International Journal of Scientific & Engineering Research, Volume 7, Issue 8, August ISSN

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1 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August DEMAND FORECASTING OF A FRUIT JUICE MANUFACTURING COMPANY R.A. Kazeem, E.S.Orsarh, N.C. Ehumadu, S.Igboba Abstract - The am of most fruts juce compaes s to develop a effectve ad effcet model that wll provde forecast for optmum producto quatty for the selected compay. Fruts are hghly pershable products; therefore t s hghly mportat that they are well preserved to avod losg ts freshess. Due to ths codto, t s a problem for the producers to kow exactly the ecessary quatty of fruts to order from the prmary source of supply, ot kowg the exact amout of fresh fruts to order makes t ueasy to meet up wth demad for the compay s product ad also to create a opportuty for heavy losses due to the persh ablty of the fruts ordered from the market. Ths study focuses o selectg the best forecastg model for a leadg frut juce compay based o the sales record usg a operatoal perod data set of 48 weeks each obtaed from a leadg frut juce compay based Ibada, Ngera. The four forecastg techques used cludes movg average model, expoetal smoothg model, weghted movg average ad lear regresso model ad the data obtaed were aalyzed accordgly. After applyg the four forecastg models to aalyze the weekly sales data of the chose compay, the results obtaed were compared. The model wth the best performace ratg (.e. the oe wth mmum mea absolute percetage error) was movg average model. It was cosdered as the most excellet forecastg model to mmze forecastg error. Sce ths partcular dustry s products are seasoal, ay forecastg techques appled must be aalyzed up to the seasoal tredg level for essetal aalyss ad justfcato of ts applcato. Idex Terms: Forecast, Sales, Mea Absolute Percetage Error, Model INTRODUCTION compettve by reducto thecost of ther varous Forecastg s a systematc approach to estmato of products. To acheve these, the varous producto future customer requremets usg statstcal ad puts must be provded therght quattes ad mathematcal methods (Krajčovč, 004). Forecastg at the rght qualtes at the rght tme ad at the s a base of every part of busess pla, cludg of lowestpossble cost (Olusak, 04). Therefore dstrbuto ad sales pla. I the feld of logstcs cosderato of all these factors forecastg s avery plag (sales-, producto- ad purchasgplag) we have to process a detaled data, Fruts are hghly pershable products, therefore t s mportat tool. structured accordg to tems, markets, tme hghly mportat that they are well preserved to behavor, etc (Krajčovč, 004). Forecastg s usable every producto eterprse depedet of appled logstcs cocept. Forecastg methods are used each of decouplg pot postos except of purchase ad make to order cocept, because ths case exst oly order-blocked vetores (Krajčovč, 004). The eed for plag, strategy ad formato s very mperatve decso makg (Lda, 00). I the tme past lttle amouts of formato usually has effect o the dfferet steps of the producto cha. For maagemet to take every mportat decso plag o a daly avod losg ther freshess ad at the same tme keep ther vtam cotet (Joh, 004). Due to ths codto t s a problem for the producers to kow exactly the ecessary quatty of fruts to order from the prmary source of supply whch s the locals the rural areas. Not kowg the exact amout of fresh fruts to order makes t ueasy to meet up wth demad for the compay s product ad also to create a opportuty for heavy losses due to damage to the pershablty of the fruts ordered from the locals. Therefore, the certaty of the actual demad quatty ca be made avalable before bass s very mportat (Arwa et al, 04). Plag producto commeces. Frut juce compaes the form; how much has bee demaded for? How may s to be produced? How s to be stored?(undp, 009). determe the quatty to be produced based o ther persoal judgmet o the amout of juce packs sold the prevous day. For the producto For every food based dustry especally quatty to be as close as possble to the actual cofectoares, hgher productvtys the ultmate goal terms of reducto producto costs, greaterdemad of products ad ablty to rema demad quatty, relable forecasts eeds to be made to esure that the producto quatty s as close as possble to the actual demad quatty.

2 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August Relable forecasts wll help maxmzg sales ad mmzg wastages ad losses (Ada ad Murad, 0). The am of the study s to develop a effectve ad effcet model that wll provde forecast for optmum producto quatty for the selected frut juce dustry. Ths study wll also demostrate the use of the proposed model the operatos ad sales servces of the frut juce dustry. MATERIALS AND METHODS The sales data was collected from a Frut Juce Compay Ibada (captal cty of Oyo state, Ngera) usg a combato of desk study, prmary data collecto through feld vst. Prmary data sources were explored to geerate the formato requred for varous aspects of the study. The compay produces four dfferet products amely; Orage juce, Peapple juce, Orape juce (mxture of orage ad peapple) ad Vogue cocktal juce. A total of forty eght (48) weeks sales data was collected for aalyss. The table below shows the sales data for the compay year 008. TABLE : WEEKLY SALES DATA IN NAIRA GATHERED FOR THE BASELINE 008 MONTH WEEK WEEK WEEK 3 WEEK 4 Jauary,,065,4470,89,40 707,355 February,778,880,556,50,,980,000,60 March 984,000,968, ,600,08,400 Aprl,887,950 3,850,600,95,300 96,650 May, ,64 86,76 3,44,400 Jue,80,060,396,545,37,575 3,74,0 July 4,54, ,50 908,50,75,560 August 690,00 345,00,380,400,035,300 September,36,90,699, ,940,0,40 October,97,0,95,480,439,350,439,350 November,343,845 4,569,90 5,375,380,50,5 December 643,80,464,90 3,86,560 8,640 Forecastg models wll be developed ad compared The best opto each model wll be detfed for for each moth whle the model wth the least error each moth of the year. The opto wth the least wll be chose for that partcular moth. Expoetal smoothg (wth α= 0., 0.4, 0.6, 0.8) ad movg average (of -moth, 3-moth, 4-moth ad 5- moth) ad weghted average models were appled. mea absolute percetage error(m.a.p.e) wll be chose ad recommeded as the best for each partcular week of the moth.. Lsts of Relevat Equatos Used the Study.. Weghted Movg Average Model F WA = = t = W W = Subject to = W = weght of the forecast A = actual demad at tme t Ft = forecasted demad at tme t () ().. Smple Expoetal Smoothg Model Ft = αdt + α( α) Dt + α( α) Dt (3) Ft = αdt + ( α) Ft (4) Where Ft = Forecasted demad/sales perod t. Dt = Actual sales at perods t. Ft = Forecast sales at perod t αα = Expoetal smoothg costat (0 αα ) Ifαα= 0, the the smoothg reduces to a o sescal (meagless or potless) result.e. New forecast = Orgal forecast..3 Smple Movg Average Model Ft + = t t + t +... t Ft + = D = t + (6)..4 Lear Regresso Model ( D + D +... D ) (5)

3 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August The geeral regresso model could be defed as follows: Y = F( X, B) (7) Where X s a set of depedet varables, B s a set of fucto parameters. Y s the depedet varable F (X, B) may be polyomal of ay other or expoetal curve. For a smple regresso, the followg geeral M th degree polyomal may be used. Y = B b X B X... bmx (8) Where Y = the forecast perod X = depedet varable b = set of fucto parameters, The assocated error, e s gve as m e( Y Y ) (9) Where Y = observed demad perod. SS. EE. = 00 Dt Ft Y = the correspodg estmated value. The sum of t = Dt the square of errors s as gve: (3) 3 RESULTS AND DISCUSSION TABLE : EXPONENTIAL SMOOTHING MODEL FOR WEEK EXPONENTIAL SMOOTHING FOR WEEK MAPE Moth Sales (N) αα = 0. αα = 0.4 αα = 0.6 αα = Jauary 065 February March Aprl May Jue July August September October November December Sum N = e = N = Y Y (0) Where N = umber of data set for M =, frst degree polyomal Y = b0 + b X (a lear fucto) N X Y ( X )( Y ) bb = N X ( X ) () Y b X bboo = N N ()..5 Forecastg Model I ths study, the forecastg model cosdered s mea absolute percetage error (MAPE) ad s gve as: Mea TABLE 3: EXPONENTIAL SMOOTHING MODEL FOR WEEK EXPONENTIAL SMOOTHING FOR WEEK MAPE Moth Sales (N) αα = 0. αα = 0.4 αα = 0.6 αα = Jauary 4470 February

4 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August March Aprl May Jue July August September October November December SSSSSS TABLE 4: EXPONENTIAL SMOOTHING MODEL FOR WEEK 3 EXPONENTIAL SMOOTHING FOR WEEK 3 MAPE αα MMMMMMMMh SSSSSSSSSS (NN) αα = 0. = 0.4 αα = 0.6 αα = Jauary 8940 February March Aprl May Jue July August September October November December Sum Mea TABLE 5: EXPONENTIAL SMOOTHING MODEL FOR WEEK 4 EXPONENTIAL SMOOTHING FOR WEEK 4 MAPE MMMMMMMMh SSSSSSSSSS (NN) αα = 0. αα = 0.4 αα = 0.6 αα = Jauary February March Aprl May Jue July August September October November December Sum Mea

5 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August TABLE 6: MOVINGAVERAGE MODEL FOR WEEK MOVING AVERAGE FOR WEEK MONTH SALES (N) moth MAPE 3moth MAPE 4moth MAPE 5moth MAPE Jauary 065 February March Aprl May Jue July August September October November December Sum Mea TABLE 7: MOVINGAVERAGE MODEL FOR WEEK MOVING AVERAGE FOR WEEK MONTH SALES (N) moth MAPE 3moth MAPE 4moth MAPE 5moth MAPE Jauary 4470 February March Aprl May Jue July August September October November December Sum Mea TABLE 8: MOVINGAVERAGE MODEL FOR WEEK 3 MOVING AVERAGE FOR WEEK 3 MONTH SALES (N) moth MAPE 3moth MAPE 4moth MAPE 5moth MAPE Jauary 8940 February 980 March Aprl May Jue July August September October November

6 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August December Sum Mea TABLE 9: MOVINGAVERAGE MODEL FOR WEEK 4 MOVING AVERAGE FOR WEEK 3 MONTH SALES (N) moth MAPE 3moth MAPE 4moth MAPE 5moth MAPE Jauary February March Aprl May Jue July August September October November December Sum Mea TABLE 0: WEIGHTED MOVINGAVERAGE MODEL FOR WEEK WEIGHTED MOVING AVERAGE FOR WEEK MONTH WEIGHT(W) ACTUAL SALES (N) FORECAST MAPE Jauary February March Aprl May Jue July August September October November December SSSSSS MMMMMMMM TABLE : WEIGHTED MOVINGAVERAGE MODEL FOR WEEK WEIGHTED MOVING AVERAGE FOR WEEK MONTH WEIGHT(W) ACTUAL SALES (N) FORECAST MAPE Jauary February March Aprl May Jue July August September October November December Sum Mea 6.9

7 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August-06 4 TABLE : WEIGHTED MOVINGAVERAGE MODEL FOR WEEK 3 WEIGHTED MOVING AVERAGE FOR WEEK 3 MONTH WEIGHT(W) ACTUAL SALES (N) FORECAST MAPE Jauary February March Aprl May Jue July August September October November December Sum Mea TABLE 3: WEIGHTED MOVINGAVERAGE MODEL FOR WEEK 4 WEIGHTED MOVING AVERAGE FOR WEEK 4 MONTH WEIGHT(W) ACTUAL SALES (N) FORECAST MAPE Jauary February March Aprl May Jue July August September October November December Sum Mea TABLE 4: LINEAR REGRESSION MODEL FOR WEEK LINEAR REGRESSION MODEL WEEK MONTH SALES (N) FORECAST MAPE Jauary February March Aprl May Jue July August September October November December Sum Mea 48.9 TABLE 5: LINEAR REGRESSION MODEL FOR WEEK LINEAR REGRESSION MODEL WEEK MONTH SALES (N) FORECAST MAPE Jauary February March Aprl May Jue

8 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August-06 4 July August September October November December Sum 97.9 Mea TABLE 6: LINEAR REGRESSION MODEL FOR WEEK 3 LINEAR REGRESSION MODEL WEEK 3 MONTH SALES (N) FORECAST MAPE Jauary February March Aprl May Jue July August September October November December Sum 79. Mea 66.0 TABLE 7: LINEAR REGRESSION MODEL FOR WEEK 4 LINEAR REGRESSION MODEL WEEK 4 MONTH SALES (N) FORECAST MAPE Jauary February March Aprl May Jue July August September October November December Sum 76.6 Mea The four forecastg techques.e. lear regresso, expoetal smoothg, weghted movg average ad movg average were compared for all the weeks the gve year. The mea absolute percetage error obtaed from usg the forecastg models are tabulated below. The model wth the mmum performace crtera s pcked as the most optmal forecastg techque for aalysg sales data. TABLE 8: COMPARISON OF OBTAINED RESULTS FOR THE FOUR MODELS WEEK LINEAR REGRESSION ANALYSIS MODEL (MAPE) EXPONENTIAL SMOOTHING MODEL α = 0., 0.4, 0.6, 0.8 (MAPE) MOVING AVERAGE MODEL (M =,3,4,5) (MAPE) WEIGTHED MOVING AVERAGE MODEL (M= 3)(MAPE) , αα = , mm = , αα = , mm = , αα = , mm = , αα = , mm =

9 Iteratoal Joural of Scetfc & Egeerg Research, Volume 7, Issue 8, August Wth the comparso results table 8, the followg relevat formato could be reached; for week, the model that s most sutable ad wth the least value s movg average model. It has a mea absolute percetage error (MAPE) of I week, weghted movg average & movg average models have the mmum values of mea absolute percetage error. For week 3, movg average model s chose wth M take as 5. Fally, movg average model s the least week 4 compare to the other three models. Due to the cosstecy of the movg average, the frut juce dustry wll be advsed to always use ths model to mmze the forecastg error of ther compay. 4CONCLUSIONS Forecasts eed ot be accurate sce they provde a pot to start plag. It s better that the best use of the avalable data s made accordg to the stuatoal demads. What s mportat s the proper use of data that s avalable. Normally, the forecast should be put a rage rather tha exact data. Rage helps may ways terms of hghest fgure ad lowest fgure. Accordgly, a judcous plag ca be made. Ths case study tres to hghlght the mportat of selectg the most sutable ad relevat forecastg models for the orgazatos product whch the geerated formato from the selected forecastg models are later tegrated to acto-decso makg processes utlzg every advatageous chaces avalable to the orgazato cosderato. I ths partcular case study, four forecastg models were cosdered for the aalyss of data collected from a well-kow frut juces dustry based Ibada, Ngera. After applyg the four forecastg models to aalyse the weekly sales data of the chose compay, comparso of results were observed at the same tme. The model wth the best performace ratg (.e. the oe wth mmum mea absolute percetage error) was cosdered as the most excellet forecastg model to mmze forecastg error. The comparso tables for the examed forecastg model for the four weeks are as represeted table. 5 ACKNOWLEDGEMENTS The authors wsh to thak the staffs of Fuma Juce Compay, Ibada, Oyo state, Ngera for the data provded to carred out ths study. 6REFERENCES [] Ada Mukattash ad MuradSahour, (0). Supply Plag Improvemet: A casual Forecastg Approach. Joural of Appled Scece (): 07-3, 0. Asa Network for Scetfc Iformato. [] Arwa A. Altameem, Abeer I. Aldrees ad Nuha A. Alseed, (04). Strategc Iformato Systems Plag (SISP).Proceedgs of the World Cogress o Egeerg ad Computer Scece 04 Vol I. [3] Joh Wlkso, (004). The Food Processg Idustry, Globalzato ad Developg Coutres.Electroc Joural of Agrcultural ad Developmet Ecoomcs.Agrcultural ad Developmet Ecoomcs Dvso (ESA) FAO. [4] Krajčovč Mart, (004). Demad Forecastg as a Tool for Precse Producto Plag ad Ivetory Cotrol.TH Iteratoal Workshop, Advaced Methods ad Treds Producto Egeerg.Uversty of Zla, SjF VelkyDel, Zla, Slovak Republc. [5] Lda Parker Gates, (00). Strategc Plag wth Crtcal Success Factors ad Future Scearos: A Itegrated Strategc Plag Framework. Techcal Report CMU/SEI-00-TR-037 ESC-TR [6] Olusak S Akdpe, (04). The Role of Raw Materal Maagemet Producto Operatos.Iteratoal Joural of Maagg Value ad Supply Chas (IJMVSC) Vol.5, No. 3, September 04. [7] Uted Natos Developmet Orogramme UNDP, (009). Hadbook ON Plag, Motorg ad Evaluatg for Developmet Results.Maufactured the Uted States of Amerca.

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