International Journal of Industrial Engineering Computations

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1 Internatonal Journal of Industral Engneerng Computatons 5 (04) Contents lsts avalable at GrowngScence Internatonal Journal of Industral Engneerng Computatons homepage: wwwgrowngscencecom/jec An nvestgaton on research and development cost reducton and channel strateges n competng supply chans Qnqn L * and Zhyng Lu School of Management, Unversty of Scence and Technology of Chna, Hefe 006, Chna C H R O N I C L E A B S T R A C T Artcle hstory: Receved September 0 0 Receved n Revsed Format Aprl 04 Accepted Aprl 04 Avalable onlne Aprl 4 04 Keywords: Supply chan competton Cost reducton Cournot competton Game theory Wth the ntensfcaton of market competton, the competton form of frms s evolvng from the competton among frms to the competton among supply chans Ths paper consders a market wth two competng supply chans consstng of one suppler and one manufacturer The two supply chans compete on products quanttes and research and development (R&D) level when the two manufacturers conduct technologcal nnovaton Ths paper analyses the supply chan competton n three scenaros: two decentralzed supply chans (DD), one decentralzed supply chan and one centralzed supply chan (DC) and two centralzed supply chans (CC) The results ndcate that the producton quantty, the R&D level and the total proft of the ntegrated supply chan n DC scenaro are the largest, CC scenaro comes second, those of the DD scenaro come thrd and those of the decentralzed supply chan n DC scenaro are the smallest CC strategy s the supply chan system s Nash equlbrum, whch s good for the both supply chans, and there s no prsoner's dlemma 04 Growng Scence Ltd All rghts reserved Introducton Wth the ntensfed competton among supply chans, the enterprses have to mantan contnual technologcal nnovaton to mprove qualty of products, to reduce the costs of produce, as well as to develop new products, n an effort to ncrease compettve edge For example, automoble makers conduct cost-reducng R&D to lower prces of ther products and to sell more cars Most manufacturers who buy ther products through supplers have to decde whether to establsh an ntegrated supply channel or a decentralzed one In ths paper, we study ths queston n the presence of competng supply chans under Cournot competton Pror lterature examned R&D cooperaton n dfferent modes An mportant stream of lterature n duopoly competton, startng wth D'Aspremont and Jacquemn (988), focused on horzontal R&D cooperaton under Cournot competton and dd not consder the effect of competton on channel coordnaton ncentves, and cooperaton was shown to be the optmal decson (Suzumura, 99; Motta, 99; Suetens, 005) Suzumura (99) examned the postve and normatve effects of cooperatve R&D Motta (99) analyzed a partal equlbrum model wth vertcal product * Correspondng author E-mal: lqqzzu@malustceducn (Q L) 04 Growng Scence Ltd All rghts reserved do: 0567/jjec044004

2 88 dfferentaton, Cournot competton and qualty determned by R&D expenses Qu (997) compared Bertrand wth Cournot equlbrum n a dfferentated duopoly wth R&D competton and found that Cournot competton could nduce more R&D effort than Bertrand competton Banker et al (998) examned whether equlbrum R&D levels ncrease as competton ntensfed n three dfferent compettve envronment; namely asymmetrc duopolstc competton, a symmetrc duopoly and symmetrc olgopolstc competton Myagwa and Ohno (00) extended the lterature on cooperatve R&D n an olgopoly wth spllovers by ntroducng uncertanty and focused on spllover of nnovaton De Fraja and Slpo (00) compared the subgame perfect equlbrum emergng n four regmes of R&D competton among duopolsts; namely full competton, coordnaton of research strateges, jont venture wth cross lcensng of patents, and full colluson n R&D and the product market Amr et al (00) focused on the performance of noncooperatve and cooperatve R&D n product market competton and compared the equlbrum levels of R&D, producer wth consumer surplus, and socal welfare Suetens (005) analyzed the relatonshp between technologcal spllovers and R&D cooperaton n a duopoly experment based on the model of D'Aspremont and Jacquemn Celln and Lambertn (009) nvestgated dynamc R&D for process nnovaton n a Cournot duopoly where frms may ether undertake ndependent ventures or form a cartel for cost-reducng R&D nvestments Besanko and Wu (0) explored the trade-off between R&D cooperaton and competton wth learnng The above lterature on R&D cooperaton focused manly on horzontal R&D cooperaton among frms who are compettors n the same product market However, more and more frms wth supply chan relatonshps are cooperatng n R&D actvtes On the other hand, a parallel stream of lterature, represented by McGure and Staeln (98), focused on the channel desgn problem n competng supply chans under Bertrand competton Ths stream of lterature started wth McGure and Staeln (98), who nvestgated the effect of product substtutablty on Nash equlbrum dstrbuton structures n a duopoly where each manufacturer dstrbutes ts goods through a sngle exclusve retaler, whch may be ether a franchsed outlet or a factory store Gupta and Loulou (998) analyzed a four-stage game wth two manufacturers and two retalers, where the nter-channel contracts are lnear and observable and manufacturers nvest n process mprovements to reduce ther producton costs They found that the optmal channel structure decson depends on nteractons between two parameters: the degree of substtutablty between products cost reducton They also reported that process nnovaton accents the proft dfference between ntegrated and decentralzed channels and makes the Prsoner s Dlemma stuaton worse n the choce of dstrbuton channel structure Banerjee and Ln (00) examned the ncentves of frms n vertcal RJVs and analyzed two cost-sharng contracts, the proportonal and the fxed fracton schemes Ish (004) analyzed the effects of cooperatve R&D n two vertcally related duopoles, whch are two fnal-good manufacturers and two nput supplers, wth horzontal and vertcal spllovers They compared the equlbrum outcomes under four vertcal R&D organzaton modes: noncooperatve R&D, vertcal R&D cartels, vertcal non-cooperatve RJVs and vertcal RJV cartels Boyac and Gallego (004) modeled customer servce competton of two competng supply chans, each consstng of one wholesaler and one retaler They dscussed the dervaton of the equlbrum servce strateges, resultng nventory polces, and profts for each scenaro They found coordnaton was a domnant strategy for both supply chans, but as n the prsoner s dlemma, both supply chans were often worse off under the coordnated scenaro relatve to the uncoordnated scenaro and the consumers are the only guaranteed benefcares of coordnaton Wu et al (007) addressed the problem of dstrbuton channel desgn under demand uncertanty and focused on how demand uncertanty and producton cost nfluence on the equlbrum dstrbuton channel structure Ha and Tong (008) nvestgated contractng and nformaton sharng n two competng supply chans Xe et al (0) analyzed qualty mprovement n competng supply chans Wu et al (0) addressed the decson of ntegraton or decentralzaton from manufacturers perspectve n competng supply chans under demand uncertanty They found the mpact of demand uncertanty on ntegraton/decentralzaton was complcated snce t could favor ether ntegraton or decentralzaton, dependng on how demand uncertanty was characterzed Manasaks et al (04) examned the

3 Q L and Z Lu / Internatonal Journal of Industral Engneerng Computatons 5 (04) 89 downstream frms' ncentves to nvest n cost-reducng R&D and to form a RJV, under two alternatve structures of nput supply: exclusve vertcal relatons and a sngle suppler Snce the effect of the Cournot competton s not consdered n competng supply chans wth manufacturers R&D reducng the cost, the usual conclusons from the above lterature may be dfferent from ths study Ths paper analyzes the channel decsons of two competng supply chans consstng of one suppler and one manufacturer The two supply chans compete on products quanttes as well as non-prce factor, R&D level, when the two manufacturers conduct technologcal nnovaton Ths paper analyses the supply chan members producton, R&D level and proft n three scenaros: DD (two decentralzed supply chans), DC (one decentralzed supply chan and one centralzed supply chan) and CC (two centralzed supply chans) Ths paper s organzed as follows: the problem s descrbed n secton Secton analyzes the competton equlbrum n DD, DC and CC and the results are dscussed and compared n secton 4 Fnally, conclusons and mplcatons for further research are gven n secton 5 Model Descrpton Consder two competng supply chans both consstng of one suppler and one manufacturer Each supply chan produces the same product as the other supply chan The supply chan members have symmetry nformaton The manufacturer uses one unt of the ntermedate product to produce one unt of fnal product Smlar to D'Aspremont and Jacquemn (988), Hnloopen (997), Banerjee and Ln (00) and Ish (004), we assume that the demand for the fnal product s lnear: p a q q j(, j=, and j) q s the demand for product, p s the prce of product Assume the margn producton cost of both manufacturers s c To mantan analytcal tractablty, we don t consder the supplers margn producton cost The manufacturers both take on process nnovaton to reduce ther cost by x (R&D level), we assume the nnovaton cost s rx /, whch assures that the proft functon s concave on x (Gupta & Loulou, 998) In ths paper, the manufacturer domnates the whole supply chan n each supply chan, so the manufacturer s the Stackelberg leader Our model can be descrbed as a four-stage game At stage one, each manufacturer decdes between a centralzed and a decentralzed channel smultaneously and noncooperatvely At stage two, dependng on the choces of the two manufacturers, there are three channel structures: DD, DC, CC, where DD represents that the two supply chans are decentralzed, DC represents that one supply chan s decentralzed and the other s centralzed, CC represents that the two supply chan are centralzed Next, the competng supply chans make ther decsons accordng the followng order: () the manufacturers or supply chans determne the R&D level at the same tme; () the supplers determnes the wholesale prce; ()the manufacturers or supply chans take on Cournot quantty competton, and the customer buys the product Next, we wll analyze the equlbrum decsons of the three supply chan structures Equlbrum decsons In ths secton, we establsh and explore the subgame soluton for each of the three supply chan structures from the stage one game: DD, DC and CC DD case In the DD case, the two manufacturers smultaneously determne ther R&D level frst, and then the two supplers smultaneously set ther wholesale prces Fnally, the two manufacturers take on Cournot quantty competton We use backward nducton to study the equlbrum decsons of the DD scenaro The manufacturer s proft functon s

4 90 DD m q ( a q q j w c x) () Solvng the frst order condton of producton quantty yelds, q a w j w c x x j The supplers proft functon s as follows, s w q w a w w c x x ) ( j j Solvng the frst-order condtons of 7 w a c x x j 5 5 s wth respect to w yelds, Insertng Eq () and Eq (4) nto Eq() results the followng, m ( a c x ) x j rx () () (4) (5) Solvng the frst order condton of x 56( a c) 56 DC case m wth respect to x yelds, In the DC case, one supply chan s decentralzed and the other supply chan s centralzed The decentralzed manufacturer and the centralzed supply chan smultaneously determne ther R&D level frst, and then the decentralzed suppler sets the wholesale prce Fnally, the decentralzed manufacturer and the centralzed supply chan take on Cournot quantty competton We use backward nducton to study the equlbrum decsons of the DC scenaro In the decentralzed supply chan, the suppler s proft functons and the manufacturer s proft functons are as follows: m q ( a q q w c x ), (8) s w q (6) (7) The total proft functon of the centralzed supply chan s as follows, sc q ( a q q c x) Solvng the frst order condton of producton quantty yelds, q a x c x w (9) (0)

5 Q L and Z Lu / Internatonal Journal of Industral Engneerng Computatons 5 (04) 9 q a x c x w () For the decentralzed suppler, the optmal wholesale prce s as follows, w a 4 x c x 4 4 Insertng Eqs (0)-() nto Eq (7) and Eq (9) yelds the followng, m ( a x c x) sc ( a x c x) 6 () () (4) Therefore, we get the frst order condton of the R&D level 4( a c)(6r 7) x 6r 95r 8 x 7( a c)(5r 4) 6r 95r 8 (5) (6) Based on the equlbrum R&D level, we derve the equlbrum producton quantty, manufacturers and supplers proft and the total proft of whole supply chan CC case When the two supply chans both follow the centralzed strategy, based on the collectve ratonalty, the members of both supply chans choose the strategy to maxmze the whole supply chans proft The two supply chans smultaneously determne ther R&D level frst, and then they take on Cournot quantty competton The competton between the two supply chans s the same as competton between duopoly Then, the problem can be descrbed as followng functons sc q ( a q q c x) (7) sc q ( a q q c x) (8) Solvng the frst order condton of quantty, we have a c x q q x a c x x Insertng q and q nto Eq (7) and Eq (8), we obtan sc a c x x ( ) (9) (0) ()

6 9 sc a c x ( x ) () Dervng the frst order condton wth respect to x and x yelds the followng, x 4( a c) 4 () Based on the equlbrum R&D level, we derve the equlbrum producton quantty and the total proft of both supply chans 4 Analyss of equlbrum results The equlbrum results, ncludng producton quantty, R&D level, wholesale prce, players proft and the supply chans total proft, are dfferent n the three channel structures, shown n Table Next we compare the results 4 Comparson of equlbrum results () Producton quantty DC CC DD DC q q q q Proposton : In DC scenaro, the supply chan whch takes centralzed supply chan structure generates the largest producton quantty; In CC scenaro, the two supply chans get the second producton quantty; In DD scenaro, the two supply chans get the thrd producton quantty; In DC scenaro, the supply chan whch takes decentralzed supply chan structure gets the least producton quantty Table Equlbrum solutons under three scenaros Varable DD DC CC Quantty q 90r ( a c) 56 ( a c)(6r 6r 4r) 95r 8 r ( a c) 4 Quantty q 90r ( a c) 56 ( a c)(90r 6r 4r) 95r 8 r ( a c) 4 R&D level x 56( a c) 56 4( a c)(6r 7) 6r 95r 8 4( a c) 4 R&D level x 56( a c) 56 7( a c)(5r 4) 6r 95r 8 4( a c) 4 Total proft r( a c) 50[ 56 ] + 90r( a c) 568r( a c) [ ] 56 ( 56) ( a c)(6r 7) [ ] (6r 8r) 6r 95r 8 a c [ ] (6r 8r)(54r 6r 95r 8 6 ) r r( a c) a c [ ] 8r[ ] 4 4 Total proft r ( a c) + 50[ ] 56 90r ( a c) 568r( a c) [ ] 56 ( 56) a c)(90r 4r) 4 ( a c)(5r 4) r ( a c) a c ] ] [ ] 8r[ ] 4 4 ( [ 6r 95r 8 6r 95r 8 () R&D level DC CC DD DC x x x x

7 Q L and Z Lu / Internatonal Journal of Industral Engneerng Computatons 5 (04) 9 Proposton : The R&D level of the supply chan choosng centralzed supply chan structure n DC scenaro s the largest, and the R&D level of CC scenaro s the second largest, and the R&D level of DD scenaro s the less, whle the R&D level of the supply chan choosng decentralzed supply chan structure n DC scenaro s the least () Total proft DC CC DD DD DC DC m s m s Proposton : The total proft of the supply chan choosng centralzed supply chan structure n DC scenaro s the largest, and the total proft of CC scenaro s the second largest, and the total proft of DD scenaro s the less, whle the total proft of the supply chan choosng decentralzed supply chan structure n DC scenaro s the least 4 Nash equlbrum analyss We get the Nash equlbrum of supply chan competton as Table shows Table Nash equlbrum of supply chan competton SC SC Decentralzed Centralzed Decentralzed,, Centralzed DD, CD DD CD DC, CC DC CC As Table shows, for supply chan and, takng centralzed supply chan structure s ther strctly domnant strategy The equlbrum soluton for ths supply chan system s CC strategy Prevous study shows that the coordnaton of supply chan wll lead to prsoner's dlemma under prce competton Ths study shows that, under quantty competton, the supply chan system s equlbrum soluton s CC strategy, whch s good for both supply chans, and there s no prsoner's dlemma The management mplcatons of ths study are that CC strategy wll be helpful to ncrease the profts of supply chan companes In the real busness, enterprses should cooperate more closely wth other enterprses n the supply chan, share nformaton and make decsons together They should determne the producton quantty accordng to the market demand so as to obtan beneft from the coordnaton of supply chan Furthermore, they should not blndly expand the scale of the enterprse, to avod the phenomenon of excess producton capacty 5 Concluson Ths paper consders the Cournot competton of two competng supply chans, n whch each conssts of one suppler and one manufacturer The two manufacturers both conduct technologcal nnovaton Ths paper analyses the supply chan members producton, technology strategy and proft n three scenaros: DD (two decentralzed supply chans), DC (one decentralzed supply chan and one centralzed supply chan) and CC (two centralzed supply chans) By means of game theory, we analyze the competton equlbrum and coordnaton strategy The results ndcate that the producton, the R&D level and the total proft of the supply chans n DC scenaro are the largest, those of the CC scenaro come second, those of the DD scenaro come thrd and those of the decentralzed supply chan n DC scenaro are the smallest The two supply chans could obtan a balanced soluton n CC scenaro, and the classcal prsoner s dlemma wll not appear n the supply chan system, and that the CC supply chan structure strategy s good for both supply chans

8 94 Acknowledgement The authors would lke to thank the anonymous referees for valuable suggestons References Amr, R, Evstgneev, I, & Wooders, J (00) Noncooperatve versus cooperatve R&D wth endogenous spllover rates Games and Economc Behavor, 4 (),8-07 Banerjee, S, & Ln, P (00) Vertcal research jont ventures Internatonal Journal of Industral Organzaton, 9 (), 85-0 Banker, RD, Khosla, I, & Snha, KK (998) Qualty and Competton Management Scence, 44 (9), 79-9 Besanko, D, & Wu, J (0) The mpact of market structure and learnng on the tradeoff between R&D competton and cooperaton The Journal of Industral Economcs, 6 (),66-0 Boyac, T, & Gallego, G (004) Supply chan coordnaton n a market wth customer servce competton Producton and Operatons Management, (),- Celln, R, & Lambertn, L (009) Dynamc R&D wth spllovers: Competton vs cooperaton Journal of Economc Dynamcs and Control, (), D'Aspremont, C, & Jacquemn, A (988) Cooperatve and noncooperatve R & D n duopoly wth spllovers The Amercan Economc Revew,-7 De Fraja, G, & Slpo, DB (00) Product market competton, R&D, and welfare Research n Economcs, 56 (4),8-97 Gupta, S, & Loulou, R (998) Process nnovaton, product dfferentaton, and channel structure: Strategc ncentves n a duopoly Marketng Scence, 7 (4),0-6 Ha, AY, & Tong, S (008) Contractng and nformaton sharng under supply chan competton Management Scence, 54 (4),70-75 Hnloopen, J (997) Subsdzng cooperatve and noncooperatve R&D n duopoly wth spllovers Journal of Economcs, 66 (),5-75 Ish, A (004) Cooperatve R&D between vertcally related frms wth spllovers Internatonal Journal of Industral Organzaton, (8),-5 Manasaks, C, Petraks, E, & Zkos, V (04) Downstream Research Jont Venture wth upstream market power Southern Economc Journal, 80 (),78-80 McGure, TW, & Staeln, R (98) An ndustry equlbrum analyss of downstream vertcal ntegraton Marketng Scence, (),6-9 Myagwa, K, & Ohno, Y (00) Uncertanty, spllovers, and cooperatve R&D Internatonal Journal of Industral Organzaton, 0 (6), Motta, M (99) Cooperatve R&D and vertcal product dfferentaton Internatonal Journal of Industral Organzaton, 0 (4),64-66 Qu, LD (997) On the dynamc effcency of Bertrand and Cournot equlbra Journal of Economc Theory, 75 (),-9 Suetens, S (005) Cooperatve and noncooperatve R&D n expermental duopoly markets Internatonal Journal of Industral Organzaton, (),6-8 Suzumura, K (99) Cooperatve and Noncooperatve R&D n an Olgopoly wth Spllovers The Amercan Economc Revew,07-0 Wu, C, Du, H, & Lu, X (0) Vertcal ntegraton n competng supply chans under addtve stochastc demand Internatonal Journal of Intercultural Informaton Management, (),8-06 Wu, C, Petruzz, NC, & Chhajed, D (007) Vertcal Integraton wth Prce Settng Compettve Newsvendors Decson Scences, 8 (4),58-60 Xe, G, Wang, S, & La, K (0) Qualty mprovement n competng supply chans Internatonal Journal of Producton Economcs, 4 (),6-70