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Game theoretic pricing and ordering decisions with partial lost sales in two-stage supply chains

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  • Cai, Gangshu (George)
  • Chiang, Wen-Chyuan
  • Chen, Xiangfeng

Abstract

Few papers have studied the optimal pricing and ordering with partial lost sales from a two-stage game theoretic perspective. This paper considers a supply chain game with a buyer and a seller through pricing and ordering models with partial lost sales. We evaluate the optimal solutions for the buyer and the seller and provide insights into both the deterministic and stochastic demand models. We also propose search algorithms to obtain the global optimum when convexity and concavity conditions are not satisfied.

Suggested Citation

  • Cai, Gangshu (George) & Chiang, Wen-Chyuan & Chen, Xiangfeng, 2011. "Game theoretic pricing and ordering decisions with partial lost sales in two-stage supply chains," International Journal of Production Economics, Elsevier, vol. 130(2), pages 175-185, April.
    • Handle: RePEc:eee:proeco:v:130:y:2011:i:2:p:175-185
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    References listed on IDEAS

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    1. Cai, Gangshu (George), 2010. "Channel Selection and Coordination in Dual-Channel Supply Chains," Journal of Retailing, Elsevier, vol. 86(1), pages 22-36.
    2. Ganesh Janakiraman & Robin O. Roundy, 2004. "Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock Policies," Operations Research, INFORMS, vol. 52(5), pages 795-803, October.
    3. Teng, Jinn-Tsair & Chang, Chun-Tao & Goyal, Suresh Kumar, 2005. "Optimal pricing and ordering policy under permissible delay in payments," International Journal of Production Economics, Elsevier, vol. 97(2), pages 121-129, August.
    4. Liao, Jui-Jung, 2008. "An EOQ model with noninstantaneous receipt and exponentially deteriorating items under two-level trade credit," International Journal of Production Economics, Elsevier, vol. 113(2), pages 852-861, June.
    5. Brian Downs & Richard Metters & John Semple, 2001. "Managing Inventory with Multiple Products, Lags in Delivery, Resource Constraints, and Lost Sales: A Mathematical Programming Approach," Management Science, INFORMS, vol. 47(3), pages 464-479, March.
    6. James P. Monahan, 1984. "A Quantity Discount Pricing Model to Increase Vendor Profits," Management Science, INFORMS, vol. 30(6), pages 720-726, June.
    7. Abad, P. L., 2003. "Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale," European Journal of Operational Research, Elsevier, vol. 144(3), pages 677-685, February.
    8. Hill, Roger M., 1999. "On the suboptimality of (S-1, S) lost sales inventory policies," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 387-393, March.
    9. P Melchiors & R Dekker & M J Kleijn, 2000. "Inventory rationing in an (s, Q) inventory model with lost sales and two demand classes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(1), pages 111-122, January.
    10. Yu, Yugang & Chu, Feng & Chen, Haoxun, 2009. "A Stackelberg game and its improvement in a VMI system with a manufacturing vendor," European Journal of Operational Research, Elsevier, vol. 192(3), pages 929-948, February.
    11. Chung, Kun-Jen, 2008. "Comments on the EOQ model under retailer partial trade credit policy in the supply chain," International Journal of Production Economics, Elsevier, vol. 114(1), pages 308-312, July.
    12. Maqbool Dada & K. N. Srikanth, 1987. "Pricing Policies for Quantity Discounts," Management Science, INFORMS, vol. 33(10), pages 1247-1252, October.
    13. Kamran Moinzadeh, 1989. "Operating Characteristics of the (S - 1, S) Inventory System with Partial Backorders and Constant Resupply Times," Management Science, INFORMS, vol. 35(4), pages 472-477, April.
    14. Cai, Gangshu (George) & Zhang, Zhe George & Zhang, Michael, 2009. "Game theoretical perspectives on dual-channel supply chain competition with price discounts and pricing schemes," International Journal of Production Economics, Elsevier, vol. 117(1), pages 80-96, January.
    15. L. San José & J. García-Laguna, 2003. "An EOQ model with backorders and all-units discounts," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 253-274, December.
    16. Rajeev Kohli & Heungsoo Park, 1989. "A Cooperative Game Theory Model of Quantity Discounts," Management Science, INFORMS, vol. 35(6), pages 693-707, June.
    17. Thomas E. Morton, 1971. "The Near-Myopic Nature of the Lagged-Proportional-Cost Inventory Problem with Lost Sales," Operations Research, INFORMS, vol. 19(7), pages 1708-1716, December.
    18. Steven Nahmias, 1979. "Simple Approximations for a Variety of Dynamic Leadtime Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 27(5), pages 904-924, October.
    19. Khouja, Moutaz & Park, Sungjune & Cai, Gangshu (George), 2010. "Channel selection and pricing in the presence of retail-captive consumers," International Journal of Production Economics, Elsevier, vol. 125(1), pages 84-95, May.
    20. Hau L. Lee & Meir J. Rosenblatt, 1986. "A Generalized Quantity Discount Pricing Model to Increase Supplier's Profits," Management Science, INFORMS, vol. 32(9), pages 1177-1185, September.
    21. Lodree, Emmett Jr., 2007. "Advanced supply chain planning with mixtures of backorders, lost sales, and lost contract," European Journal of Operational Research, Elsevier, vol. 181(1), pages 168-183, August.
    22. Jorgensen, Steffen, 1986. "Optimal production, purchasing and pricing: A differential game approach," European Journal of Operational Research, Elsevier, vol. 24(1), pages 64-76, January.
    23. Li, Susan X. & Huang, Zhimin & Zhu, Joe & Chau, Patrick Y. K., 2002. "Cooperative advertising, game theory and manufacturer-retailer supply chains," Omega, Elsevier, vol. 30(5), pages 347-357, October.
    24. Lau, Amy Hing Ling & Lau, Hon-Shiang, 2003. "Effects of a demand-curve's shape on the optimal solutions of a multi-echelon inventory/pricing model," European Journal of Operational Research, Elsevier, vol. 147(3), pages 530-548, June.
    25. Lau, Amy Hing Ling & Lau, Hon-Shiang, 2005. "Some two-echelon supply-chain games: Improving from deterministic-symmetric-information to stochastic-asymmetric-information models," European Journal of Operational Research, Elsevier, vol. 161(1), pages 203-223, February.
    26. Johansen, Soren Glud, 2001. "Pure and modified base-stock policies for the lost sales inventory system with negligible set-up costs and constant lead times," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 391-399, May.
    27. Mendoza, Abraham & Ventura, José A., 2008. "Incorporating quantity discounts to the EOQ model with transportation costs," International Journal of Production Economics, Elsevier, vol. 113(2), pages 754-765, June.
    28. Dye, Chung-Yuan, 2007. "Joint pricing and ordering policy for a deteriorating inventory with partial backlogging," Omega, Elsevier, vol. 35(2), pages 184-189, April.
    29. Lodree, Emmett Jr., 2007. "EOQ revisited: The case of unequal and integral order quantities," International Journal of Production Economics, Elsevier, vol. 105(2), pages 580-590, February.
    30. Chu, Peter & Yang, Kuo-Lung & Liang, Shing-Ko & Niu, Thomas, 2004. "Note on inventory model with a mixture of back orders and lost sales," European Journal of Operational Research, Elsevier, vol. 159(2), pages 470-475, December.
    31. repec:inm:ormnsc:v:30:y:1984:i:12:p:1524-1539(2 is not listed on IDEAS
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    5. Ding, Huiping & Zhao, Qilan & An, Zhirong & Xu, Jia & Liu, Qian, 2015. "Pricing strategy of environmental sustainable supply chain with internalizing externalities," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 563-575.

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