Game Study of the Closed-loop Supply Chain with Random Yield and Random Demand

Transcription

1 , pp Gae Study of the Closed-loop Supply Chain with ando Yield and ando Deand Xiuping Han, Dongyan Chen, Dehui Chen, Ling Hou School of anageent, Habin Univesity of Science and Technology, Heilongjiang, Habin , china Abstact: In this pape, we studied the gae odels of the closed-loop supply chain with ando yield and ando deand and deive the optial ode quantity and optial planned poduction of new poducts unde anufactue-leade stackelbeg, etaile-leade stackelbeg and Nash gae odels. The findings indicated that when etailes doinate the supply chain, optial ode quantity, optial planned poduction of new poduct and the pofits of anufactue and etaile s in the supply chain odel doinated by detailes wee geate than those in othe odels. Accoding to the nueical calculation esults, optial planned poduction of new poduct will decease as ecovey pice inceases, but total pofit and expected pofit of anufactue and etaile will incease as ecovey pice inceases in the thee aket powe stuctues. Keywods: Close-loop supply chain; eanufactuing; ando yield; ando deand 1 Intoduction Due to the esouce shotage and envionent deteioation, anufactuing entepises ae facing the challenge of the coodinated developent of poduction and envionent. These entepises ae equied to ake the integated optiization fo the fowad logistics of new poducts and evese logistics of waste poducts and cay out the closed-loop supply chain anageent. Copaed with the taditional fowad supply chain, the closed-loop supply chain could educe envionent pollution, ipove the utilization ate of esouces, extend the sevice life of the poducts and iniize the esouce consuption and envionental influence fo sustainable developent. Theefoe, it attacts extensive attention fo acadeia and entepises In the taditional supply chain, ando outputs and deands ae one of ost coon and ost ipotant aspects in supply and deand uncetainty. any pevious studies wee based on ando outputs o ando outputs and deands. Isail et al. had studied the influence of diffeent picing and odeing decision on entepise pofit in the condition of ando eanufactued poduct outputs [1]. He et Coesponding autho Eail addess::xiupinghan1979@126.co(dongyan Chen) ISSN: ASTL Copyight 2014 SESC

2 al. pointed out that those ando outputs ight lead to the isk of ovepoduction and insufficient poduction in the supply chain, established 4 diffeent collaboation contacts based on isk shaing, and copaed these 4 contacts based on nueical analysis [2]. On the basis of ando supplie outputs and distibuto deand, Guohong Shi et al. assued that thee was a seconday aket and studied the poduction and odeing stategy fo centalized and decentalized decision [3]. In the above studies, aket stuctue doinated by anufactues was ainly consideed and aket foces of etailes wee neglected. ecently, the aket foces in the supply chain have been tansfeed fo poduce to etail entepises with the cobination of etail businesses and eegence of big-box etailes. Hence, thee ae thee diffeent aket foces o gae stuctues: Stackelbeg Gae doinated by anufactues, Stackelbeg Gae doinated by etailes and Nash Equilibiu Gae without leade. Choi studied decision-aking of duopoly anufactues unde the above thee diffeent gae stuctues when they shaed one etaile and analyzed the influences of aket foces, poducts diffeence and poduction cost on decision-aking [4]. Seng et al. also studied the supply chain consisting of single anufactue and single etaile unde the above thee diffeent gae stuctues, and copaed the decision vaiables and channel pofits of diect selling channel, indiect selling channel and hybid selling channel [5]. Lin Zhu et al. established the supply-deand gae odel of two-echelon supply chain unde ando outputs and obtained the optial odeing aount and planned poduction unde thee diffeent aket foces and stuctues [6]. This pape studied a two-echelon closed-loop supply chain consisting of single anufactue and single etaile. Fistly, the ando outputs wee intoduced into the closed-loop supply chain and thee gae stuctues of supply and deand sides wee studied unde ando outputs and deands. Secondly, we analyzed optial decisions and pofits of each ebe unde these thee gae stuctues. Thidly, we intepeted the influence of ecovey pice on the pofits of each ebe in the supply chain though nueical exaples. 2 odel Desciptions and Assuptions 2.1 Notation Desciption: The sybols used in the pape wee intoduced as follows: c c ( c ) The aginal cost of a new poduct anufactued ( eanufactuing); c The wholesale pice; p The sale pice; h Inventoy holding cost pe unit; b Inventoy shotage cost pe unit; q The ode aount; The acquisition pice of used-poduct; p The tansfe payent pice which the anufactue paid to the etaile. 106 Copyight 2014 SESC

3 2.2 Assuptions To facilitate this discussion, it is assued that: 1) Q (decision vaiable) is the planned poduction of new poducts of the anufactue; U is the ando output facto of new poducts; uq is the actual yield; u is a ando vaiable in the ange 0,1 with the density function of g ( u ) and the distibution function of G ( u ) ; Eu is the ean value; 2) The etailes ae facing the ando aket deand X, whose distibution function and density function ae espectively F ( x ) and f ( x ). The ean value is E ( x ) d ; 3) Waste ecovey aount is an inceasing function of aket ecovey pice and set as ; Accoding to the above sybols and assuptions, we obtained the following equations: The expected pofit functions of the etaile. The function is: p E [ in { U Q, X, q} ] E [ in { U Q, q} ] ( )( p ) U X U h E [ in { U Q, q } X ] b E [( X in { U Q, X } ) ] (1) U U X The expected pofit functions of the anufactue. The function is: E [ in { U Q, q} ] he [( U Q c Q c ( ) p ( ) q ) ] (2) U U 3 Poduction Odeing Stategies unde Thee Diffeent aket Foces 3.1 Stackelbeg Gae Doinated by anufactues When anufactues doinate the supply chain, the gae steps ae intepeted as follows. Fist, the anufactues will deteine the planned poduction Q of new poducts. Secondly, the etailes will deteine the ode aount of the poducts. Since the gae is a dynaic gae unde coplete infoation, whose equilibiu is sub-gae pefect Nash Equilibiu, we can use the backwad induction fo analysis and conside the optial decision of etailes unde the given Q value. Theoe 1 In the odel of Stackelbeg Gae doinated by anufactues, unde the designated planned poduction Q of new poducts of anufactues, the expected pofit of etailes have only one axiu value fo its ode aount q and Copyight 2014 SESC 107

4 the optial ode aount q of etailes is q 1 p b F ( ) (3) p b h Theoe 2 In the odel of Stackelbeg Gae doinated by anufactues, the expected pofit of anufactues is a concave function about Q and the optial planned poduction Q of new poducts of anufactues is expessed as q 0 Q / u g u d u h c h (4) 3.2 Stackelbeg Gae Doinated by etailes When etailes doinate the supply chain, We could also use backwad induction fo analysis and conside the optial decision unde the given q. Theoe 3 In the odel of Stackelbeg Gae doinated by etailes, the expected pofit of anufactues is a concave function of its planned poduction Q. When the ode aount q of etailes is designated, the optial planned poduction Q of new poducts is expessed as q Q u g u d u h c / h. 0 (5) Theoe 4 In the odel of Stackelbeg Gae doinated by etailes, the expected pofit of etailes is a concave function of its odeing aount q and the optial ode aount q of etailes is expessed as 0 1 [( p b ) ( p b h) F( u ( q ) )] u g( u) d u 1 1[( p b ) ( p b h) F( q )] g ( u) d u 0 (6) 3.3 Nash Equilibiu Gae of anufactues and etailes In the odel of Nash Equilibiu Gae of anufactues and etailes, if the pofit is to be axiized fo the anufactues, accoding to Theoe 1, the optial planned poduction of new poducts should satisfy Eq. (3). Fo the etailes, if the pofit is to 108 Copyight 2014 SESC

5 be axiized, accoding to Theoe 3, the optial planned poduction of new poducts should satisfy Eq. (5). 4 Nueical Analysis In ode to validate the influence of ecovey pice on the closed-loop supply chain, we ake a coesponding nueical calculation. Assuing all paaetes in the odel is given as: p 15, 6, h 3, b 2, 10, 4, c 2, c 0.5, p 1.2, d 100, 0.5, X The unifo distibution in the ange [80,120] and U follows the unifo distibution in the ange [0, 1] The calculation esults obtained with Theoe 1-5 ae povided in Table 1: Table 2. The equilibiu esults unde the ecovey pice vaiation Stackelbeg Gae doinated by etailes Stackelbeg Gae doinated by anufactues q Q q Q Fo Table 2, we can know that the ecovey aount and the quantity of eanufactued poducts incease with the ising ecovey pice, inceases. Then the anufactues will educe the planned poduction of new poducts, and the optial ode aount of etailes and expected pofits of each ebe in the supply chain will incease. In the odel of Stackelbeg Gae doinated by etailes, the etailes will incease the ode aount of poducts to educe the shotage isk. At this tie, the optial planned poduction of new poducts of anufactues will be geate than the optial ode aount in ode to satisfy the ode deands of etailes and the equieents of custoes ae lagely et. 5 Conclusion In the pape, we established a closed-loop supply chain odel unde ando outputs and deands and ae focused on the study of poduction ode decision of the anufactues and etailes, pofits of ebes in the supply chain and oveall pofits in the supply chain unde thee non-coopeation gae behavios. The solution of Copyight 2014 SESC 109

6 Nash Equilibiu is the sae to the optial solution doinated by supplies. The pofits of ebes and oveall pofits in the whole supply chain in the odel of Stackelbeg Gae doinated by etailes ae geate than those of odel of Stackelbeg Gae doinated by anufactues. Acknowledgeent. This wok was suppoted in pat by the National Natual Science Foundation of China (NSFC) unde Gant No and Heilongjiang Povincial Depatent of Education Science and Technology eseach Poject No efeences 1. S. B. Isail, A. Elifi, Effects of ando yield in eanufactuing with pice-sensitive supply and deand, Poduction and Opeations anageent, Vol. 15-3, 2006, Y. He, J. Zhang, ando yield isk shaing in a two-level supply chain, Poduction Econoics, Vol. 112, 2008, G. H. Shi, C. L. Yu, W. W. Gong, Study of supply chain coodination based on uncetain aket deand and uncetainty poduction, Industial Engineeing and anageent, Vol. 16-2, 2011, S. C. Choi, Pice copetition in a duopoly coon etaile channel, Jounal of etaile, Vol. 72-2, 1996, Y. P. Seng, T. K. Hean, odeling hybid distibution channels: A gae-theoetic analysis, Jounal of etailing and Consue Sevice, Vol. 10-3, 2003, L. Zhu, S. D. Wang, Gae analysis of a two-echelon supply chain with ando yield, Jounal of Systes & anageent, Vol. 20-6, 2011, Copyight 2014 SESC