I-Hsuan Hong Hsi-Mei Hsu Yi-Mu Wu Chun-Shao Yeh

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1 Poceedngs of he 8 Wne Smulaon Confeence S. J. ason, R. R. Hll, L. önch, O. Rose, T. Jeffeson, J. W. Fowle eds. PRICING DECISION AND LEAD TIE SETTING IN A DUOPOL SEICONDUCTOR INDUSTR I-Hsuan Hong Hs-e Hsu -u Wu Chun-Shao eh Ta Hsueh Road Depamen of Indusal Engneeng and anagemen Naonal Chao Tung Unvesy Hsnchu (3), TAIWAN ABSTRACT Pcng and lead me seng ae wo mpoan decsons n semconduco foundy nduses. Ths eseach consdes he compeon of a duopoly make conssng of wo make-o-ode fms n semconduco foundy nduses and pesens a model o deemne he equlbum pce and lead me of hese wo compeng fms whee each fm maxmzes s own evenue and s subec o s own consans n a duopoly make. In he model, cusome mean demand aes of wo compeng fms ae assumed as funcons of commed lead mes and pces povded by hese wo fms and he make. Fuhemoe, hs pape ulzes a smulaed pocedue o vefy he equlbum pce and lead me obaned by he analycal model pesened n hs pape. INTRODUCTION Hgh qualy, low cos, sho lead me, and quck esponse o cusome odes ae fundamenal keys o a successful busness n a me-based compeon make place. Recen obsevaon ndcaes ha successful me-based fms povde moe poduc and sevce n shoe lead mes a lowe coss and hey can geneally chage a hgh pce and capue a hgh make shae (Salk 988; Salk and Hou 99). In hs pape, we capue he essence of he compeon of a duopoly of wo compeng fms and examne he equlbum behavos of ndependen fms n a make. Semconduco manufacung o s elaed nduses ae ypcally acng as he duopoly n he make. Fo example, Inel and AD ae wo mao leadng companes poducng mcopocesso chps n he wold. Tawan Semconduco anufacung Company (TSC) and Uned coeleconcs Copoaon (UC) domnae he semconduco foundy ndusy accounng fo moe han 8% make shae (The Regse 3). Anohe smla example of a duopoly s he hn-flm ansso lqud cysal dsplay (TFT-LCD) ndusy whee Samsung Eleconcs and LG Phlps n Koea and AUO and CO n Tawan ae he domnan manufacues n he TFT-LCD ndusy (Chang 5). In such a duopoly make, an ndvdual fm has s own pof funcon and s ofen unwllng o eveal s own nfomaon o each ohe o he publc. In addon, decsons of compeng fms ae ofen nfluenced by each ohe. Due o a sho poduc lfe cycle, a pomp lead me and a compeve sellng pce ae wo mao facos o a successful busness n he compeve ea especally n consume poduc makes. In hs pape, we focus on hese wo cucal ssues of decsons of compeng semconduco manufacues: lead me quoaon and pcng. The maoy of he eseach done n he aea of pcng and lead me seng has been focused on opmzaon whn one fm. The undelyng concep s ha pcng and lead me quoaon ae ade-offs whee a sho lead me ypcally esuls o a hgh pce. Palaka, Elebache, and Kopp (998) examne he lead me seng, capacy ulzaon, and pcng decsons facng a fm sevng cusomes ha ae sensve o quoed lead mes. Haoum and Chang (997) pesen a model o deemne he opmal demand level usng a mechansm of quoed lead me and pce. Ray and Jewkes (4) pesens an analycal appoach fo a fm o maxmze s pof by opmal selecon of a lead me. ElHafs () develops a model ha ncludes as much deal as possble so ha ealsc day-oday lead me and pce can be acheved and quoed o he cusome. So and Song (998) sudy he mpac of usng delvey me guaanees as a compeve saegy n sevce nduses whee demands ae sensve o boh pce and delvey me. These sudes geneally only focus on he decson whn one fm whou consdeaon of compeon among fms n he make /8/$5. 8 IEEE 9

2 Hong, Hsu, Wu, and eh Thee ae a gowng numbe of eseach papes on compeon models focusng on he ssues of pcng, lead me sengs, o elaed decsons among compeve fms. Economc heoy s used o analyze he behavo of ndependen fms n he make equlbum whee no fm can be bee-off by a unlaeal change n s decson (efe o Gbbons 99). Seveal papes examne he compeve supply of goods o sevces o me-sensve cusomes. Fo example, Kala, Kamen, and Rubnovch (99) sudy compeon n sevce aes whou consdeaon of pcng compeon. Chen and Wan (3) consde he duopoly pce compeon of make-o-ode (TO) fms. The esuls n Chen and Wan (3) show ha wheneve he equlbum exss and s unque, he fm wh a lage capacy, a hghe sevce value o a lowe wang cos can enoy a pce pemum and a lage make shae. L and Lee (994) pesen a model of make compeon n whch a cusome values cos, qualy as well as speed of delvey and sudy he consequence of compeon on pce, qualy and delvey speed. Ledee and L (997) sudy compeon beween fms ha poduce goods o sevces fo cusomes sensve o delay me whee fms compee by seng pces and poducon aes fo each ype of cusome and by choosng schedulng polces. So () sudes a smla ssue of delvey me guaanees and pcng fo sevce delvey. Ths pape examnes he compeon n a duopoly semconduco foundy make conssng of wo leadng fms and ohe elavely small foundy plans. Fms compee o povde goods o sevces o cusomes. Tools and deas fom queueng heoy and economcs ae used o sudy hs compeve suaon. The obecve of hs pape s o pedc he equlbum decson of pces and lead mes of he goods povded by wo compeng fms whee no fm can benef by devang fom he cuen decson. The emande of hs pape s oganzed as follows. In Secon, we pesen a mahemacal model o solve fo he equlbum soluon of pcng and lead me seng n a duopoly make. In Secon 3, we ulze a smulaed decson-makng pocedue o vefy he equlbum soluon obaned by he analycal model pesened n Secon. Fnally, we conclude hs pape n Secon 4. THE ODEL. Duopoly ake odel Ths pape consdes a duopoly make conssng of wo mao leadng semconduco foundy fms and ohe small foundy fms. These wo mao leadng fms compee non-coopeavely o povde a ype of goods n a TO fashon. Boh fms ae wo ndependen enes and ae modeled as queues wh exponenal sevce mes wh a common souce of poenal cusome avals. Ofen he decson vaables fo each fm ae also nfluenced by he ohe fm s decsons. In addon o he wo mao leadng fms, he effec of ohe small foundy fms decsons s consdeed n he model. Denoe he se of wo compeng fms of neess by N = {, }. We le epesen he goup of ohe small foundy fms n he make. Cusomes ae seved on a fs-come-fs-seved bass. We assume ha he cusome aval ae of fm N, λ, depends on he fm s decson of he lead me,, and pce, p. In a compeve make, λ s also nfluenced by he decsons of he ohe compeo, fm N,, and of ohe small fms. In ohe wods, λ s also a funcon of, pces and lead mes of fms p,, and p n addon o and N p. The ae wh he gven nonnegave lowe and uppe bounds, p, p,, and, especvely. Typcally, cusomes pefe shoe lead mes and lowe pces compaed o hose decsons offeed by ohe fms as shown n (), whee λ s popoonal o he dffeences of lead mes and pces beween ohe fms and fm N. λ λ λ λ ( ) ( ) ( p p ) ( p p ) To fuhe chaaceze he analycal model, we now elaboae on he pecse elaonshps beween pces and lead mes of fms n he make as shown n (). The cusome aval ae λ of fm s a funcon of he dffeence beween fm s decsons and ohe compeos decsons. We le α and α denoe he pefeence facos accounng fo he effec of he decson dffeences fom ohe small fms and he compeo, fm. Smlaly, β and β epesen he pefeence facos fo explanng he effec of lead mes and pces on he aval ae. Hee, we assume ha he compeon effec s a convex combnaon beween s compeos, ohe small fms, and fm ( α + α =, α, α ), and he decson effec s a convex combnaon of he pce and lead me ( β + β =, β, β ). We now assume he aval ae s λ = λ mβ[ α( ) + α( )] m β [ α ( p p ) + α ( p p )] whee λ denoes he aval ae when boh pces and lead mes of all fms n he make ae dencal, and m () () 3

3 Hong, Hsu, Wu, and eh and m epesen he lead me and pce sensves of he aval ae, especvely ( λ, m, m ). The lnea funcon of he cusome aval ae helps us oban qualave nsghs whou much analycal complexy. I also has he desable popees fo appoachng he equlbum decsons of pces and lead mes of he fms n he make. Fo llusaon puposes, λ s wen as λ (, p, p,, p) epesenng ha and p ae decsons of fm, and, p,, p ae decsons of ohe fms. The obecve of each fm s o maxmze s own expeced pof. Snce he capacy s fxed, maxmzng he expeced pof s equvalen o maxmzng he expeced evenue. Ths sudy also assumes an // queueng sysem wh mean sevce ae μ fo fm N. To peven fom quong unealsc lead mes, we assume ha he fm manans a cean mnmum sevce level, s, whch may be se by he fm self n esponse o compeveness o he ndusy n geneal. The pobably ha he oal sooun me n fm s less han he quoed lead me s ( ) e μ λ fo an // sysem (Klenock 975). Theefoe, he equemen ha he pobably of meeng he quoed lead me fo fm mus be a leas s (e.g. 95%) can be epesened n he followng consan as ( μ λ) e s o equvalenly, ( μ λ ) ln( s). Snce fm N s assumed o maxmze s own pof pe un me, he maxmzaon model fo fm can be wen as ax π (, p, p,, p) = pλ(, p, p,, p), p (3) s.. ( μ λ) ln( s) (4) λ(, p, p,, p) = λ mβ[ α( ) + α( )] (5) mβ[ α( p p) + α( p p)] p p p, (6) Fm maxmzes s pof funcon π by quong he lead me,, and pce, p. Clealy, fm s pof funcon, π, s a funcon of and p, bu also depends on, p,, and p. Consan (4) ensues fm o manan a mnmum sevce level. Consans (5) and (6) ae he aval ae defnon and bounds fo lead mes and pces.. Equlbum of Pcng and Lead Tme Seng In hs secon, we elaboae ou algohm of solvng fo he equlbum decson of pces and lead mes n a compeve duopoly make. In equlbum, no fm can be bee-off by a unlaeal change n s soluon. In ohe wods, each fm has no ncenve o devae fom he cuen quoaon of s pce and lead me soluon gven ohe fms decsons... Pelmnay We pepae he equed pelmnaes n he secon fo devaon puposes. Consde a eal sngle-valued scala funcon f(x) defned on some nonempy closed se n he n-dmensonal Eucldean space. Funcon f(x) s assumed o be wce connuously dffeenable on. We le f ( x) and f ( x) especvely denoe he gaden and he Hessan max of f evaluaed a x. We gve a suffcen condon fo funcon f o be pseudo-convex. Le (, β ) be he n n max and T denoe he anspose opeao. (, β) = f( x) + β f( x) f( x) T, (7) whee β s a nonnegave eal numbe. Defnon (see eeau and Paque 974) A suffcen condon fo f(x) o be pseudo-convex on he convex se s ha hee exs a eal numbe β, β <+, such ha (, β ) s posve sem-defne... The Soluon Algohm Ou goal s o solve fo he equlbum soluon of compeng fms n he make. In hs secon, we demonsae he Kaush-Kuhn-Tucke (KKT) appoach o fnd he Nash equlbum soluon. An equlbum s defned as a se of decsons ha sasfy each fm s fs-ode condons (KKT) fo maxmzaon of s pof. A soluon sasfyng hose condons possesses he popey ha no fm wans o ale s decson unlaeally and such a soluon s efeed o he Nash equlbum soluon (Hobbs ). Howeve, we pon ou ha KKT condons ae necessay opmaly condons fo he local opmum n geneal, no suffcen condons fo he opmum. In ode o sasfy he popees of he Nash equlbum, we need o solve he globally suffcen KKT condons smulaneously fo he duopoly fms nsead of solvng he geneal locally ne- 3

4 Hong, Hsu, Wu, and eh cessay KKT condons. Nex we have he followng lemma fo he soluon algohm devaon. Lemma The pof funcon (3) of fm N s pseudo-concave funcon. Poof. See Appendx. Lemma The feasble egon of consans (4) (6) s a convex se. Poof. See Appendx. Fom Lemma and Lemma, we can conclude ha he Kaush-Kuhn-Tucke (KKT) opmaly condons o he poblem (3) (6) of fm N ae no only necessay condons bu also suffcen condons (Bazaaa, Sheal, and Shey 993). The KKT opmaly condons of fm N ae saed as: ( ( ) ln( )) Ω = pλ a μ λ s ( ) ( ) ( ) ( ) a p p a p p 3 a a 4 5 (8) Ω p (9) Ω () a ( ( μ λ) ln( s) ) () a p p = () ( ) ( ) ( ) ( ) a p p = (3) 3 a = (4) 4 a5 (5) ( μ λ ) ln( s) (6) p p p (7) (8) a, a, a3, a4, a5 (9) whee a, a, a3, a 4, and a 5 ae dual vaables o consans (4) and (6). Consan (8) s he funcon defnon fo noaon smplcy. Consans (9), (), and (9) ae coesponded o dual feasbly equales, () (5) ae complemenay slackness condons, and (6) (8) ae pmal feasbly equales. Smlaly, we also deve he KKT condons of he ohe compeng fm n he make. The equlbum soluon of pces and lead mes can be obaned by smulaneously solvng he combned KKT condons of duopoly fms. Snce he KKT opmaly condons of he model pesened n hs pape ae suffcen, any soluon smulaneously sasfyng he combned KKT opmaly condons s opmal o each fm. In ohe wods, hs soluon follows he defnon of he Nash equlbum whee no fm would lke o ale s decson unlaeally..3 A Demonsaon Example To llusae he use of he KKT appoach, we consuc a smple and symmec example of duopoly fms, and, n he semconduco foundy make. A goup of small fms s epesened as. We assume ha he pce and lead me of ohe small fms ae gven; ha s p = and = 5. The cusome aval ae, λ, when wo compeng fms ae wh he same pces and lead mes, s 3. The mean sevce aes of fms and ae: μ = μ = 5. The mnmum sevce levels, s, fo boh fms ae se o be 95%. Ohe equed paamees ae α =., α =.8, β =.5, β =.5, and m =, m =.5. The lowe bounds of pces and lead mes fo boh fms ae se o be a small posve value appoachng o zeo, and he uppe bounds of pces and lead mes ae especvely. The KKT opmaly condons of fm can be saed as: (4.5 p +. p ) +.5a + a a3.5 p a(.5 p +. p +.4 ) + a4 a5 a (.5 p +. p ) + 3 ap a3 ( p ) a 4 a5 ( ) (.5 p +. p ) 3 < p < a, a, a3, a4, a5. Smlaly, he KKT opmaly condons of fm can be saed as: (4.5 p +. p ) +.5a6 + a7 a8.5 p a6(.5 p +. p +.4 ) + a9 a a6 (.5 p +. p ) + 3 ap 7 a8 ( p ) a 9 3

5 Hong, Hsu, Wu, and eh ( ) a (.5 p +. p ) 3 < p < a6, a7, a8 a9, a. Snce we only focus on a nonval soluon, we assume ha he equlbum soluon of pces and lead mes locae nehe he lowe bound no uppe bound. Ths allows us o smplfy he combned KKT condons by leng a, a 3, a 4, a 5, a 7, a 8, a 9, and a be zeo. We use he commecal package o solve he combned KKT condons of fms and fo he equlbum pce and lead me. The equlbum soluon of he pce and lead me of hese wo compeng fms s (,,, ) (.5,.5, 6.67, 6.67) p p =, and a = a6 = 3.9, a, =...,5,7,...,. The coespondng pofs of fms and ae 5.4 especvely. Inuvely, he soluon and pofs ae dencal fo hese wo fms n hs symmecal demonsaed example. 3 A SIULATED PROCEDURE In hs secon, hs sudy noduces a smulaed pocedue fo appoachng he equlbum soluon o vefy he soluon obaned by he combned KKT example pesened n hs pape. Inuvely, gven ohe compeos decsons, each fm would lke o move o a decson ha epesens an mpovemen on he cuen decson. We noduce he opmum esponse funcon whch euns he se of fms acons wheeby hey all y o unlaeally maxmze he especve opmzaon models. We le Z(, p ) denoe he opmum esponse funcon o fm s opmzaon model (3) (6), whee Z(, p ) euns fm s bes move gven fm s cuen decson of lead me,, and pce, p. Each fm eavely ales s decson based upon s compeo s pevous decson. A each eaon, duopoly fms wsh o move o a pce pon and lead me quoaon ha epesens an mpovemen on he cuen decson. In ohe wods, o oban he fnal decson of he pce and lead me quoaon, fms ake uns seng he decson, and each fm s chosen decson s a bes esponse o he decsons s compeos chose n he las eaon. The eaons connue unl no fm has ncenves o change s decson, and hus a fnal decson of pce and lead me quoaon have been obaned. The smla calculaon pocesses can be also found n (Kawczyk and Uyasev ; Coneas, Klusch, and Kawczyk 4; Hong, Ammons, and Realff 8) fo dffeen applcaons. Unde hs conex, havng an nal esmae he lead me,, and pce, p, of one fm (say fm ), he bes move of he lead me and pce of fm a each eaon s ( n +, n + ) ( n, n p Z p) = n,,,. () I s also neesng o noe ha he concep of he smulaed pocedue self maches he dea of a compeve vew on fms n he make. In each eaon, one fm can access he ohe fm s pevous acons and deemnes s bes move n pce and lead me decson based on s own neess and consans. In ohe wods, he poblem s a calculaon of he successon of pce and lead me decsons, whee fms choose he opmum esponse gven he pce and lead me decsons of he compeos n he pevous eaon. Nex, we demonsae he smulaed pocedue o solve fo he equlbum lead me and pce n he example demonsaed n Secon.3. The pocedue sas fom an nal esmae of he lead me and pce as (,,, p p ) = (5,,5,). The dealed seps of calculaon ae llusaed n Fgue. Fm s decson = 5, p = Fm s decson = 5, p = =.5, p = 6.8 =.5, p = 6.8 =.5, p = 6.76 =.5, p = =.5, p = =.5, p = =.5, p = 6.67 =.5, p = =.5, p = 6.76 =.5, p = =.5, p = =.5, p = =.5, p = =.5, p = Fgue : The calculaon of he smulaed pocedue fo he example A eaon 7, he opmal move of he lead me and pce s numecally dencal o he soluon of he pevous eaon. Nehe fm no can mpove s pof by a unlaeal change n s soluon of he lead me and pce. The successve pocedue euns ha he equlbum lead me and pce ae.5 and 6.67 especvely and he assocaed pof s 5.4. The smulaed esuls ae dencal o he soluon obaned n he combned KKT appoach. I s also easy o vefy ha he opmal soluon 33

6 Hong, Hsu, Wu, and eh * * of fm s (, ) (.5,6.67) * * (, ) (.5,6.67) p = gven fm s soluon, p =, and vce vesa. The soluon obaned n he KKT appoach s ndeed an equlbum decson wheeby no one has ncenve o devae fom s cuen soluon. 4 CONCLUSIONS Ths pape examnes he compeon n a duopoly semconduco foundy make conssng of wo leadng fms and ohe elavely small foundy plans, whee pcng and lead me seng ae wo mpoan decsons. Fms compee o povde goods o sevces o cusomes. We vew each fm as a sysem, whch s behaved as an // queue. Each ndependen fm consdes s own obecve funcon and s subec o s own consans. eanwhle, he obecve funcon of each fm no only depends on s own decson vaables bu also depends on he decson vaables of he ohe compeng fm. In hs pape, each fm es o maxmze s own evenue by choosng s quoaon of he lead me and pce subec o he consan ha he fm needs o sasfy he mnmum equed sevce level, whch s defned as he pobably of meeng he pomsed lead me quoaon. Noe ha he quoaon of he lead me and pce of he ohe compeng fm affecs each fm s evenue funcon n ou model. Ths pape poposes a mehod, he combned KKT appoach, o solve fo he equlbum decson of he lead me and he pce fo each compeng fm n he make. In equlbum, no fm would lke o devae fom s cuen decson gven ohes decson. The equlbum soluon s obaned by smulaneously solvng he suffcen KKT opmaly condons nsead of necessay condons. We show ha he KKT opmaly condons of he duopoly model pesened n hs pape ae suffcen so ha he soluon o he KKT condons s an equlbum decson. Fnally, hs pape ulzes a smulaed pocedue o vefy he equlbum soluon of he pce and lead me obaned by he analycal KKT appoach pesened n hs pape. Ths example numecally shows ha boh soluons obaned fom he combned KKT appoach and he eave smulaed mehod ae dencal. The model pesened n hs pape s a pooypcal duopoly model and can be used as a ool o analyze a moe complcaed compeng make and o daw manageal nsghs fo such sysems n fuue eseach. ACKNOWLEDGENTS Ths eseach was suppoed n pa by he Naonal Scence Councl, Tawan unde Gans NSC96--E and NSC96--E APPENDI Poof of Lemma. Fo noaonal smplcy, we ewe he aval ae λ as follows: whee λ(, p, p,, p) = λ mβ[ α( ) + α( )] mβ[ α( p p) + α( p p)] = u ' u u p + u + u p 3 4 u' = λ + αβ m + αβ mp u = βm u = βm u3 = αβ m u4 = αβ m u, u, u, u >. 3 4 By nseng () no (4) and eaangng, we have whee () ( u u u p ) ln( s) () u = u + u + u p μ. ' 3 4 Povng ha he pof funcon of fm, π, s pseudoconcave s equvalen o showng ha π ' = π s pseudoconvex. Snce π ' s wce connuously dffeenable, he gaden, ( π '), and Hessan max, ( π '), of π ' can be compued as and ' ' π π ( π ') T = = + [ λ up up ] p π ' π ' p p u u ( π ') = = π ' ' u π p Reaangng (7), we have., 34

7 Hong, Hsu, Wu, and eh u u (, β) = + ( λ up ) up ( λ up ) β ( λ ) ( ) ( ) ( ). ( ) ( ) u up up up u + β λ up u βup λ up = u βup λ up β up The deemnan of (, ) β = ϕ whee ϕ p β s ( ) u β p λ. We le = λ and λ = u' u u p + u3 + u4 p. I s obvous ha ϕ s a lowe bound of he pof funcon of fm snce he cusome aval ae s wh he hghes value fo he vaable wh negave coeffcens and he lowes value fo he vaable wh posve coeffcens. As a esul, he deemnan of (, β ) s posve fo such β. In addon, he dagonal elemens of (, β ) ae nonnegave. Ths gves he esul ha hee exs a eal numbe β, β < +, such ha (, β ) s posve sem-defne. Followng Defnon, π ' s a pseudo-convex funcon. Poof of Lemma. The feasble egon C of consans (4) (6) can be epesened as, p p p, C = (, p) ( u u up ) ln( s ) We le z = (, p ) C and z = (, p) C. Consde he pon z = (, p) = α z + ( α) z, α. Because and, we have = α + ( α) α + ( α) =. Snce and, we have = α + ( α) α + ( α) =. Theefoe,. Smlaly, p p p. These show ha (6) holds fo z = (, p). Consan (4) can be epesened as (). Fo z and z, we have and u u u p ln( s) / (3) u u u p ln( s) /. (4) Consdeng z = (, p), he lef hand sde of () can be ewen as follows: ( u u up) ( u u( α ( α) ) u( αp ( α) p) )( α ( α) ) α( u u u p ) α ( u u u p ) ( α α ) = = + ( ) + ( ). Because of (3) and (4), we have ( ) u u u p α ln( s) ln( s) ( ) ( ) α + α + α ( ) = ln( s) α ( α) α( α)( ). Due o he Cauchy nequaly (see Bale 976), we have Theefoe, ln( s) α + ( α) + α( α)( + ) ln( s) α + ( α) + α( α) ( ) ( α α ) = ln( s) + ( ) = ln( s). ( ) u u up ln( s). (5) Due o (5), z = (, p) also sasfes (4) and (5). In summay, fo z = (, p ) C and z = (, p) C, we show ha he pon z = (, p) = α z+ ( α) z, α sasfes consans (4) (6). I complees he poof. REFERENCES Bale, R. G The Elemens of Real Analyss. nd edon. John Wley & Sons, New ok. Bazaaa,. S., H. D. Sheal, and C.. Shey Nonlnea Pogammng Theoy and Algohm. John Wley & Sons, New ok. Chang, S.-C. 5. The TFT-LCD ndusy n Tawan: compeve advanages and fuue developmens. Technology n Socey 7: Chen, H., and. W. Wan. 3. Pce compeon of make-o-ode fms. IIE Tansacons 35: Coneas, J.,. Klusch, and J. B. Kawczyk. 4. Numecal soluons o Nash-Couno equlba n coupled consan eleccy makes. IEEE Tansacons on Powe Sysems 9(): ElHafs,.. An opeaonal decson model fo leadme and pce quoaon n congesed manufacung 35

8 Hong, Hsu, Wu, and eh sysem. Euopean Jounal of Opeaonal Reseach 6: Gbbons, R. 99. Game Theoy fo Appled Economss. New Jesey: Pnceon Unvesy Pess. Haoum, K. W., and. L. Chang Tade-off beween quoed lead me and pce. Poducon plannng and conol 8(): Hobbs, B. F.. Lnea complemenay models of Nash-Couno compeon n blaeal and POOLCO powe. IEEE Tansacons on Powe Sysems 6(): 94-. Hong, I-H., J. C. Ammons, and. J. Realff. 8. Cenalzed vese decenalzed decson-makng fo ecycled maeal flows. Envonmenal Scence & Technology, 4(4): Kala, E.,. I. Kamen, and. Rubnovch. 99. Opmal sevce speeds n a compeve envonmen. anagemen Scence 38(8): Kawczyk, J. B., and S. Uyasev.. Relaxaon algohm o fnd Nash equlba wh economc applcaons. Envonmenal odelng and Assessmen 5: Klenock, L Queueng Sysems. John Wley & Sons, New ok. Ledee, P. J., and L. L Pcng, poducon, schedulng, and delvey-me compeve. Opeaons Reseach 45(3): L, L., and. S. Lee Pcng and delvey-me pefomance n a compeve envonmen. anagemen Scence 4(5): eeau, P., and J.G. Paque Second ode condons fo pseudo-convex funcons. SIA Jounal on Appled ahemacs 7(): Palaka, K., S. Elebache, and D. H. Kopp Leadme seng, capacy ulzaon, and pcng decsons unde lead-me dependen demand. IIE Tansacons 3: Ray, S., and E.. Jewkes. 4. Cusome lead me managemen when boh demand and pce ae lead me sensve. Euopean Jounal of Opeaonal Reseach 53: So, K. C.. Pce and me compeon fo sevce delvey. anufacung & Sevce Opeaons anagemen (4): So, K. C., and J. S. Song Pce, delvey me guaanees and capacy selecon. Euopean Jounal of Opeaonal Reseach : Salk, G. J Tme-he nex souce of compeve advanage. Havad Busness Revew July-Augus 4-5. Salk, G. J., and T.. Hou. 99. Compeng Agans Tme. The Fee Pess, New ok. The Regse 3. TSC foundy make shae dps. Avalable va < hp:// //smc_foundy_make_shae_dps/> [accessed Apl 4, 8]. AUTHOR BIOGRAPHIES I-HSUAN HONG s an Asssan Pofesso n he Depamen of Indusal Engneeng and anagemen a Naonal Chao Tung Unvesy n Tawan. He eceved hs S degee fom Naonal Tawan Unvesy and hs PhD n Indusal and Sysems Engneeng fom Geoga Insue of Technology, Alana, U.S.A. Hs eseach aeas nclude evese logscs sysems, compeon models n mul-echelon supply chans, applcaon and mehodologes fo game heoy. HSI-EI HSU eceved he BA degee fom Osaka Unvesy, Osaka, Japan, n 975, and he PhD degee n ndusal engneeng fom Naonal Tsng-Hua Unvesy, Tawan, n 99. She s a Pofesso n he Depamen of Indusal Engneeng and anagemen, Naonal Chao Tung Unvesy, Tawan. He eseach neess nclude poducon managemen, supply chan managemen, and mulple cea decson makng. I-U WU eceved hs S degee fom Naonal Chao Tung Unvesy n Tawan and cuenly woks n he ndusy. CHUN-SHAO EH s cuenly a ase suden n he Depamen of Indusal Engneeng and anagemen a Naonal Chao Tung Unvesy n Tawan. 36