การประช มว ชาการด านการว จ ยด าเน นงานแห งชาต ประจ าป 255 ว นท 24 25 กรกฎาคม พ.ศ. 255 Time-Series Forecasing Model for Auomobile Sales in Thailand Taweesin Apiwaanachai and Jua Pichilamken 2 Absrac Invenory managemen a car dealers is generally no efficien because dealers place orders based on heir prior sales experiences o ensure ha cars will be readily available o cusomers. If socks are held a dealers for a long ime, especially unil he end of model life, i will be difficul o clear ou hose socks. Cusomers are hus offered financial incenives (such as free insurance) which are hen subsidized by car manufacurers. We propose o se up Informaion Daabase Cener ha collecs sales daa in real ime. A modified Hol-Winer s forecasing model is buil o esimae cusomer demand, insead of using hisorical sales daa. We evaluae our forecasing model by comparing forecass (from he Hol-Winer s and our modified model) wih acual daa. Keywords: invenory managemen, ime-series forecasing model, Hol-Winer s mehod Inernaional Graduae Program in Indusrial Engineering, Faculy of Engineering, Kasesar Universiy, Bangkok, Thailand E-mail: aweesin_api@homail.com 2 Indusrial Engineering, Faculy of Engineering, Kasesar Universiy, Bangkok, Thailand ;E-mail: jua.p@ku.ac.h 298
การประช มว ชาการด านการว จ ยด าเน นงานแห งชาต ประจ าป 255 ว นท 24 25 กรกฎาคม พ.ศ. 255. Inroducion In Thailand, auomobile indusry is considered one of he major indusries which significanly conribue o he naion s economy. As of 27, auomobiles and pars rank second in expor values (9.5% of oal) and accouns for 4% of he Gross Domesic Producs (GDP) []. Figure shows ha he auo indusry employs % of he Thai workforce. As a resul, he Royal Thai Governmen has been promoing Thailand as he Deroi of Asia by providing funds and ax incenives, such as reducing impor duy for vehicles under Free Trade Area (FTA) Agreemens. Because of many suppors from he governmen o promoe auomobile indusries in Thailand, compeiion among car manufacures is fierce. They realize ha if hey are unable o know cusomer s buying behaviors well, heir produc would no be srong enough o survive in a highly compeiive marke. According o J.D. Power and Associaes Repors on he op reasons for avoiding a vehicle [2], op 3 main facors affecing decision-making of cusomers when buying a car are generally based on he following iems;. Syling 2. Reliabiliy 3. Price Considering each facor, syling is personal preference. Nowadays, car reliabiliies are no significanly differen among brands due o compliance o inernaional sandards such as Economic Commission for Europe (ECE). Moreover, vehicles are periodically benchmarked o assess heir srenghs and weaknesses in comparison wih compeiors. As a resul, auomobile manufacurers aim o compee on prices. Manufacurers focus on reducing producion cos o achieve compeiive prices as well as o gain more profi. Widely used cos reducion schemes are wase reducion, value engineering, and invenory reducion. Wase reducion considers boh maerials and producion ime. Value engineering approaches aim o measure value of a produc in erms of qualiy, performance, and reliabiliy (a an accepable price) and o remove non value-added aspecs where value is defined as worh/cos [3, 4]. In general, manufacurers mosly concenrae on reducing producion invenory. However, we hink ha invenory of finished vehicles should be considered as well. Dealers place orders based on heir prior sales daa. They ofen overesimae he order quaniies o ensure ha cars will be readily available for cusomers. Dealers are responsible for holding hose socks. However, if socks are held a dealers for a long ime, especially owards he end of model life, i would be difficul o clear ou hose socks. Thus, cusomers are offered financial incenives (such as free auo insurance) which are hen subsidized by car manufacurers. Some companies spend up o en million Bah per year o clear ou his dead sock. If we have a beer forecasing model for demands, here should be fewer dead socks. We propose an Informaion Daabase Cener ha collecs sales daa in real ime. From his daa, a forecasing model is generaed o esimae cusomers demand. Our model akes ino accoun special characerisics of he Thai auomobile marke; for example, exernal facors such as perol price, ineres rae for loan, and average household income, ogeher wih seasonal characerisics due o annual sale evens (see Figure for example). There are many forecasing echniques, such as, curve fiing (or regression) mehods, smoohing mehods, and seasonal smoohing mehods. We choose he Triple Exponenial Smoohing known as he Hol-Winer s (HW) mehod because i is ofen applied o ime series ha exhibi rend and seasonaliy such as our case. 25 2 5 5 Model Soluna A Med Med Grade Grade A/T A/T Model Soluna A Top Grade A/T A/T Model Soluna A Top Top Grade Grade M/T M/T Model Soluna A Med Med Grade Grade M/T M/T Model Soluna A Low Low Grade Grade A/T A/T Model Soluna A Low Grade M/T M/T Oc Oc Oc Oc Oc 22 23 24 25 26 27 Figure : Sale volume of one paricular model in Thailand during 22 27. HW is essenially a quaniaive mehod ha uses mahemaical recursive funcions o predic rend and seasonaliy behaviors. I assumes ha he fuure will follow he same paern as he pas. In our case, we have seasonal paerns corresponding o weekly, quarerly or annual periodiciy; herefore, we should include facors in our model ha uilize he hisorical informaion [5]. Afer he HW model is formulaed, we evaluae i by comparing he forecass wih he acual daa o see if i could help dealers place orders more effecively, e.g., o 299
การประช มว ชาการด านการว จ ยด าเน นงานแห งชาต ประจ าป 255 ว นท 24 25 กรกฎาคม พ.ศ. 255 minimize numbers of cars in heir sock yards This paper is organized as follows: We presen background on ime-series forecasing models ha are relaed o our work in Secion 2. We ouline our modeling procedure in Secion 3. We presen our resuls in Secion 4. We conclude in Secion 5. 2. Time-Series Forecasing Model We discuss exponenial smoohing models in Secion 3. and he special case of an exponenial smoohing model: Hol-Winer in Secion 3.2. 2. Exponenial smoohing One of he forecasing echniques ha can address a fairly predicable environmen is ime series [6-8]. Time series models include regression, decomposiion and various adapive mehods. Wih such echniques, one essenially seeks o idenify paerns in he daa over ime and moves o projec he esablished paerns ino he fuure. However, we have o keep in mind ha hese models assume ha wha has happened in he pas will coninue o happen in he fuure, bu, by definiion, he fuure is unpredicable. If his basic assumpion is violaed, wheher as a resul of exernal or inernal changes (e.g., he firm inends o launch a massive adverising campaign), he accuracy of he forecass becomes quesionable [9]. Time series analysis is exensively uilized in many areas, such as economic forecasing, budgeary analysis, and invenory sudies. Users selec a model-fiing mehod based on an applicaion on hand as well as preference. These mehods include Moving Average, Box-Jenkins, Auoregressive Inegraed Moving Average (ARIMA), Box-Jenkins Mulivariae model, and exponenial smoohing. In his paper, we adop he exponenial smoohing because some sudies, such as [-], show ha exponenial smoohing ouperforms he more sophisicaed Box- Jenkins models. Exponenial mehods can be classified ino hree ypes: single exponenial smoohing, double exponenial smoohing and riple exponenial smoohing or Hol-Winer s (HW) mehod. In his paper, we concenrae on HW since auomobile demand exhibi boh rend and seasonaliy behaviors. 2.2 Hol-Winer s mehod Depending on he ype of seasonaliy, HW models can be eiher a muliplicaive seasonal model (Secion 2.2.) or an addiive seasonal model (Secion 2.2.2). 2.2. Muliplicaive Seasonal Model The muliplicaive seasonal model is appropriae for ime series in which ampliude of he seasonal paern is proporional o he average level of he daa [2]. I assumes ha he ime series is represened by Equaion (): F = ( b + b ) S + ε () 2 where F is he forecas a ime =,2,3, K, b is he base signal or he permanen componen, b is a linear rend 2 componen, S is a muliplicaive seasonal facor, andε is he random error componen which is a sandard normal random variable N (,). From Model (), we obain he following recursive formula: F = ( R + G ) S L where R sands for he esimaor of he permanen componen ( b ) a ime, G sands for he esimaor of he rend componen ( b ), L sands for he number of periods of 2 hisorical daa ha is used o obain forecass. Le y sand for he acual daa a ime. Parameers R, G, and G S are updaed as follows: y α α (2) ( α )( R + G ) = + S L = ( S S ) + ( β ) G R β, β (3) y S = γ + ( ) S L R γ γ (4) where α, β and γ are smoohing consans. The value of forecas T periods afer ime is given by: F + T = ( R + TG ) S. (5) + T L To iniialize seasonal facors, minimum hisorical daa of one full seasons (or m periods) is needed: ym y G = (6) m m (7) R S = y i n i= = y R. (8) 2.2.2 Addiive Seasonal Model The addiive seasonal model is suiable for daa whose ampliude of seasonaliy is independen of he average level of he series. The addiive seasonal model has he following form: F = b + b + S + ε (9) 2 3
การประช มว ชาการด านการว จ ยด าเน นงานแห งชาต ประจ าป 255 ว นท 24 25 กรกฎาคม พ.ศ. 255 where all variables have previously been defined in Equaion (). Parameers R, G, and S are updaed as follows: R = α ( y S L ) + ( α )( R + G ) α () G = β ( S S ) + ( β ) G β () S = γ ( y R ) + ( γ ) S L γ (2) The forecas for he nex period is given by: F = R + G + S. L (3) 3. Model Developmen We consider one paricular car model which has a lo of sales daa, where we collec and caegorize i. For his sudy, we divide he daa ino 5 groups; op grade auomaic ransmission (Top A/T), medium grade auomaic ransmission (Med A/T) and manual ransmission (Med M/T), low grade auomaic ransmission (Low A/T) and manual ransmission (Low M/T). We choose eiher a muliplicaive seasonal model (Equaion ()) or addiive seasonal model HW model (Equaion (9)) by considering Mean Absolue Percenage Error (MAPE) as shown in Equaion (4). For his daa se, ime is in monh and m is 2 because auomobiles are classified by year. The daa used in his sudy are from uary 22 o il 27. n y F MAPE = (4) n = y where n sand for oal number of daa. Boh he muliplicaive and he addiive model require all 3 smoohing consans, α, β and γ, since auomobile sale has boh rend and seasonaliy behaviors. As a rule of humb, values beween. and.3 are used when he forecass depend on a large number of pas values, while larger values of smoohing consans are used when forecass depend more heavily on a few recen values [3]. We use Excel s solver o deermine smoohing consans (Table ). Table : Smoohing consans of each configuraion. α β γ Muli Add Muli Add Muli Add Top A/T.3.59.3.3.8.3 Med A/T.3.33.3.3.69.54 Med M/T.6.3.3.3.9.62 Low A/T.8.3.3.3..77 Low M/T.66.54.3.3..3 Table 2: MAPE of he muliplicaive model and addiive model. MAPE Muliplicaive Addiive Top A/T.4.33 Med A/T.64.25 Med M/T.55.32 Low A/T N/A.23 Low M/T.45.32 Table 2 shows he resuling MAPE. Because he addiive model has a lower MAPE, we only consider his model from now on. The forecass can be graphically compared wih he acual daa as shown in Figure 2. Since he overall appearance of his auomobile model was compleely overhauled in ember 22, i migh cause a drasic increase in cusomer demand. To beer respond o his kind of flucuaion, we need o modify how our seasonal componen is updaed. In addiion, we consider smoohing our daa before we fi a forecasing model. 3 25 2 5 5 Acual daa Forecasing done by addiive seasonal model - -2-4 -5 Oc-6-8 Figure 2: Comparison of forecass from he addiive model wih acual daa for Top A/T configuraion. We smooh our daa by using moving averages. For he daa during he firs season (when forecasing canno be done), i.e., m, if ( y y )/ y c for some hreshold c, we replace y wih ( y+ + y )/2. Afer he firs season (when forecass exis), i.e., > m, if ( y F )/ y c for some hreshold c, we replace y wih ( y+ + y )/2. We consider he hreshold c of %, 2%,, % and see which value gives he lowes MAPE. Our resuls show ha seing c o % is bes. Even afer smoohing he daa, our forecasing model sill canno capure he flucuaion paern in 3
การประช มว ชาการด านการว จ ยด าเน นงานแห งชาต ประจ าป 255 ว นท 24 25 กรกฎาคม พ.ศ. 255 he daa. Thus, we modify he seasonal componen S. The idea is ha if S is a real seasonal componen, is value should remain relaively consan from one season o he nex. Thus, if error, defined as ( y F )/ y %, and ( y F ) I < ( y F ) S (5) where I is he inerpolaed value of he seasonal componen of he mos recen pas daa and he fuure daa which have error beween forecased value and acual value lower han %. Figure 3 shows he comparison beween he original HW and our modified HW wih he acual daa. The original HW model produces highly inaccurae forecass for ember sales of every year due o he unusual observaion in he firs season. Our modified HW model can reduce he effec of his oulier and produce forecass ha beer rack he general rend in he daa. 3 25 2 5 5 Acual daa of TOP AT Forecased value of TOP AT calculaed by original HW Forecased value of TOP AT calculaed by modified HW - -2-4 -5 Oc-6-8 Figure 3: Comparison of wo ypes of forecass from he addiive model wih acual daa for Top A/T configuraion. 4. Model Evaluaion We evaluae our models wih he daa ha are no used for model fiing: 27 o ch 28. Table 3 shows he MAPE of he forecass ha his auomobile company came up wih, he forecass from he original HW and he forecass from our modified model. We see ha boh HW models, alogeher, perform beer han he company s forecass for 4 ou of 5 daa ses. The modified HW, by iself, wins in 3 ou of five cases, bu he original HW wins for he Low M/T daa se, and he company s forecass fares he bes for he Low A/T daa se. Table 3: MAPE of he company s forecass, he original HW forecass and he modified HW forecass. MAPE Company's forecass Forecasing by original HW Forecasing by modified HW Top A/T.574.445.37 Med A/T.394.594.73 Med M/T.543.22.79 Low A/T.67.236.259 Low M/T.33.96.224 Average.398.338.23 To apply he modified HW ino he invenory managemen for car dealers, hisorical sale record should be periodically uploaded ono Informaion Daabase Cener. This daa is hen fed o some compuer program o calculae sale forecass which can be used for producion planning. 5. Conclusion Despie a beer performance han he convenional forecasing mehod ha he company currenly uses, our proposed models can be improved furher if we do a beer job of deermining smoohing consans (α, β and γ in Equaions (2) (4) and () (2)). Alhough inerpolaed values can improve seasonal componens, someimes i migh cause worse forecass if inerpolaed value canno be represenaive of seasonal componen suiably due o a coincidence and high flucuaion of acual daa during value inerpolaion, as we can see in Low A/T and Low M/T configuraions in Table 3. 6. Acknowledgemen The firs auhor would like o hank he Inernaional Gradae Program in Indusrial Engineering for financial suppors on uiion fee during he firs year of sudy. References Thailand Auomoive Indusry Associaion, y 9 h 27, Fuure Direcion of Thailand Auomobile Indusries. 2 J.D. Power and Associaes Repors, ember s 24, Launch Models Ofen Face Low Awareness Levels among New- Vehicle. 3 Value engineering, Available a hp://en.wikipedia.org/wiki/value_engineering 4 Fowler, C.T. 98, Value Analysis in Design, Van Nosrand Reinhold, New York, NY, 32
การประช มว ชาการด านการว จ ยด าเน นงานแห งชาต ประจ าป 255 ว นท 24 25 กรกฎาคม พ.ศ. 255 5 Deecing loss of performance in Dynamic Boleneck Capaciy (DBCap) measuremens USING THE Hol-Winers, Algorihm Felipe H., M. Chhaparia, Les Corell SLAC, Available a hp://www-iepm.slac.sanford.edu/monioring/forecas/hw.hml 6 Aiken, L.S and S.G. Wes 99, Muliple Regression: Tesing and Inerpreing Ineracions, Sage, London. 7 Seber, G.A.F. 977, Linear Regression Analysis, Wiley & Sons, New York, NY. 8 Weisberg, S. 985, Applied Linear Regression, Wiley & Sons, New York, NY. 9 Caruana A. 2, s in forecasing wih seasonal regression: a case sudy from he carbonaed sof drink marke, Journal of Produc & Brand Managemen, Volume Number 2, pp. 94-2. Geurs, M.D., and I.B. Ibrahim 975, "Comparing he Box- Jenkins approach wih he exponenially smoohed forecasing model applicaion o Hawaii ouriss", Journal of keing Research, Vol. 2 pp.82-8 Makridakis S., and M. Hibon 979, "Accuracy of forecasing: an empirical invesigaion", Journal of he Royal Saisical Sociey, Vol. 42 No.2, pp.97-45. 2 Time Series Forecasing using Hol-Winers Exponenial Smoohing, Available a hp://www.i.iib.ac.in/~praj/acads/seminar/43298_exponenial Smoohing.pdf 3 Exponenial smoohing, Available a hp://www.is.massey.ac.nz/clai/6342/lecurenoes- 7/Lecures%2(Ch%28).doc 33