk MAPE 1 397500 2 302500 I 3 325500 350000 7.526882 4 320000 314000 1.875 341833.3 6.822917 L 5 345000 322750 6.449275 316000 8.405797 336375 2.5 6 389000 332500 14.52442 330166.7 15.12425 323250 16.90231 338100 13.08483 7 352000 367000 4.261364 351333.3 0.189394 344875 N2.024148 336400 4.431818 8 302000 370500 22.68212 362000 19.86755 351500 16.39073 346300 14.66887 9 264880 327000 23.45213 347666.7 31.2544 347A000 31.00272 341600 28.96406 10 298700 283440 5.108805 306293.3 2.542127 326970 9.464345 330576 10.67158 11 325400 281790 13.40197 288526.7 11.33169 D304395 6.455132 321316 1.255071 12 265000 312050 17.75472 296326.7 11.82138 297745 12.3566 308596 16.45132 13 345600 295200 14.58333 296366.7 14.24A576 288495 16.52344 291196 15.7419 14 312540 305300 2.316503 312000 IB0.172778 308675 1.236642 299916 4.039163 15 345600 329070 4.782986 307713.3 10.96258 312135 9.68316 309448 10.46065 16 196540 329070 67.43157 33F4580 70.23507 317185 61.38445 318828 62.22041 17 325460 271070 16.71173 284893.3 12.46441 300070 7.801266 293056 9.956369 18 298750 261000 12.63598O 289200 3.196653 295035 1.243515 305148 2.14159 19 387500 312105 19.45677 273583.3 29.39785 291587.5 24.75161 295778 23.67019 20 356470 343125 3.7436 53 337236.7 5.395498 302062.5 15.26286 310770 12.82015 21 346500 371985 7.Y354978 347573.3 0.309764 342045 1.285714 312944 9.684271 22 312500 351485 12.4752 363490 16.3168 347305 11.1376 342936 9.73952 23 365400 3295I00T 9.824849 338490 7.364532 350742.5 4.011357 340344 6.857143 24 302540 338950 12.03477 341466.7 12.86662 345217.5 14.1064 353674 16.90157 SSum 300.389 290.2878 265.524 273.7605 Mean 13.65405 13.82323 13.2762 14.40845 R Table 15. Moving average analysis for Sunday Week SEunday 2 week MAPE 3 week MAPE 4 week MAPE 5 week MAPE 1I V482500 2 405000 N3 385000 443750 15.25974 4 356000 395000 10.95506 424166.7 19.14794 U 5 355000 370500 4.366197 382000 7.605634 407125 14.6831 6 402500 355500 11.67702 365333.3 9.233954 375250 6.770186 396700 1.440994 7 397000 378750 4.596977 371166.7 6.507137 374625 5.63602 380700 4.105793 8 312500 399750 27.92 384833.3 23.14667 377625 20.84 379100 21.312 9 298740 354750 18.74874 370666.7 24.07668 366750 22.76562 364600 22.04593 10 315000 305620 2.977778 336080 6.692063 352685 11.96349 353148 12.11048 11 302500 306870 1.444628 308746.7 2.065014 330810 9.358678 345148 14.09851 12 278900 308750 10.70276 305413.3 9.506394 307185 10.14163 325148 16.58229 13 298700 290700 2.678273 298800 0.033478 298785 0.028457 301528 0.946769 14 325600 288800 11.30221 293366.7 9.899672 298775 8.238636 298768 8.240786 15 287000 312150 8.763066 301066.7 4.901278 301425 5.026132 304140 5.972125 16 178900 306300 71.21297 303766.7 69.79691 297550 66.32197 298540 66.87535 17 298970 232950 22.08248 263833.3 11.75257 272550 8.837007 273820 8.412215 18 312000 238935 23.41827 254956.7 18.28312 272617.5 12.6226 277834 10.95064 19 312540 305485 2.257311 263290 15.75798 269217.5 13.86143 280494 10.25341 11 20 314500 312270 0.709062 307836.7 2.118707 275602.5 12.36804 277882 11.64324 21 321500 313520 2.482115 313013.3 2.63971 309502.5 3.731726 283382 11.8563 22 320540 318000 0.792413 316180 1.360205 315135 1.686217 311902 2.694827 23 287950 321020 11.48463 318846.7 10.72987 317270 10.18232 316216 9.816288 24 298750 304245 1.839331 309996.7 3.764575 311122.5 4.141423 311406 4.236318 Sum 267.671 259.0196 249.2047 243.5943 Mean 12.16687 12.33426 12.46023 12.82075 4. CONCLUSION This study has shown the value of forecasting in strategic planning as well as the way forecasting models can boost the productivity of bakeries and confectionery businesses. The goal of the case study was to emphasize the sign selecting the most appropriate and effectRive Y ificance of forecasting models for the company's goods and services. The generated data information from the selected models was subsequently integrated into active decision-making Astrategy processes to make the best possible use of the lRimited resources available to the company. To reduce production costs, increase product demand, and maintain compeItiBtiveness by lowering the cost of Figure 2. Bakery and confectionery sales data for 24 weeks their varied goods, higher productivity is the target for all food-based industries, notably confectionaries. Without using Using the combined data, models were created, compared, accurate and dependableL facts and figures, which can only be and the model with the lowest error would be picked for each achieved by applNying forecasting models to the available data, day. Moving averages of two, three, four, and five weeks no manager can make accurate strategy decisions. For the would be used, along with exponential smoothing (with = 0.2, study of the data that could be obtained from the company for 0.4, 0.6, and 0.8). For each day of the week, the best option in this project, primarily two forecasting models were considered. each model was determined. Based Don thAe information available, forecasting models were The mean absolute percentage error obtained from using the contrasted. The best forecasting model for the day was the one two forecasting models are provided in Table 16 and a better with the highest performance rating, or the one with the lowest comparison is shown in Figure 3. The model with the MAPE (i.e., Monday or Tuesday or Wednesday, etc.). minimum performance criteria was picked as the most optimal Considering varying forecasting models, other models could forecasting technique as supported in the research [17, 18] for Bbe explored further for possibility of adopting a better model analyzing sales data. The mean values of MAPE for all the I days cumulative together are found to be 3.7347 and 15. for the exponential smoothing and moving ave OF with relatively minimum forecasting error. Also, the period of 1713 sales data collected could be extended to one or two years for rage, clearer understanding of factors influencing the sales, and respectively. better performance by the models. Table 16. MAPE comparison for the forecasting models Day of the Exponential Y REFERENCES Moving average model week of smoothing model (MAPE) production (MAPE) IT [1] Mintzberg, H. (2017). 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