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A NonCooperative Approach to Cost Allocation in Joint Replenishment

Author

Listed:
  • Simai He

    (School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, China 200433)

  • Jay Sethuraman

    (Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Xuan Wang

    (Department of Information Systems, Business Statistics and Operations Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Jiawei Zhang

    (Leonard N. Stern School of Business, New York University, New York, New York 10012; and New York University Shanghai, Shanghai, China 200122)

Abstract

We consider the infinite-horizon multiple retailer joint replenishment problem with first-order interaction. In this model, the joint setup cost incurred by a group of retailers placing an order simultaneously consists of a group-independent major setup cost and retailer-specific minor setup costs. The goal is to determine an inventory replenishment policy that minimizes the long-run average system-wide cost. In this paper, we adopt a noncooperative approach to study the joint replenishment game. We consider the allocation rule in which the major setup cost is split equally among the retailers who place an order together, and each retailer pays his own holding and minor setup costs. Given the preannounced allocation rule, each retailer determines his replenishment policy to minimize his own cost anticipating the other retailers’ strategy. We show that a payoff dominant Nash equilibrium exists, and quantify the efficiency loss of the noncooperative outcome relative to the social optimum. Although the worst-case ratio between the best decentralized outcome and the social optimum is O ((ln n ) 1/2 ), where n is the number of retailers, numerical results suggest that the best equilibrium is near optimal.

Suggested Citation

  • Simai He & Jay Sethuraman & Xuan Wang & Jiawei Zhang, 2017. "A NonCooperative Approach to Cost Allocation in Joint Replenishment," Operations Research, INFORMS, vol. 65(6), pages 1562-1573, December.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:6:p:1562-1573
    DOI: 10.1287/opre.2017.1645
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    References listed on IDEAS

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    1. Moshe Dror & Bruce C. Hartman, 2007. "Shipment Consolidation: Who Pays for It and How Much?," Management Science, INFORMS, vol. 53(1), pages 78-87, January.
    2. Zied Jemai & Adel Elomri & Asma Ghaffari & Yves Dallery, 2012. "Coalition Formation and Cost Allocation for Joint Replenishment Systems," Post-Print hal-01672397, HAL.
    3. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, April.
    4. Ana Meca & Ignacio García-Jurado & Peter Borm, 2003. "Cooperation and competition in inventory games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 481-493, August.
    5. Andrew Colman & Michael Bacharach, 1997. "Payoff Dominance And The Stackelberg Heuristic," Theory and Decision, Springer, vol. 43(1), pages 1-19, July.
    6. Awi Federgruen & Yu-Sheng Zheng, 1992. "The Joint Replenishment Problem with General Joint Cost Structures," Operations Research, INFORMS, vol. 40(2), pages 384-403, April.
    7. Jiawei Zhang, 2009. "Cost Allocation for Joint Replenishment Models," Operations Research, INFORMS, vol. 57(1), pages 146-156, February.
    8. Awi Federgruen & Yu-Sheng Zheng, 1995. "Efficient Algorithms for Finding Optimal Power-of-Two Policies for Production/Distribution Systems with General Joint Setup Costs," Operations Research, INFORMS, vol. 43(3), pages 458-470, June.
    9. Simai He & Jiawei Zhang & Shuzhong Zhang, 2012. "Polymatroid Optimization, Submodularity, and Joint Replenishment Games," Operations Research, INFORMS, vol. 60(1), pages 128-137, February.
    10. Daniel Adelman & Diego Klabjan, 2005. "Duality and Existence of Optimal Policies in Generalized Joint Replenishment," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 28-50, February.
    11. Nagarajan, Mahesh & Sosic, Greys, 2008. "Game-theoretic analysis of cooperation among supply chain agents: Review and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 719-745, June.
    12. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    13. Georgia Perakis & Guillaume Roels, 2007. "The Price of Anarchy in Supply Chains: Quantifying the Efficiency of Price-Only Contracts," Management Science, INFORMS, vol. 53(8), pages 1249-1268, August.
    14. John C. Harsanyi, 1967. "Games with Incomplete Information Played by "Bayesian" Players, I-III Part I. The Basic Model," Management Science, INFORMS, vol. 14(3), pages 159-182, November.
    15. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    16. Körpeoğlu, Evren & Şen, Alper & Güler, Kemal, 2013. "Non-cooperative joint replenishment under asymmetric information," European Journal of Operational Research, Elsevier, vol. 227(3), pages 434-443.
    17. Dror, Moshe & Hartman, Bruce C. & Chang, Wei, 2012. "The cost allocation issue in joint replenishment," International Journal of Production Economics, Elsevier, vol. 135(1), pages 242-254.
    18. Robin Roundy, 1985. "98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems," Management Science, INFORMS, vol. 31(11), pages 1416-1430, November.
    19. Michal Feldman & Tami Tamir, 2012. "Conflicting Congestion Effects in Resource Allocation Games," Operations Research, INFORMS, vol. 60(3), pages 529-540, June.
    20. Ramesh Johari & John N. Tsitsiklis, 2004. "Efficiency Loss in a Network Resource Allocation Game," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 407-435, August.
    21. Victor Martínez-de-Albéniz & David Simchi-Levi, 2009. "Competition in the Supply Option Market," Operations Research, INFORMS, vol. 57(5), pages 1082-1097, October.
    22. Fernando Bernstein & Awi Federgruen, 2003. "Pricing and Replenishment Strategies in a Distribution System with Competing Retailers," Operations Research, INFORMS, vol. 51(3), pages 409-426, June.
    23. Shoshana Anily & Moshe Haviv, 2007. "The Cost Allocation Problem for the First Order Interaction Joint Replenishment Model," Operations Research, INFORMS, vol. 55(2), pages 292-302, April.
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