A comparison study between time series model and ARIMA model for sales forecasting of distributor in plastic industry

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1 OSR Journal of Engineering (OSRJEN) SSN (e): , SSN (p): Vol. 04, ssue 02 (February. 2014), V1 PP A comparison sudy beween ime series model and ARMA model for sales forecasing of disribuor in plasic indusry Paimaporn Udom 1,a, Naragain Phumchusri 1,b 2 Deparmen of ndusrial Engineering, Faculy of Engineering, Chulalongkorn Universiy, Bangkok, Thailand Absrac: - The number of disribuors in plasic indusry is increasing every year. Therefore, hey go a problem abou compeiive cos more han in he pas. One of he ways o solve his problem is managemen by invenory. Before hey improve invenory, he forecasing is imporan for his process. n he pas, hey were looking for convenional ime series for forecasing sales volume before manages invenory. This sudy would like o compare he applicaion of hree forecasing mehods on he amoun of he sales volume for plasic disribuor, he ARMA ime series mehod,moving average mehod and Hol s and Winer exponenial mehod. Afer applying five daa ses of raw maerial from plasic disribuor by four forecasing mehods, he ARMA model shows beer resuls han oher models when compare wih oher mehods by using MAPE (Mean Absolue Percenage Error). Keywords: - Forecasing, ARMA, nvenory,naive.. NTRODUCTON Thermoformed plasics are plasics used in he process of injecion, exrusion and hermoforming. The regularly used polymers for he process include acrylonirile buadiene syrene (ABS), high impac polysyrene (HPS), polypropylene (PP) and polymehyl mehacrylae (PMMA) among ohers. These plasics have applicaions in auomoive par, elecronics par, food packaging and consumer produc. The main requiremen for he plasic indusry is a disribuor o provided plasic o plasic facory. The plasics indusry shapes he world we live in oday wheher i is indusrial, echnological or commodiies used on a regular basis. Qualiy marke analysis, forecass and rends deermined from key marke drivers help shape he fuure of he plasics indusry. The curren domesic marke for disribuor business is compeiive raher high when compare wih 5-6 years ago. Business and dealer happens quie a lo in he plasic indusry. n he pas, plasic disribuor also have a small amoun so hey can add more margin o cover heir cos bu currenly we have plasic disribuor more han 40 company in Thailand marke. And he way o keep heir marke has reduced prices and o analyze ways o reduce coss. Forecasing, i is he beginning of he adminisraion in he oher due o forecasing analysis will help hem o undersand he emerging echnologies and applicaions by key marke. For forecasing process, i purposes o find he bes model wih hisorical daa. Neverheless, uncerainy of daa collecion will be occurring due o he error caused in ime lag and effec beween variables. However, from he radiional model, mos of forecasing mehods usually use a saisical model as a ool for forecasing fuure daa. n indusry segmen, usually use normal forecasing model o forecas fuure daa such as simple moving average, Exponenial smoohing and Hol s and Winer exponenial,.ec. For example, Suwadee [2] find forecasing model for auomoive par and hey found Regression suiable for auomoive par daa. n recen years, due o he innovaion of forecasing mehods and improvemen of forecasing accuracy, he forecasing mehodology becomes indispensable for furher decision making process in boh indusry and governmen. For example, Zadeh [3] defines a fuzzy algorihm is an ordered se of fuzzy insrucions which upon execuion yield an approximae soluion o a specified problem. The concep is applied o differen fields of daa o solve he problems. Currenly, he concep of fuzzy logic is successfully o analysis forecasing mehods. Volkan S. Edigera and Serac Akar [4] used ARMA mehod o forecas of primary energy demand by fuel in Turkey. The ARMA forecasing of he oal primary energy demand appears o be more reliable han he summaion of he individual forecass. Chi-Chen Wang [5] sudy forecasing model by comparison beween fuzzy ime series model and ARMA model for forecasing Taiwan expor. When he sample period is shorer wih only a small se of daa available, he fuzzy ime series models can be uilized o predic expor values accuraely, ouperforming he ARMA model. James W. Taylor [6] found he resuls indicae srong poenial for he use of seasonal ARMA modeling and he exension of Hol-Winers for predicing up o abou wo o hree days ahead and ha, for longer lead imes, a simplisic hisorical average is difficul o bea. However, never saw he research pay aenion o discuss he forecasing model for disribuor in plasic applicaion alhough plasic fields. Besides, previous researches only compue he forecasing daa using a general forecasing model o forecas fuure daa for plasic fields, and sudy new model of forecasing for nernaional organizaion of Scienific Research 32 P a g e

2 A comparison sudy beween ime series model and ARMA model for sales forecasing of disribuor anoher fields excep plasic or plasic disribuor as well. This research aemps o use informaion of sales values from plasic pelles disribuor as an example o es wheher he ARMA is indeed pracical in is forecas of variables. By comparing he ime series as Naïve mehod, Moving average and Winer mehods by use MAPE value o decision. Furhermore, his paper inen o idenify which model is suiable o provide informaion in decision making for plasic pelles disribuor.. METHODOLOGY 2.1 Time series Time series is a sequence of daa poins, measured ypically a successive poins in ime spaced a uniform ime inervals. Examples of ime series is he annual flow volume of he rain-fall and show frequenly ploed via line chars. Time series analysis comprises mehods for analyzing ime series daa in order o exrac parameer saisics and oher characerisics of he daa o predic fuure values based on previously observed values. While regression analysis is ofen employed in such a way as o es heories ha he curren values of one or more independen ime series affec he curren value of anoher ime series, his ype of analysis of ime series is no called "ime series analysis", which focuses on comparing values of ime series a differen poins in ime. A sochasic model for a ime series will generally reflec he fac ha observaions close ogeher in ime will be more closely relaed han observaions furher apar. n addiion, ime series models will ofen make use of he naural one-way ordering of ime so ha values for a given period will be expressed as deriving in some way from pas values, raher han from fuure values. [7] (1) Moving average model F 1 ( A A 1 A 2... A n1) n A = Daa a ime F +1 = Forecas value a ime +1 n = Number of daa (2) Hol s and Winer exponenial model S A L ( 1 )( S1 T 1 ) T S S 1 ( 1 ) T 1 A S ( 1 ) L F p ( S T p) L p S = Smoohing value α = Consan of smoohing value (0 < α < 1) A = Acual value a ime β = Consan of rend value (0 < β < 1) T = Trend parameer a ime = Consan of seasonal value (0 < < 1) = Seasonal parameer a ime p = Number of forecasing L = Lead ime F +p = Forecasing value a ime p 2.2 Auo Regression nvesigae Moving Average (ARMA) model The model was propose by Box Jenkins in 1970, which examines each variable by using auo-regression, AR (P) and Moving Average, MA (Q) o invesigae he hisorical daa and economic flucuaions. The algorihm presened as follows: [8] nernaional organizaion of Scienific Research 33 P a g e

3 A comparison sudy beween ime series model and ARMA model for sales forecasing of disribuor (1) The firs sep in developing ARMA model: deermine if he series is saionary and if here is any significan seasonaliy ha needs o be modeled. The auocorrelaion funcions (ACF) or parial auocorrelaion funcions (PACF) are used o define he disribuion of sample daa. f daa se are no saionary, differencing o achieve saionary. (2) denificaion: idenifying he phase of he series by using auocorrelaion funcions (ACF) and parial auocorrelaion funcion (PACF). (3) Esimaion: he good condiional and exac likelihood are used o esimae he parameers. (4) Diagnosic check: he process of diagnosic check involves esing he assumpions of he model o idenify any areas where he model is no enough. The saisical idenificaion process includes parameers saisical significance and he residual. f he model is found o be ou of conrol, i is necessary o calculae and repea Sep (4) unil a beer model is idenified.. Fig. 1 ARMA flow diagram [8] The accuracy of he fied model is measure by he mean average percenage error (MAPE), which is a measure of accuracy of he fied model. The mean average percenage error (MAPE) is no very informaive by iself, bu i can be used o compare fis of differen models ha we use in his paper. For all measures, smaller values generally indicae a beer fiing model for quaniy of sale for plasic disruor. [5]. RESULT AND DSCUSSON 3.1 Daa preparing The seleced daa were he amoun of plasic sale from plasic disribuor in Thailand during he ime period beween January 2004 and December A oal of daa is 108 monhs and 90 monhs for raining and 18 monhs for esing. Plasics disribuor have many iems in heir sock herefore we should selec daa by ABC analysis. s showed in he able 1. We chose daa by use summary value of each produc iems and we selec produc iems have summary value more han 75% from all of produc iems. We go five iems o find forecasing model for suiable wih each daa. Table 1 ABC analysis for plasic disribuor company nernaional organizaion of Scienific Research 34 P a g e

4 A comparison sudy beween ime series model and ARMA model for sales forecasing of disribuor Producs Average Uni cos per Annual Sales (kg) Code kg (25/2/13) Usage THB per year ,657, ,812,588, % ,123, ,610, % ,053, ,469, % ,150, ,272, % ,374, ,169, % ,201, ,114, % ,021, ,743, % , ,143, % , ,298, % ,024, ,867, % , ,653, % , ,895, % , ,059, % , ,876, % , ,937, % , ,871, % , ,247, % , ,048, % , ,233, % , ,894, % , ,107, % , ,966, % , ,349, % , ,412, % , ,291, % , ,717, % , ,423, % , ,451, % , ,432, % , ,326, % , , % 3,659,308, Uni roo es To deermine ARMA (p,d,q)(p,d,q) x model, we have o es review and rend saionary by use ACF and PACF as showed in Fig 3. We can analyze by calculae daa a ime and +1, if he daa a bi differen from 1 so we have o re-calculae. Moreover, ACF and PACF provide a saisical summary a a lag. The maximum number of lags is deermined by dividing number of acual daa by 4, for a series wih less han 240 based on Box and Jenkins mehod. The resul of ACF and PACF of produc iem 1101 were no saionary so we have o differeniaed daa 1 ime can see in Fig 4. f he daa no saionary we can no forecas by ARMA because forecasa value have an error from daa. From Fig.2 sandard devision of produc iem 1101 is 595, and mean is 2,888, Example for uni roo es for produc iem 1101 showed as below. Fig. 2 Time series of iem 1101 Fig. 3ACF and PACF graph of iem 1101 nernaional organizaion of Scienific Research 35 P a g e

5 A comparison sudy beween ime series model and ARMA model for sales forecasing of disribuor Fig. 4 ACF and PACF graph of iem 1101 (difference 1 ime) 3.3 Esimaion Parameer When we ge he saionary daa se from uni roo es we will defind he parameer for ARMA model. From Fig 4. We ge he saionary daa for produc iem 1101 hen idenify model o go he parameer and we ge model ARMA is ARMA (1,0,1)(1,0,1) 12. Parameer esimae from his model can show as Fig 5. The ARMA model has been originaed from he auoregressive model (AR), he moving average model (MA) and he combinaion of he AR and MA, he ARMA models. From Fig 5 show esimae parameer for produc iem 1101 and have seasonal for ARMA as AR1(1) = 0.147, AR2(12) = 0.854, MA1(1) = , MA2(12) = and B = 2,937,546 and can show he formular as below. (0.147 )( B)(0.854 )( B 12 )(1 B) 0 (1 B 12 1 ) Y 366, ( )( B)(0.455 )( B 12 a ) Fig. 5 Parameer esimae and forecasing of iem Diagnosic check n his case where have seasonal componens are included in he ARMA model, he model is called as he Seasonal ARMA or SARMA. The ARMA forecasing gives he resuls in differen opions which are upper limis, lower limis, and forecased values. Upper and lower limis provide a confidence inerval of 95%, in oher words any realizaion wihin he confidence limis will be accepable. The process of diagnosic check for idenificaion process includes parameers saisical significance can analyze by he residual in Fig 6 and 7. f he residual is random or upper and lower limis have a confidence inerval more han 95%, is mean parameer esimae from model can accep. nernaional organizaion of Scienific Research 36 P a g e

6 A comparison sudy beween ime series model and ARMA model for sales forecasing of disribuor Fig. 6 Residual from ARMA (1,0,1)(1,0,1)12 of iem 1101 Fig. 7 ACF and PACF from residual of ARMA (1,0,1)(1,0,1)12 of iem 1101 Afer es all of produc iems ha we chose 5 iems hen will defind mean average percenage error (MAPE) for each model and each iem. The resul can show in able 2. We find he bes model from four model for forecasing sale volume of plasic disribuor in Thailand is ARMA. ems Table 2 MAPE from four forecasing model of he resul MAPE Value (%) Naive Moving Average Winer Exponenial ARMA V. CONCLUSON The researcher ries o find a way o forecas more accuraely han he old mehod. The five daa ses were colleced from he sales volume from one of disribuor for plasic indusry. Then, he four models were used o apply ino five of he raw daa ses in order o find suiable forecasing model which ge beer error more han currenly model. The resuls showed ha he ARMA model ge he bes MAPE (Mean Absolue Percenage Error) which is he measuremen of his sudy. nernaional organizaion of Scienific Research 37 P a g e

7 A comparison sudy beween ime series model and ARMA model for sales forecasing of disribuor REFERENCES [1] S. Samuhananon, nvenory managemen sysem developmen in spare-par business, Engieering managemen, Chulalongkorn Universiy, [2] M.Z. Babai, M.M. Ali and J.E. Boylan, Forecasing and invenory performance in a wo-sage supply chain wih ARMA (0,1,1) demand: Theory and empirical analysis, nernaional Journal of Producion Economics, [3] J. W. Taylor, A comparison of Univariae Time Series Meshods for Forecasing nraday Arrivals a a Call Cener, Managemen Science, vol. 54, pp , [4] L. Bianchi, J. Jarre and R. Choudary Hanumara, mproving forecasing for elemarkeing ceners by ARMA modeling wih inervenion, nernaional Journal of Forecasing 14, pp , [5] W. A. NG, A simple classifier for muliple crieria ABC analysis, European Journal of Operaional Research, vol177, pp , [6] Chi-Chen Wang. A comparison sudy beween fuzzy ime series model and ARMA model. Deparmen of Financial Managemen Naional Defense Universiy. Exper Sysems wih Applicaions 38,pp , [7] Lisa Bianchi, Jeff Jarre and R. Choudary Hanumara. mproving forecasing for elemarkeing ceners by ARMA modeling wih inervenion. nernaional Journal of Forecasing 14, pp , nernaional organizaion of Scienific Research 38 P a g e