Proceedings of the 2008 Winter Simulation Conference S. J. Mason, R. R. Hill, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds.

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1 Proceedngs of he 008 Wner Smulaon Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. DEMAND FORECAST OF SEMICONDUCTOR PRODUCTS BASED ON TECHNOLOGY DIFFUSION Chen-Fu Chen, Yun-Ju Chen Deparmen of Indusral Engneerng & Engneerng Managemen Naonal Tsng Hua Unversy Hsnchu 3003, TAIWAN, ROC Jn-Tang Peng Deparmen of Busness Admnsraon Yuanpe Unversy Hsnchu 3005, TAIWAN, ROC ABSTRACT Demand forecas plays a crcal role o deermne capal nvesmen for capacy plannng. Gven he nvolved unceranes and long lead-me for capacy expanson, semconducor companes have o predc fuure demands as a bass for relaed manufacurng sraegc decsons. As semconducor producs n a consumer era become more dversfed wh shorenng lfe cycle, demand forecas also becomes more complex and dffcul. Ths sudy ams o develop a demand forecas model based on produc lfe cycle and echnology dffuson. Whle lle research has been done o employ dffuson models o forecas he demands of semconducor producs. The proposed model modfes a mul-generaon dffuson model ncorporang markeng varables no he model for semconducor produc and uses nonlnear leas square mehod o esmae he parameers. An emprcal sudy s conduced o valdae he proposed model wh real daa of semconducor producs. Ths research concludes wh dscusson on fuure research drecons. INTRODUCTION In order o ulze he resources effecvely, semconducor companes need o make manufacurng sraegc decsons and assocaed operaons ncludng capacy plannng, producon plannng, maeral requremen plannng, nvenory conrol, and schedulng (Wu and Chen 008). Demand forecas plays a crcal role o deermne capal nvesmen for capacy plannng o mprove capacy ulzaon and capal effecveness. However, gven he nvolved unceranes and long lead me for capacy expanson, semconducor companes have o predc fuure demands as a bass for relaed manufacurng sraegc decsons under he rsks of capacy shorage and/or surplus along he me. Moore s Law has drven he semconducor ndusry o keep echnology mgraons and wafer enlargemen o manan he cos reducon per ranssor and he growh of semconducor ndusry (Leachman, Dng, and Chen 007). In oher words, Moore s Law shorens he echnology produc lfe cycle and producs subsuon me. On he oher hand, consumpon of dversfed semconducor producs s affeced by varous economcs facors, whch lead o demand uncerany and ncreasng rsks of capacy shorage and/or surplus n he demand forecas. As semconducor producs n a consumer era become more dversfed wh shorenng lfe cycle, demand forecas also becomes more complex and dffcul. Mos of all companes forecas demand n he fuure by usng marke nformaon and her relaed experence or doman knowledge. They deal wh he problem subjecvely. The resul of hs mehod mgh have low accuracy and large errors. Addonally, needs o repea he process wh her marke nformaon, relaed experence or doman knowledge for dfferen producs. Thus, s necessary o consruc a suable and general model o forecas demand precsely. Dfferen forecasng mehods have been appled n dfferen areas. Mos of exsng demand forecasng sudes employed he me seres mehods. Bu hese mehods are dffcul o express he enre adopon process of he new producs. Therefore, s necessary o consruc a model for express he enre adopon process. I can help managers o make well decsons for he new produc. Inheren forecasng mehods are manly desgned for a sngle generaon whou consderng he subsuon beween generaons and herefore hey needs o execue he forecasng repevely. However, he characerscs of semconducor producs are mul-generaon under a segmen. A segmen s manufacured under dfferen echnologes. For hs reason, s crucal o forecas a semconducor produc under dfferen generaons one me. Mul-generaon dffuson models can deal wh he problem for he characerscs of semconducor producs. On he oher hand, dffuson models are appled o consumer durables prmarly. Lle research has been done o employ dffuson models o forecas he demands of semconducor producs. I s crucal o consruc a mulgeneraon dffuson model for semconducor producs /08/$ IEEE 33

2 Chen, Chen, and Peng Ths sudy ams o consruc a dffuson model for forecasng semconducor producs based on hsorcal daa. Demand forecas s a fundamenal of producon decsons and producon plannng. Manufacurng sraegc decsons nvolve he radeoffs among producvy, qualy, delvery, and cos (Chen, Wang, and Wang 007). The precson of demand forecas may decrease nvenory cos, promoe he qualy of cusomer servce and ncrease marke compeon. Ths sudy develops a produc lfe cycle based on he proposed dffuson model and employs o forecas demand, n whch nonlnear leas square mehod s employed o esmae he parameers. DEMAND FORECAST FRAMEWORK Ths sudy proposes a demand forecas framework for semconducor producs n order o predc he demand and plan he capacy as shown n Fgure. The framework consss of sx phases correspondng o he sx subsecons. The ermnology and noaons used n hs sudy are as follows: F () - he cumulave densy funcon a me for generaon f () - he probably densy funcon a me for generaon s () - he acual sales of producs a me for generaon X () - he cumulave marke effecs sˆ () - he esmaed sales of producs a me for generaon τ - he nroducon me for generaon, τ p q m ρ M - α β pr () g n l - he proporon of mass meda communcaon for generaon - he proporon of word of mouh for generaon - he marke poenal (ncremenal marke poenal) for generaon - he average repea purchase rae for generaon Toal marke poenal for generaon, M = m ρ - he seasonal facor a me - he effecveness of he prce - he prce a me for generaon - he growh rae a me - he number of generaons - he number of perods. Problem Defnon Fgure : Research framework The orders n he semconducor ndusry are cusomzed and make-o-order. For he momen, he developmens of he semconducor manufacurng echnologes face o shoren he lne-wdh and expand he dameer of he wafer n order o provde beer producs wh more applcaons and funcons o he markes. Semconducor ndusry grows rapdly ha shoren he produc lfe cycle (PLC) of semconducor producs. PLC s mporan nformaon o plan marke sraeges. In semconducor ndusry, R&D coss and capal nvesmens are a huge amoun of money. In order o make o allocae he resource effcenly and well plannng, s a crcal ssue o descrbe he PLC and forecas he demand n he fuure. Bu he process of forecasng demand n semconducor ndusry s dffcul for uncerany and rsk. In addon, s hard o forecasng he medum and long erm only for hsorcal daa of old echnologes because of he echnologcal mgraon and demand varaon. How o plan he capacy s an mporan decson for companes. However, capacy plannng reles on demand forecasng. If demand forecasng values are overesmaed han he acual values unfolded laer, capacy can- 34

3 no be ulzed effcenly. I mgh lead he dle capacy and wase. When demand forecasng values are underesmaed han acual values unfolded n he fuure, capacy wll no be suffcen o fulfll he demands hen. I mgh lose he orders or cusomers. In order o predc produc demand precson, hs sudy wll consruc a demand forecas framework o forecas produc demand n he fuure and asss he manager o decson he capacy plannng. Furhermore, he demand forecas framework could be appled o suppor capacy allocaon and capacy expanson decsons.. Daa Preparaon The markeng sales deparmen records and sores each ransacon record n he daabase. The colleced daa ofen ncludes nosy, mssng and nconssen daa. I s necessary o assure he qualy of daa n order o accelerae he effecveness of he model. Hence, daa preparaon can be used mprove he qualy of he daa and consruc he effecve demand forecasng model. The daa preparaon process ncludes daa collecon, daa cleanng, and daa negraon. Collec he requse daa for hs sudy from he daabase. To mprove he qualy of daa, s necessary o deal wh redundan daa, nconssen daa, mssng daa, and so on. Mssng daa can be deleed or replaced by some daa cleanng mehods n he daa cleanng process. The daa cleanng of hs sudy needs o delee he some rows and columns ha are redundan n hs sudy. Daa negraon merges he daa of dfferen sources Table : Produc demand Inegraon Cusomer Produc Technology 00x Q 00x Q X A X B 5 30 X C X C Y B X D X B X D Y C Produc Technology 00x Q 00x Q X A X B X C 0 70 X D Y B Y C no a fle for hs sudy. For example, he prce of he producs, he growh rae of semconducor ndusry, and he demand of he producs need o merge n he same fle n order o analyze he daa convenenly. The daa need o be pued n suable segmens by quarers and dfferen Chen, Chen, and Peng echnologes, respecvely. Addonally, s necessary o sum up he same echnology and he same produc daa such as Table. The daa also need o ransform o suable formas for hs sudy..3 Dffuson Model Consrucon Ths secon ams o develop a dffuson model for semconducor producs. Ths sudy consrucs a mulgeneraon dffuson model based on Noron and Bass model. Frsly, es he parameers wheher hey changes across generaons. Based on he resul of sascal hypoheses, deermne he parameers wheher hey change across generaons. In he semconducor ndusry, some characerscs affec he demand ncludng he prce effec, he growh rae of semconducor ndusry, and so on. The proposed dffuson model n hs sudy maches up he characerscs of he semconducor produc o aan he valuable nformaon and herefore ncorporaes he echnologcal subsuon, repea purchases, prce effec, marke growh rae and seasonal facor no he model..3. The Effec Varables There are fve facors consdered n hs sudy ncludng he echnologcal subsuon, repea purchases, prce, marke growh rae and seasonal facor. The facors are seleced hrough leraure revew, judgmens from doman expers or sascal mehodologes.. Technologcal subsuon effecs As he resul of Moore s law, semconducor ndusry develops rapdly. Newer echnologes connually nroduce o he marke. Newer echnologes are always superor due o newer echnologes wh aached applcaons and funcons, hence newer echnologes wll replace older ones sep by sep. The nroducon of newer echnology also wdens he marke poenal and affecs he buyers of he older echnology o buy he newer echnology o subsue he older ones. In oher words, he sales of he older generaon producs mgh be subsued for he newer generaon producs. Mos forecasng mehods only focus on he new produc self and gnore he older generaon producs ha mgh compee wh new producs. The sngle generaon dffuson models or oher forecasng mehods are no suable for semconducor producs. I s essenally echnologcal nnovaon for he new producs of semconducor ndusry. I needs o consder boh dffuson and subsuon for semconducor producs n hs sudy and herefore mulgeneraon dffuson models are feasble for semconducor producs.. Repea purchases 35

4 Consder repea purchase n hs hess, because Adopers don purchase only one un. Boh Noron and Bass (987) and Bass and Bass (00) consder repea purchase n her model. Bass and Bass (00) revsed manly he mulgeneraon model proposed by Noron and Bass. The model dvded he adopers no wo pars: frs adopers and repeaed adopers respecvely. In he Noron and Bass model, consdered ha he average purchase rae s a consan ρ and herefore M = ρ m. M can be esmaed, bu hey ddn denfy ρ and m respecvely. 3. Prce effecs Prce s a pvo facor o affec cusomers wha o buy and herefore he prce effec of mulgeneraon producs s mporan. The prcng sraegy consders no only he sages of he produc lfe cycle bu also he subsuon of newer generaon producs. In general, he demand curve shows as he exponenal curve. The hgher s he prce of he producs, and he smaller s he quany of he demand. On he oher hand, he prce of produc s down, he demand mgh be up. As he newer generaon producs nroduce o he marke, he prce of he newer generaon producs wll affec cusomers o decde wha o buy. If he expeced fuure prce wll be ncreased or reduced, he behavors of he cusomers also change. For semconducor producs, he prce goes down quckly n he nal sage of he producs and vares seady n he laer sage. Bass, Krshnan, and Jan (994) ncorporaed he markeng effec no he Bass model for a sngle generaon. The markeng effec conaned prce and adversng expendures n hs model. The model has been appled o consumer durables such as he color elevson, room ar condoner and so on. Ths approach exends hs model o mul-generaon model for semconducor producs. 4. Marke growh raes Growh rae s a facor o descrbe he socal envronmen. The varaon of cusomer behavors s affeced by he growh rae. When he growh rae s rse, he demand mgh be up. 5. Seasonal facors In general, many busness acves wll be affeced by seasonal facors. Semconducor producs appled o varous ndusres such as PC manufacurng, communcaon ndusry, and so on. However, he sales of PC may be affeced by seasonal facors. For example, he sales of PC wll ncrease a Chrsmas. Chen, Chen, and Peng I needs o consder he effec of seasonaly for neglecng he effec of seasonaly may lead o overesmae/underesmae demand..3. The Proposed Model (SMPRT model) Mos mul-generaon dffuson models only consdered he basc adopon process and herefore ddn ncorporae markeng effecs no he models. We exend he basc models o ncorporae he seasonal facor, marke growh rae, prce and echnologcal subsuon effec no he proposed model. The proposed model s called SMPRT model (seasonal facor, marke growh rae, prce, repea purchases and echnologcal subsuon). The producs wh dfferen generaons are same producs for dfferen echnologes and herefore he dffuson process of he producs s smlar. Noron and Bass (987) assumed ha he nernal and exernal coeffcens are consan across dfferen generaons n order o reducng he complexy of he parameers. On he oher hand, Islam and Meade (997) released he assumpon, and es he consancy of parameers. Followng, we sae he seps n SMPRT model. Sep. Compare Noron and Bass (NB) and Islam and Meade (IM) model The models are expressed as follows. s () = f ()[ M + f ()[ M + f ()[ M + f ()[ M + f () M ] ]]][- f ()] The dfference beween NB and IM model s he parameers wheher hey changes across generaons or no. Noron and Bass model In hs model, he parameers are consan across generaons, and herefore p=p and q=q for all. [- e ] [- e ] [( / ) + ] -( p+ q)( - τ +) -( p+ q)( - τ +) () = = -( p+ q)( - τ+) -( p+ q)( - τ+) [( q / p) e + ] q p e F Islam and Meade model In hs model, he parameers change across generaons, and herefore p and q are dfferen for all. -( p+ q)( - τ +) [- e ] F () = -( p+ q)( - τ +) [( q / p) e + ] Sep. Tes he consancy of parameers Ths sep dscusses he consancy of parameers. Tes he parameers o see wheher hey change across generaons or no n order o deermne o apply NB model or IM model, respecvely. The processes are as follows:. Defne Noron and Bass model as resrced model Defne Islam and Meade model as unresrced model. Se up he hypohess H : Δ p = and Δ q = for all H :, 0 A leas one of Δp Δq 3. Tes sasc Compue he es sasc under he assumpon ha H 0 s rue. The W sasc follows a ch-square dsrbuon as follows.w = (log lkelhood (unresrced model)- 36

5 Chen, Chen, and Peng log lkelhood (resrced model)) ~ χ () v, where v s he number of parameer resrcons. Ths hypohess can be esed by a lkelhood rao es or usng full nformaon maxmum lkelhood (FIML) esmaon. 4. Compue sample es sasc We can use he hsorcal demand daa o compue he sample es sasc. Afer compung he sample es sasc ( W 0 ), we can make a decson o rejec he H 0 or we do no rejec H Tes rules Ths sep shows ha how o make a decson rule o rejec H 0 assumpon or we do no rejec H 0. The decson rules are as follows: If W0 > χ α () v, hen we rejec H 0. We have suffcen evdence o prove ha p and q change across generaons. If W0 < χ α () v, hen we don rejec H 0. We do no have suffcen evdence o prove ha p and.q change across generaons. 6. Conclusons We can know p and q wheher hey change across generaons or no va hs es of hypohess. Sep3. Incorporae prce effecs Incorporae he dffuson model (Bass, Krshnan, and Jan 994) no he proposed model n order o consder he prce facor and herefore he expresson of F() n he Noron and Bass model are subsued for he expresson of F() n he model whch Bass e al. suggesed. The expressons n hs proposed model are as follows. -( X( )- X(0))( p+ q) [- e ] F () = -( X( )- X(0))( p+ q) [( q/ p) e + ] X() = + ln( pr()/ pr(0)) β Sep4. Incorporae growh raes and seasonal facors Growh raes and seasonal facors are sgnfcan facors for demand. Hence, needs o ncorporae hese facors n he proposed model. In SMPRT model, we use mulplcave model o express he seasonal varaon and growh rae effec. The mehod o express he seasonaly and growh rae s o mulply he seasonal facor and marke growh rae drecly. The deals are as follows.. The expresson of he revsed demand: sˆ () α exp( g). Prepare o esmae he parameers by usng nonlnear leas square mehod and revse he objecve funcon as follows. n l Orgnal: Mn [ s ( )- sˆ ( )] = = n l Revsed: Mn [ s ( )- sˆ ( ) α exp( g )] = = where α =, α = α 4, α 0 g : consan Fnally, SMPRT model negraes as follows: n l Mn [ s ( )- sˆ ( ) α exp( g )] = = subjec o s ( ) = f ( )[ M + f ( )[ M + f ( )[ M + f ( )[ M + f ( ) M ] ]]][- f ( )] f() = F()- F( -) -( ( )- (0))( ) -( ( )- (0))( ) (- X X p + q ) /(( / ) X X p + e q q p e + ), τ F () = 0, < τ X () = ( -τ + ) + ln( pr()/ pr(0)) β α =, α = α, α 0 4 g : consan 0< < p 0 < q < M > 0, =,,,.4 Parameers Esmaon n There are several parameers n SMPRT model. Ths sudy esmaes he parameers wh nonlnear leas square mehod. To esmae he parameers n SMPRT model s based on he hsorcal demand daa from he ransacon daabase. In hs approach, he parameers esmaon can be dvded no wo sages. Esmae he parameers n SMPRT model. In SMPRT model, he coeffcen of nnovaon (p ), he coeffcen of maon (q ), he oal marke poenal (M ), he seasonal facor ( α ), he effecveness of he prce ( β ) mus be esmaed..5 Forecasng In he par of forecas, he daa wll be dvded no wo groups: ranng daa and esng daa. Tranng daa are used o esmae he parameers n SMPRT model and subsequenly he forecasng demand can be predc by he values of parameers n SMPRT model. However, esng daa are used o valdae he resuls of he forecasng demand and he acual demand..6 Resuls Inerpreaon and Evaluaon The useful nformaon or paerns can be exraced from he proposed demand forecas framework. The produc lfe cycle and produc demand forecas may help frms o plan her sraeges for uncerany and rsk suaons n he fuure. If he proposed demand forecas framework fals o forecas demand, wll lead he dle capacy or lose he orders. The resul of demand forecas can be nerpreed and analyzed n he dscussons wh doman expers o fnd he bes model o solve he problem. 37

6 Ths sudy flows hrough he research framework. Afer esmang he parameers n he dffuson model, he sascal analyss wll show he resuls of he esmaed values. The coeffcen of deermnaon ( R ) represens he explanaon ably of he model accordng o he resul of sascal analyss. The hgher R represens he dffuson model ha has hgher explanaon ably for explanng he demand of semconducor producs. Though he resul of sascal analyss, he values of he esmaed parameers can be esed by p-value. Tes he values of he esmaed parameers wheher hey can be acceped or no. The complee dffuson model can be obaned afer geng he value of he parameers. Through he dffuson model, we can descrbe he paerns of he produc lfe cycle and forecas produc demand. Forecasng error s a creron o evaluae forecasng performance. In hs sudy, uses MAPE o measure he forecasng performance of he proposed model. The followng s he formula of MAPE: S Y - ˆ j Yj MAPE = 00% S Y j= where Y j : acual value, Ŷ j : esmaed value and S: he number of samples. The value of MAPE represens he forecasng performance. The smaller MAPE represens a hgher performance for forecasng he produc demand n he fuure. 3 EMPIRICAL STUDY An emprcal case sudy n semconducor ndusry s conduced o evaluae and valdae he demand forecas framework n hs chaper. 3. Problem Defnon Newer echnologes connually develop nowadays. Newer echnologes are more complexy and hgh level han j Chen, Chen, and Peng older one due o shoren he lne-wdh and he ulzaon of a wafer. Whle newer echnologes have less nformaon o forecas demand, he dffculy and complexy are ncreased o predc he demand of newer echnologes. The quany of semconducor producs affecs he capacy allocaon and capacy level. Ths sudy s appled o long-erm and shor-erm capacy plannng. Capacy allocaon for he quany of dfferen semconducor producs under each echnology belongs o shor-erm capacy plannng. On he oher hand, capacy expanson for he oal quany of dfferen semconducor producs under each echnology belongs o long-erm capacy plannng. The proposed dffuson model s conduced o valdae by usng he real case sudy n semconducor ndusry. Ths sudy consruced a sysemac framework o handle wh he demand forecasng problems. I hopes o descrbe he PLC and predc he demand of semconducor producs precsely for well capacy allocaon and capacy expanson ha maxmum he ulzaon and profs by usng he consruced demand framework n secon. 3. Daa Preparaon The hsorcal ransacon daa are colleced by quarers and sored n he daabase. Before proceedng wh he demand forecas framework, needs o exrac hsorcal demand daa from he daabase and hen conduc he daa preparaon ncludng daa collecon, cleanng, paron and negraon. Snce he real daa are propreary nformaon, he real daa need o ransform o proec he company. Whou loss of generaly, he real daa are ransformed for hs emprcal sudy. Ths sudy amed o predc he semconducor demand precsely for well capacy plannng. Semconducor producs conan varous producs. Ths sudy selecs a semconducor produc o conduc a valdaon. Ths semconducor produc X, whch s a leadng produc, s adoped n hs sudy. The me scale of hs emprcal case sudy s quarer. The oal me horzon for he daa of he semconducor Quany Technology A Technology C Technology B Technology D Tme Fgure : Semconducor produc demand under dfferen echnologes 38

7 produc X s 36 quarers. The semconducor produc X s manufacured under dfferen echnologes. Addonally, he daa of four generaons of hs semconducor produc X cover 36, 9, 7 and 9 quarers. The daa are colleced from he ransacon daabase. Afer collecng he daa, has o conduc daa cleanng, daa paron, and daa negraon. The requse daa n he proposed dffuson model ncludes he prce of he produc, he growh rae of he semconducor ndusry and he quany of he produc demand and herefore have o ge rd of he unnecessary daa for hs proposed model. Furhermore, negrae he requse daa n he proposed dffuson model no a workshee n order o conduc a valdaon convenenly. Fnally, sum up he quany of he produc X under he same echnology n he same quarer. The daa consss of hsorcal demand semconducor produc X under dfferen echnologes, un prce (dollar/per ranssor), and sales growh rae (%). Sales growh rae of quarerly fnancal repors (%) = (ne sales of curren quarer ne sales of he prevous quarer)/ ne sales of he prevous quarer. Fgure shows he hsorcal demand semconducor produc X under each echnology. 3.3 Dffuson Model Consrucon Semconducor produc X has four generaons and he oal me horzon for he daa s 36 quarers. We use he quany of demand o replace he sales. Addonally, he nroducon me of four generaons of hs semconducor produc X denoes s, 8h, 0h, 8h quarers respecvely correspondng he me relave o generaon sarng a =. Sep. Expand NB / IM model wh four generaon s() = f() M[- f()] s() = f()[ M + Mf()][- f3()] s3( ) = f3( )[ M3 + f( )[ M + Mf( )]][- f4( )] s4() = f4()[ M4 + f3()[ M3 + f()[ M + f() M]]] where f() = F()- F( -) -( p+ q)( -τ + ) [- e ], τ -( p+ q)( -τ + ) F () = [( q / p) e + ] 0, < τ τ=, τ= 8, τ3= 0, τ 4= 8 Sep. Tes he consancy of parameers () H0 : Δ p = 0 and Δ q = 0 for all, =, 3, 4 H : A leas one of Δp, Δq 0, =, 3, 4 () Ge he values of log lkelhood for unresrced and resrced by usng he FIML esmaon n SAS. The expressons are as follows: W = ( ( )) = Chen, Chen, and Peng (3) Because χ = < W = (4) , we have suffcen evdence o prove ha p and. q change across dfferen generaons. We can know ha p and q n hs emprcal case sudy change across dfferen generaons va hs es. Sep3. The proposed model for hs emprcal case sudy The expressons for he semconducor produc X of hs emprcal case sudy are as follows: 4 36 Mn [ s ( )- sˆ ( ) α exp( g )] = = subjec o s() = Mf()[- f()] s() = f()[ M + Mf()][- f3()] s3( ) = f3( )[ M3 + f( )[ M + Mf( )]][- f4( )] s4() = f4()[ M4 + f3()[ M3 + f()[ M + f() M]]] f() = F()- F( -) -( X ( )- X (0))( p+ q ) -( X ( )- X (0))( p+ q (- e ) /(( q ) / p) e + ), F () = 0, < -( X ( )- X (0))( p+ q ) -( X ( )- X (0))( p+ q (- e ) /(( q ) / p) e + ), 8 F () = 0, < 8 -( X3 ( )- X3 (0))( p3+ q3 ) -( X3 ( )- X3 (0))( p3+ q3 (- e ) /(( q ) 3 / p3) e + ), 0 F3 () = 0, < 0 -( X4 ( )- X4 (0))( p4+ q4 ) -( X4 ( )- X4 (0))( p4+ q4 (- e ) /(( q ) 4 / p4) e + ), 8 F4 () = 0, < 8 X () = ( -+ ) + ln( pr()/ pr(0)) β X () = ( -8+ ) + ln( pr ()/ pr (0)) β X () = ( -0+ ) + ln( pr ()/ pr (0)) β X () = ( -8+ ) + ln( pr ()/ pr (0)) β α α α-4 α =, =, 0 g : consan 0< < p 0 < q < M > 0, =,, 3, Esmaon Ths sudy used nonlnear leas squares procedure SYSNLIN n SAS o esmae he parameers n SMPRT model. The values of esmaed parameers are sgnfcance due o her p-values are smaller han The parameer esmaes show ha nnovave coeffcens (p -p 4 ) are smaller han mave coeffcens (q -q 4 ) n each echnology. Addonally, he parameer esmaes of oal marke poenal (M -M 4 ) are posve whch are expeced. The effecveness of prce (β ) s negave. If he prce decreases, he sales wll ncrease. Seasonal facors show ha he frs quarer s larger han oher quarers. 39

8 3.5 Forecasng The daa wll be dvded no wo groups: ranng daa and esng daa. There are 36 daa n hs emprcal case sudy. We use 34 quarers daa pror o esmae he parameers n he proposed mul-generaon dffuson model and forecas he quany of he produc demand for prospecve quarers. Afer forecasng he produc demand for prospecve perods, compare he forecased resuls wh he acual daa. 3.6 Resuls Inerpreaon and Evaluaon Table : Esmaed resuls of dfferen models Speece and MacLachlan model (whou growh rae and seasonal facor) SMPRT model (whou growh rae and seasonal facor) Speece and MacLachlan model (wh growh rae and seasonal facor) SMPRT model (wh growh rae and seasonal facor) Average adjused R 87.6% 9.7% 88.3% 94.8% Table 3: The forecasng resuls for all echnologes MAPE (for Q-ahead) MAPE (for Q-ahead) Technology A 97.% 97.6% Technology B 4.6% 6.35% Technology C 4.6% 5.6% Technology D 0.% 0.9% Overall.0% 0% Chen, Chen, and Peng In hs secon, we summarze he resuls of esmaon and forecas. Speece and MacLachlan (99) also ncorporaed he prce facor no mul-generaon model for mlk package ype. SMPRT model s compared wh Speece and Mac- Lachlan model for semconducor produc X wh he resuls summarzed n Table. SMPRT consss of marke growh rae and seasonal facor s a good f han oher models from Table. Fgure 3 shows he resuls of predced and acual demand for all echnologes. Table 3 shows he forecasng resuls for -ahead and -head of all echnologes wh MAPE. SMPRT model has a precson forecas n one perod excep for echnology A. As he forecasng perods expand, he forecasng performances are down. The forecasng resuls of echnology A are no good. I can fnd ha he demand of echnology A flucuaes n he las perods. Because echnology A s he older echnology, some caegores mgh have been mananed o produce by echnology A. As a resul of he suaon, SMPRT model doesn have good performances n echnology A. In general, he forecasng performances are reasonable. 4 CONCLUSION Ths sudy consruced a sysemac mehod o forecas semconducor producs demand and herefore proposed a mul-generaon dffuson model wh consderng he echnologcal subsuon, repeang purchases, prce, growh rae, and seasonal facors for semconducor producs n order o mprove he nheren forecasng mehods are manly desgned for a sngle produc or a sngle echnology. An emprcal sudy s conduced o valdae he proposed SMPRT model wh real daa of semconducor producs. The resuls have shown a good f and precse forecas for he semconducor producs. Ths approach can provde valuable nformaon for managers o make her decsons. Furhermore, here are oher facors n oher dffu- Quany predced demand for Technology A predced demand for Technology B predced demand for Technology C predced demand for Technology D acual demand for Technology A acual demand for Technology B acual demand for Technology C acual demand for Technology D Tme Fgure 3: Resuls of SMPRT model for all echnologes 30

9 son models can be nvesgaed n fuure sudes o examne s appropraeness of ncorporang hem no he proposed model. Also, some assumpons n he proposed SMPRT model ha need furher nvesgaons connually n fuure research. Thus, more suaons can be consdered no he mul-generaon dffuson model n order o expand he mul-generaon dffuson model effecvely. ACKNOWLEDGEMENTS Ths research s suppored by Naonal Scence Councl (NSC E MY3) and he Fauly Empowermen Award of Naonal Tsng Hua Unversy from he fundng of he Mnsry of Educaon n Tawan. REFERENCES Bass, F. M A new produc growh model for consumer durables. Managemen Scence 5:5-7. Bass, F. M., T. V. Krshnan, and D. C. Jan Why he Bass model fs whou decson varables. Markeng Scence 3:03-3. Chen, C.-F., H. Wang, and M. Wang A UNISON Framework for Analyzng Alernave Sraeges of IC Fnal Tesng for Enhancng Overall Operaonal Effecveness. Inernaonal Journal of Producon Economcs 07:0-30. Islam, T., and N. Meade The dffuson of successve generaon of a echnology: A more general model. Technologcal Forecasng and Socal Change 56: Kurawarwala, A. A., and H. Masuo Produc growh models for medum-erm forecasng of shor lfe cycle producs. Technologcal Forecasng and Socal Change 57: Leachman, R., S. Dng, and C.-F. Chen Economc Effcency Analyss of Wafer Fabrcaon. IEEE Transacons on Auomaon Scence and Engneerng 4(4): Mahajan, V., E. Muller, and F. M. Bass New produc dffuson models n markeng: A revew and drecons for research. Journal of Markeng 54:-6. Meade, N., and T. Islam Modelng and forecasng he dffuson of nnovaon A 5-year revew. Inernaonal Journal of Forecasng : Noron, J. A., and F. M. Bass A dffuson heory model of adopon and subsuon for successve generaons of hgh-echnology producs. Managemen Scence 33: Noron, J. A., and F. M. Bass. 99. Evoluon of echnologcal generaons: The law of capure. Sloan Managemen Revew 33: Rogers, E. M Dffuson of Innovaons. 5h ed. New York: Free Press. Chen, Chen, and Peng SAS Insue Inc SAS/ETS 9. user s gude. SAS Insue, Inc. Speece, M. W., and D. L. Maclachlan. 99. Forecasng flud mlk package ype wh a mulgeneraon new produc model. IEEE Transacons on Engneerng Managemen 39: Speece, M. W., and D. L. Maclachlan Applcaon of a mul-generaon dffuson model o mlk conaner echnology. Technologcal Forecasng and Socal Change 49:8-95. Srnvasan, V., and C. H. Mason Nonlnear leas squares esmaon of new produc dffuson models. Markeng Scence 5: Wu, J.-Z., and C.-F. Chen Modelng sraegc semconducor assembly ousourcng decsons and an emprcal sudy. OR Specrum 30: AUTHOR BIOGRAPHIES CHEN-FU CHIEN s a Professor n he Deparmen of Indusral Engneerng and Engneerng Managemen and EMBA, Naonal Tsng Hua Unversy (NTHU). Snce 005, he has been on-leave o serve as he Depuy Drecor of Indusral Engneerng Dvson n Tawan Semconducor Manufacurng Company. He receved B.S. degree wh double majors (wh Ph Tao Ph Honor) n Indusral Engneerng and Elecrcal Engneerng from NTHU n 990. He receved M.S. n Indusral Engneerng and Ph.D. of Operaons Research and Decson Scences from he Unversy of Wsconsn-Madson n 994 and 996, respecvely. He was a Fulbrgh Scholar n he Deparmen of Indusral Engneerng and Operaons Research, UC Berkeley from 00 o 003 and receved Execuve Tranng n Harvard Busness School n 007. Dr. Chen s a Seerng Commee Member of Indusral Engneerng Dvson n Naonal Scence Councl, Tawan. He s Board Member of he Chnese Insue of Indusral Engneers (CIIE) and Chnese Insue of Decson Scences. He s an Assocae Edor of IEEE Transacons on Auomaon Scence and Engneerng and an Advsory Board Member of OR Specrum. Hs research and developmen effors focus on decson analyss, modelng and analyss for semconducor manufacurng, dada mnng, and manufacurng sraegy. He receved Ousandng Research Award and Ter Prncpal Invesgaor (Top 3%) from Naonal Scence Councl, Dsngushed Unversy- Indusry Collaborave Research Award from Mnsry of Educaon, Dsngushed Young Indusral Engneer Award, Dsngushed Young Faculy Research Award from NTHU, Bes Paper Award from CIIE, Bes Engneerng Paper Award by Chnese Insue of Engneers, Tawan. YUN-JU CHEN receved M.S. n Indusral Engneerng and Engneerng Managemen a he Naonal Tsng Hua 3

10 Chen, Chen, and Peng Unversy. Her research neress nclude demand forecas and sascal mehod. JIN-TANG PENG s an Asssan Professor n he Deparmen of Busness Admnsraon, Yuanpe Unversy. He receved he M.S. and Ph.D. degrees n Indusral Engneerng and Elecrcal Engneerng from NTHU n 998 and 004, respecvely. Hs research neress nclude demand forecas, daa mnng and rough se heory. 3