摘要
供应链优化指供应链上企业以自身利润最大化为目标,对企业内部各种运作决策进行优化。供应链协调是指以供应链系统整体优化为目标,使供应链上各节点企业服务于一个共同目的,企业间的决策协调一致。供应链优化及协调问题需要考虑系统内的信息流、物流、资金流、企业间的博弈等因素,是较为复杂的供应链管理问题。本论文基于无限期连续盘点的(r,Q)库存策略的基本模型研究供应链优化及协调问题。论文分别考察“零售商管理库存”和“供应商管理库存”两类供应链管理模式,针对三种供应链结构分析不同供应链管理模式下的几类供应链合同对系统的协调效果,并研究在包含多个零售商的竞争性市场环境下的库存和定价决策优化问题。
对于供应商管理库存模式,考察包含两个节点的最基本供应链模型,分别针对“供应商拥有货权”和“零售商拥有货权”两种方式设计两类合同,对不同合同下供应链的详细运作方式与决策过程进行了分析。通过数值实验考察这两类合同下供应链的整体绩效,结果表明供应商管理库存合同对这类供应链有令人满意的协调效果。
将该模型扩展为包含定价决策的供应链,同时考虑零售商的定价与库存决策的优化,以及供应链上下游节点间的协调。通过设计零售商管理库存模式下的收益共享合同与供应商管理库存模式下的依赖于补货策略的收益共享合同实现供应链的协调。通过数值实验考察合同的绩效,结果表明在零售商管理库存模式下,收益共享合同的绩效优于批发价格合同,在供应商管理库存模式下,依赖于补货策略的收益共享合同绩效优于批发价格合同,并且可以完美协调供应链。
再将模型扩展为包含多个下游库存节点的供应链,且节点之间存在市场竞争。通过近似方法将该复杂系统适当简化,并以此为基础研究库存与定价策略同时决策时的优化问题,讨论零售商博弈的均衡点的存在性与唯一性条件,并考察库存与定价策略序贯决策时的优化问题。通过数值实验分析集中控制与分散控制下系统的绩效,结果表明分散控制下同时决策系统的绩效与集中控制下系统绩效相比有较大损失,分散控制下序贯决策系统的绩效最差。
Supply chain optimization focuses on optimizing expected profits of a particular firmin a supply chain through integrating the operational decisions of the firm. Supply chaincoordination focuses on optimizing the overall performance through coordinating the ac-tivities of all the firms so that each firm’s objective is aligned with the system’s objective.To achieve optimization and coordination of a supply chain, the tasks of managing logis-tics, information and money transfer are all important issues. In this paper, the problemof optimization and coordination of a supply chain is studied based on a basic inventorymodel with continuous review (r, Q) policy. Diferent modes of supply chain manage-ment are investigated, including “retailer managed inventory” and “vendor managed in-ventory”. Based on three basic supply chain models, diferent supply chain contracts areused to coordinate the supply chain. Moreover, the optimization of decisions of pricingand inventory management are also considered in these models.
Based on continuous review (r, Q) policy, a system comprising a single vendor and asingle retailer is considered. A vendor-managed-inventory program is used to coordinatethe system. Two business scenarios that are popular in vendor-managed-inventory pro-gram are “vendor with ownership” and “retailer with ownership”. We design two types ofcontract for these two scenarios respectively, and investigate the system performance withthe contracts through numerical studies.
For a supply chain with retailer’s pricing decision, we study how to optimize thepricing and inventory management decisions, as well as how to coordinate the actions ofdiferent firms on the chain. A normal revenue-sharing contract and a policy-dependentvendor-managed-inventory contract are designed.
For a supply chain with multiple competing retailers and involves decisions of pricingand inventory management, we give an efcient approach to characterize the relationshipbetween pricing decisions and inventory management decisions. Based on the approach,solution methods for centralized decisions and Nash equilibria in Cournot competitionwith simultaneous decisions of pricing and inventory management are developed, as wellas the existence and conditions of uniqueness of the equilibrium. Besides, optimal sequen-tial decisions of pricing and inventory management are studied. Numerical computations are provided to evaluate the efciency of the solution methods and system performancesin diferent scenarios.
引文
[1] Lenius P. Elkay implements VMI with central supply. Supply House Times,2005. October.
[2] Angela D H. Vendor-Managed Inventory Growing. Air Conditioning Heating&RefrigerationNews,2005. October24.
[3] Khadar S A. VMI program improves forecasting&supply chain–Arasco’s case study. TheJournal of Business Forecasting,2007,26:29–32.
[4] Duchessi P, I C S. Enhancing business performance via Vendor Managed Inventory Applica-tions. Communications of the ACM,2008,51(12):121–127.
[5] Cooke J A. VMI: very mixed impact? Logistics Management&Distribution Report,1998.October1.
[6] Hadley G, Whitin T M. Analysis of Inventory Systems. Englewood Clifs, N.J.: Prentice-Hall,1963.
[7] Montgomery D C, Bazaraa M S, Keswani A K. Inventory models with a mixture of backordersand lost sales. Naval Research Logistics,1973,20(2):255–263.
[8] Rabinowitz G, Mehrez A, Chu C W, et al. A partial backorder control for continuous review(r,Q) inventory system with Poisson demand and constant lead time. Computers&OperationsResearch,1995,22:689–700.
[9] Johansen S G, Thorstenson A. Optimal and approximate (Q,r) inventory policies with lostsales and gamma-distributed lead time. International Journal of Production Economics,1996,30:179–194.
[10] Johansen S G, Thorstenson A. Optimal (r,Q) inventory policies with Poisson demands andlost sales: discounted and undiscounted cases. International Journal of Production Economics,1996,46:359–371.
[11] Berk E, Gu¨rlerU¨. Analysis of the (Q,r) inventory model for perishables with positive lead timesand lost sales. Operations Research,2008,56(5):1238–1246.
[12] Moinzadeh K, Lee H L. Batch size and stocking levels in multi-echelon repairable systems.Management Science,1986,32(12):1567–1581.
[13] Svoronos A, Zipkin P. Estimating the performance of multi-level inventory systems. OperationsResearch,1988,36(1):57–72.
[14] Axsa¨ter S. Evaluation of installation stock based (R,Q)-policies for two-level inventory systemswith Poisson demand. Operations Research,1998,46(3):S135–S145.
[15] Andersson J, Marklund J. Decentralized inventory control in a two-level distribution system.European Journal of Operational Research,2000,127:483–506.
[16] Chen F. Optimal policis for multi-echelon inventory problems with batch ordering. OperationsResearch,2000,48(3):376–389.
[17] Forsberg R. Exact evaluation of (R,Q)-policies for two-level inventory systems with Poissondemand. European Journal of Operational Research,1997,96:130–138.
[18] Forsberg R. Evaluation of (R,Q)-policies for two-level inventory systems with generally dis-tributed customer inter-arrival times. European Journal of Operational Research,1997,99:401–411.
[19] Zheng Y. On properties of stochastic inventory systems. Management Science,1992,38:87–103.
[20] Federgruen A, Zheng Y. An efcient algorithm for computing an optimal (r, Q) policy incontinuous review stochastic inventory systems. Operations Research,1992,40:808–813.
[21] Cachon G P. Supply chain coordination with contracts. In: Kok A, Graves S,(eds.). Proceedingsof Handbooks in Operations and Management Science. North Holland,2003:229–339.
[22] Bassok Y, Anupindi R. Analysis of supply contracts with total minimum commitment. IIETransactions,1997,29:373–381.
[23] Anupindi R, Bassok Y. Supply contracts with quantity commitments and stochastic demand.In: Tayur S, Ganeshan R, Magazine M,(eds.). Proceedings of Quantitative Models for SupplyChain Management. Boston: Kluwer Academic Publishers,1999:197–232.
[24] Henig M, Gerchak D F, Pyke D F. An inventory model embedded in designing a supply contract.Management Science,1997,43:184–189.
[25] Tsay A A. The quantity flexibility contract and supplier-customer incentives. ManagementScience,1999,45:1339–1358.
[26] Tsay A A. Quantity flexibility contracts and supply chain performance. Manufacturing andService Operations Management,1999,1:89–111.
[27] Padmanabhan V, Png I P L. Manufacturer’s returns policies and retail competition. MarketingScience,1997,16(1):81–94.
[28] Emmons H, Gilbert S M. The role of return policies in pricing and inventory decisions forcatalogue goods. Management Science,1998,44(2):276–283.
[29] Wang H. Do returns policies intensify retail competition? Marketing Science,2004,23(4):611–613.
[30] Granot D, Yin S. On the efectiveness of returns policies in the price-dependent newsvendormodels. Naval Research Logistics,2005,52(8):765–779.
[31] Song Y, Ray S, Li S. Structural properties of buyback contracts for price-Setting newsvendors.Manufacturing&Service Operations Management,2008,10(1):1–18.
[32] Anupindi R, Bassok Y. Centralization of stocks: retailers vs. manufacturer. Management Sci-ence,1999,45(2):178–191.
[33] Cachon G P, Lariviere M A. Supply chain coordination and revenue sharing contract: Strengthsand limitations. Management Science,2005,51(1):30–44.
[34] Giannoccaro I, Pontrandolfo P. Supply chain coordination by revenue sharing contract. Inter-national Journal of Production Economics,2004,89(2):131–139.
[35] Wang S, Zhu T. Control allocation, revenue sharing, and joint ownership. International Eco-nomic Review,2005,46(3):895–915.
[36] Gerchak Y, Wang Y Z. Revenue-sharing vs. wholesale-price contracts in assembly systemswith random demand. Production and Operations Management,2004,13:23–33.
[37] Yao Z, Leung S C H, Lai K K. Manufacturer’s revenue-sharing contract and retail competition.European Journal of Operational Research,2008,186(2):637–651.
[38] Linh C, Hong Y. Channel coordination through a revenue sharing contract in a two-periodnewsboy problem. European Journal of Operational Research,2009,198:822–829.
[39] Barnes-Schuster D, Bassok Y, Anupindi R. Coordination and flexibility in supply contractswith options. Manufacturing&Service operations management,2002,4(3):171–207.
[40] Wu D, Kleindorfer P R, Zhang J. Optimal bidding and contracting strategies for capital-intensive goods. European Journal of Operational Research,2002,137(3):657–676.
[41] Wu D, Kleindorfer P R. Competitive options, supply contracting, and electronic markets. Man-agement Science,2005,51(3):452–446.
[42] Mart′nez-de-Albe′niz V, Simchi-Levi D. A portfolio approach to procurement contracts. Pro-duction and Operations Management,2005,14(1):90–114.
[43] Mart′nez-de-Albe′niz V, Simchi-Levi D. Competition in the Supply Option Market. OperationsResearch,2009,57(5):1082–1097.
[44] Zhao Y, Wang S, Cheng T, et al. Coordination of supply chains by option contracts: A cooper-ative game theory approach. European Journal of Operational Research,2010,207:668–675.
[45] Fu Q, Lee C, Teo C. Procurement management using option contracts: random spot price andthe portfolio efect. IIE Transactions,2010,42:793–811.
[46] Yang Z, Ayd n G, Babich V, et al. Supply disruptions, asymmetric information, and a backupproduction option. Management Science,2009,55(2):192–209.
[47] Gomez Padilla A, Mishina T. Supply contract with options. International Journal of ProductionEconomics,2009,122:312–318.
[48] Myerson R. Optimal auction design. Mathematics of Operations Research,1982,6(1):58–73.
[49] Milgrom P, Weber R. A theory of auctions and competitive bidding. Econometrica,1982,50(5):1089–1122.
[50] Che Y K. Design competition through multidimensional auctions. RAND Journal of Eco-nomics,1993,24(4):668–680.
[51] Beil D, Wein L. An inverse-optimization-based auction mechanism to support a multiattributeRFQ process. Management Science,2002,49(11):1529–1545.
[52] Chen Y, Seshadri S, Zemel E. Sourcing through auctions and audits. Production and OperationsManagement,2008,17(2):121–138.
[53] Schummer J, Vohra R V. Auctions for procuring options. Operations Research,2003,51(1):41–51.
[54] Chen F. Auctioning supply contracts. Management Science,2007,53:1562–1576.
[55]中华人民共和国国家质量监督检验检疫总局,中国国家标准化管理委员会.中华人民共和国国家标准物流术语(GB/T18354-2006).北京:中国标准出版社,2007.
[56] Cachon G P. The allocation of inventory risk in a supply chain: Push, pull and advance-purchasediscount contracts. Management Science,2004,50:222–238.
[57] Aviv Y, Federgruen A. The operational benefits of information sharing and vendor managedinventory (VMI) programs. Working paper,1998. The John M. Olin School of Business, Wash-ington University, St. Louis, MO.
[58] Yao Y, Martin D. The inventory value of information sharing, continuous replenishment, andvendor-managed inventory. Transportation Research: Part E,2008,44:361–378.
[59] Corbett C J. Stochastic inventory systems in a supply chain with asymmetric information: cyclestocks, safety stocks, and consignment stock. Operations Research,2001,49:487–500.
[60] Kim H S. Revisiting“Retailer-vs. vendor-managed inventory and brand competition”. Man-agement Science,2008,54:623–626.
[61] Mishra B K, Raghunathan S. Retailer-vs. vendor-managed inventory and brand competition.Management Science,2004,50:445–457.
[62] Wang C X. Random yield and uncertain demand in decentralised supply chains under the tran-ditional and VMI arrangements. International Journal of Production Research,2009,47:1955–1968.
[63] Razmi J, Rad R H, Sangari M S. Developing a two-echelon mathematical model for a vendor-managed inventory (VMI) system. International Journal of Advanced Manufacturing Technol-ogy,2010,48:773–783.
[64] Choi K, Dai J G, Song J S. On measuring supplier performance under vendor-managed-inventory programs in capacitated supply chains. Manufacturing&Service operations man-agement,2004,6:53–72.
[65] Bernstein F, Chen F, Federgruen A. Coordinating supply chains with simple pricing schemes:the role of vendor-managed inventories. Management Science,2006,52:1483–1492.
[66] Cachon G P. Stock wars: inventory competition in a two-echelon supply chain with multipleretailers. Operations research,2001,49:658–674.
[67] Yao Y, Dong Y, Dresner M. Analyzing information-enabled stockout management undervendor-managed inventory. Information Technology&Management,2007,8:133–145.
[68] Nachiappan S P, Jawahar N. A genetic algorithm for optimal operating parameters of VMI sys-tem in a two-echelon supply chain. European Journal of Operational Research,2007,182:1433–1452.
[69] Xu K, Leung M T. Stocking policy in a two-party vendor managed channel with space restric-tions. International Journal of Production Economics,2009,117:271–285.
[70] Federgruen A, Zipkin P. A combined vehicle routing and inventory allocation problem. Oper-ations Research,1984,32(5):1019–1037.
[71] Bard J F, Liu H, Jaillet P, et al. A decomposition approach to the inventory routing problemwith satellite facilities. Transportation Science,1998,32(2):189–203.
[72] Trudeau P, Dror M. Stochastic inventory routing: Route design with stockouts and route failures.Transportation Science,1992,26(3):171–184.
[73] Viswanathan S, Mathur K. Integrating routing and inventory decisions in one-warehouse multiretailer multiproduct distribution systems. Management Science,1997,43(3):294–312.
[74] Kleywegt J, Nori S N, Savelsbergh W P. The stochastic inventory routing problem with directdeliveries. Transportation Science,2002,36(1):94–118.
[75] Kleywegt J, Nori S N, Savelsbergh W P. Dynamic programming approximations for a stochasticinventory routing problem. Transportation Science,2004,38(1):42–70.
[76] Anily S, Federgruen A. One Wharehouse Multiple Retailer System with Vehicle Routing Costs.Management Science,1990,36(1):92–114.
[77] Anily S, Federgruen A. Two-echelon distribution systems with vehicle routing costs and centralinventories. Operations Research,1993,41(1):37–47.
[78] Fry M J, Kapuscinski R, Olsen T L. Coordinating production and delivery under a (z, Z)-typevendor-managed inventory contract. Manufacturing&Service Operations Management,2001,3:151–173.
[79] Darwish M A, Odah O M. Vendor managed inventory model for single-vendor multi-retailersupply chains. European Journal of Operational Research,2010,204:473–484.
[80] Wang Y, Jiang L, Shen Z J. Channel performance under consignment contract with revenuesharing. Management Science,2004,50:34–47.
[81] Li S, Hua Z S. A note on channel performance under consignment contract with revenuesharing. European Journal of Operational Research,2008,184:793–796.
[82]姬小利,王宁生.信息不对称情况下的VMI协调机制设计.系统工程,2004,22(11):24–28.
[83]蔡建湖,黄卫来,周根贵.基于收益分享契约的VMI模型研究.中国管理科学,2006,14(4):108–113.
[84]杨建功,王国庆.库存竞争性产品的VMI收益分享合同模型.系统工程理论与实践,2009,29(6):46–58.
[85]曹武军,李成刚,王学林,等. VMI环境下收入共享契约分析.管理工程学报,2007,21(1):51–55.
[86] Yao Y, Dong Y, Dresner M. Managing supply chain backorders under vendor managed inven-tory: An incentive approach and empirical analysis. European Journal of Operational Research,2010,203:350–359.
[87]刘德海,王维国,王迅.不完全信息下选择供应链VMI合作伙伴的信息甄别模型.运筹与管理,2009,18(2):47–52.
[88] Yu Y, Chu F, Chen H. A Stackelberg game and its improvement in a VMI system with amanufacutring vendor. European Journal of Operational Research,2009,192:929–948.
[89] Kim J S, Kwat T C. Game theoretic analysis of the bargaining process over a long-term replen-ishment contract. Journal of the Operational Research Society,2007,58:769–778.
[90] Wong W K, Qi J, Leung S. Coordinating supply chains with sales rebate contracts and vendor-managed inventory. International Journal of Production Economics,2009,120:151–161.
[91] Nagarajan M, Rajagopalan S. Contracting under vendor managed inventory systems usingholding cost subsides. Production and Operations Management,2008,17(2):200–210.
[92] Chen J, Lin I, Cheng H. Channel coordination under consignment and vendor-managed inven-tory in a distribution system. Transportation Research Part E,2010,46:831–843.
[93] Li S, Zhu Z, Huang L. Supply chain coordination and decision making under consignmentcontract with revenue sharing. International Journal of Advanced Manufacturing Technology,2009,120:88–99.
[94] Chan A, Shen Z J, Simchi-Levi D, et al. Coordination of pricing and inventory decisions: asurvey and classification. In: Simchi-Levi D, Wu S D, Shen Z J,(eds.). Proceedings of Hand-book of quantitative supply chain analysis: Modeling in the e-business era. Boston: KluwerAcademic Publishers,2004:335–392.
[95] You P S. Ordering and pricing of service products in an advance sales system with price-dependent demand. European Journal of Operational Research,2006,170:57–71.
[96] Chang H, Teng J, Ouyang L, et al. Retailer’s optimal pricing and lot-sizing policies for de-teriorating items with partial backlogging. European Journal of Operational Research,2006,168:51–64.
[97] Transchel S, Minner S. The impact of dynamic pricing on economic order decision. EuropeanJournal of Operational Research,2009,198:773–789.
[98] Chen J, Bell P C. The impact of customer returns on pricing and order decisions. EuropeanJournal of Operational Research,2009,195:280–295.
[99] Federgruen A, Heching A. Combined pricing and inventory control under uncertainty. Opera-tions Research,1997,47(3):454–475.
[100] Chen X, Simchi-Levi D. Coordinating inventory control and pricing strategies with randomdemand and fixed ordering cost: the infinite horizon case. Mathematics of Operations Research,2004,29(3):698–723.
[101] Chen X, Simchi-Levi D. Coordinating inventory control and pricing strategies with randomdemand and fixed ordering cost: the finite horizon case. Operations Research,2004,52(6):887–896.
[102] Chen Y, Ray S, Song Y. Optimal pricing and inventory control policy in periodic-review systemswith fixed ordering cost and lost sales. Naval Research Logistics,2006,53:117–136.
[103] Li Q, Zheng S. Joint inventory replenishment and pricing control for systems with uncertainyield and demand. Operations Research,2006,54(4):696–705.
[104] Zhang J L, Chen J, Lee C. Joint optimization on pricing, promotion and inventory control withstochastic demand. International Journal of Production Economics,2008,116:190–198.
[105] He Y, Zhao X, Zhao L, et al. Coordinating a supply chain with efort and price dependentstochastic demand. Applied Mathematical Modeling,2009,33:2777–2790.
[106] Feng Y, Chen F. Joint pricing and inventory control with setup cost and demand uncertainty.Working paper,2003. The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
[107] Chen X, Simchi-Levi D. Coordinating inventory control and pricing strategies: the continuousreview model. Operations Research Letters,2006,34(3):323–332.
[108] Chao X, Zhou S X. Joint inventory-and-pricing strategy for a stochastic continuous-reviewsystem. IIE Transactions,2006,38:401–408.
[109] Zhang A, Zhang Z, Guo X. Comparative study on decentralised inventory policy and vendormanaged inventory with (r, Q) replenishment strategy. International Journal of Logistics Systemand Management,2008,4:80–97.
[110] Bernstein F, Federgruen A. Pricing and replenishment strategies in a distribution system withcompeting retailers. Operations Research,2003,51:409–426.
[111] Rosen J B. Existence and uniqueness of equilibrium points for concave N-person games. Econo-metrica,1965,33(3):520–534.
[112] Roberts J, Sonnenschein H. On the existence of Cournot equilibrium without concave profitfunctions. Journal of Economic Theory,1976,13(1):112–117.
[113] Singh N, Vives X. Price and quantity competition in a diferentiated duopoly. RAND Journalof Economics,1984,15(4):546–554.
[114] Dastidar K G. Comparing Cournot and Bertrand in a homogenous product market. Journal ofEconomic Theory,1997,75(1):205–212.
[115] Amir R, Jin J Y. Cournot and Bertrand equilibria compared: substitutability, complementarityand concavity. International Journal of Industrial Organization,2001,19(3):303–317.
[116] Chen F, Federgruen A, Zheng Y S. Near-optimal pricing and replenishment strategies for aretail/distribution system. Operations Research,2001,49:839–853.
[117] Chen F, Federgruen A, Zheng Y S. Coordination mechanisms for a distribution system withone supplier and multiple retailers. Management Science,2001,47:693–708.
[118] Wang Q, Wang R. Quantity discount pricing policies for heterogeneous retailers with pricesensitive demand. Naval Research Logistics,2005,52:645–658.
[119] Tang C S, Yin R. Joint ordering and pricing strategies for managing substitutable products.Production and Operations Management,2007,16:138–153.
[120] Aydin G, Porteus E L. Joint inventory and pricing decisions for an assortment. OperationsResearch,2008,56(5):1247–1255.
[121] Bish E K, Wang Q. Optimal invesment strategies for flexible resources, considering pricing andcorrelated demands. Operations Research,2004,52:954–964.
[122] Zhu K, Thonemann U W. Coordination of pricing and inventory control across products. NavalResearch Logistics,2009,56:175–190.
[123] Tyagi R K. On the efects of downstream entry. Management Science,1999,45(1):59–73.
[124] Corbett C J, Karmarkar U S. Competition and structure in serial supply chains with determin-istic demand. Management Science,2001,47:966–978.
[125] Carr S M, Karmarkar U S. Competition in multiechelon assembly supply chains. ManagementScience,2005,51:45–59.
[126] Majumder P, Srinivasan A. Leadership and competition in network supply chains. ManagementScience,2008,54:1189–1204.
[127] Xiao T, Qi X. Price competition, cost and demand disruptions and coordination of a supplychain with one manufacturer and two competing retailers. Omega,2008,36:741–753.
[128] Hobbs B F, Pang J S. Nash-Cournot equilibria in electric power markets with piecewise lineardemand functions and joint constraints. Operations Research,2007,55:113–127.
[129] Wu J, Zhai X, Huang Z. Incentives for information sharing in duopoly with capacity constraints.Omega,2008,36:963–975.
[130] Wang Y. Joint pricing-production decisions in supply chains of complementary products withuncertain demand. Operations Research,2006,54:1110–1127.
[131] Zhao X, Atkins D R. Newsvendors under simultaneous price and inventory competition. Man-ufacturing&Service Operations Management,2008,10:539–546.
[132] Parlar M, Weng Z K. Coordinating pricing and production decisions in the presence of pricecompetition. European Journal of Operational Research,2006,170:211–227.
[133] Guo L, Villas-Boas J M. Consumer stockpiling and price competition in diferentiated markets.Journal of Economics&Management Strategy,2007,16:827–858.
[134] Bernstein F, Federgruen A. Dynamic inventory and pricing models for competing retailers.Naval Research Logistics,2004,51:258–274.
[135] Bernstein F, Federgruen A. A general equilibrium model for industries with price and servicecompetition. Operations Research,2004,52:868–886.
[136] Bernstein F, Federgruen A. Decentralized supply chains with competing retailers under demanduncertainty. Management Science,2005,51:18–29.
[137] Gallego G, Huh W T, Kang W, et al. Price competition with the attraction demand model: exis-tence of unique equilibrium and its stability. Manufacturing&Service Operations Management,2006,8(4):359–375.
[138] Zhao X. Coordinating a supply chain system with retailers under both price and inventorycompetition. Production and Operations Management,2008,17:532–542.
[139] Lin K Y, Sibdari S Y. Dynamic price competition with discrete customer choices. EuropeanJournal of Operational Research,2009,197:969–980.
[140] Hopp W J, Xu S. A static approximation for dynamic demand substitution with applications ina competitive market. Operations Research,2008,56:630–645.
[141] Zipkin P H. Foundations of Inventory Management. New York: McGraw-Hill,2000.
[142] Lariviere M A. Supply chain contracting and coordination with stochastic demand. In: TayurS, Ganeshan R, Magazine M,(eds.). Proceedings of Quantitative Models for Supply ChainManagement. Boston: Kluwer Academic Publishers,1999:233–268.
[143] Zhao X, Fan F, Liu X, et al. Storage-space capacitated inventory system with (r,Q) policies.Operations Research,2007,55:854–865.
[144] Lee H L, Rosenblatt M J. A generalized quantity discount pricing model to increase supplier’sprofits. Management Science,1986,32:1177–1185.
[145] Munson C L, Rosenblatt M J. Coordinating a three-level supply chain with quantity discounts.IIE Transactions,2001,33:371–384.
[146] Weng Z K. Channel coordination and quantity discounts. Management Science,1995,41(9):1509–1522.
[147] Gallego G, Ryzin G. Optimal dynamic pricing of inventories with stochastic demand over finitehorizons. Management Science,1994,40(8):999–1020.
[148] Zhao W, Zheng Y. Optimal dynamic pricing for perishable assets with nonhomogeneous de-mand. Management Science,2000,46(3):375–388.
[149] Araman V F, Caldentey R. Dynamic pricing for nonperishable products with demand learning.Operations Research,2009,57(5):1169–1188.
[150] Liu L, Parlar M, Zhu S X. Pricing and lead time decisions in decentralized supply chains.Management Science,2007,53(5):713–725.
[151] Ohkawa T, Okamura M. On the uniqueness of the welfare-maximizing number of firms underCournot oligopoly. Bulletin of Economic Research,2003,55:209–219.
[152] Okuguchi K, Szidarovszky F. Changes in demand function in Cournot oligopoly. Pacific Eco-nomic Review,2005,10:371–378.
[153] Vives X. Oligopoly pricing. Cambridge, Massachusetts London, England: The MIT Press,2000.