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Partial pooling by independent firms with allocation according to contribution to pool

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  • Silbermayr, Lena
  • Gerchak, Yigal

Abstract

We consider two firms which pool some of their inventory. The pool is created by the firms' contributions, and a firm's entitlement for an allocation from the pool (if needed) is a function of its contribution. Transshipment from the pool is costly, but the firms can benefit from reduced risk through inventory sharing using the pool. We analyze the resulting non-cooperative game. We prove existence of a Nash equilibrium and compare it to a model with centralized control. An appropriate compensation cost for using the other firms contribution to the pool can induce the retailers to achieve centralized solutions. We also compare the optimal partial pooling strategy to the special cases of no pooling and complete pooling and discuss situations where it is likely that one of the special cases will be optimal. Numerical results confirm that in the prevalent practice of partial pooling the retailers can achieve higher expected profits than under no pooling or complete pooling and that there is a significant difference between a setting with independent players and a model of central control.

Suggested Citation

  • Silbermayr, Lena & Gerchak, Yigal, 2019. "Partial pooling by independent firms with allocation according to contribution to pool," International Journal of Production Economics, Elsevier, vol. 218(C), pages 375-385.
    • Handle: RePEc:eee:proeco:v:218:y:2019:i:c:p:375-385
    DOI: 10.1016/j.ijpe.2019.06.018
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    References listed on IDEAS

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    1. Silbermayr, Lena & Jammernegg, Werner & Kischka, Peter, 2017. "Inventory pooling with environmental constraints using copulas," European Journal of Operational Research, Elsevier, vol. 263(2), pages 479-492.
    2. Slikker, Marco & Fransoo, Jan & Wouters, Marc, 2005. "Cooperation between multiple news-vendors with transshipments," European Journal of Operational Research, Elsevier, vol. 167(2), pages 370-380, December.
    3. Emel Arikan & Lena Silbermayr, 2018. "Risk pooling via unidirectional inventory transshipments in a decentralized supply chain," International Journal of Production Research, Taylor & Francis Journals, vol. 56(17), pages 5593-5610, September.
    4. Charles J. Corbett & Kumar Rajaram, 2006. "A Generalization of the Inventory Pooling Effect to Nonnormal Dependent Demand," Manufacturing & Service Operations Management, INFORMS, vol. 8(4), pages 351-358, August.
    5. Niv Ben-Zvi & Yigal Gerchak, 2012. "Inventory Centralization in a Newsvendor Setting When Shortage Costs Differ: Priorities and Costs Allocation," International Series in Operations Research & Management Science, in: Tsan-Ming Choi (ed.), Handbook of Newsvendor Problems, edition 127, chapter 0, pages 263-276, Springer.
    6. Jing Shao & Harish Krishnan & S. Thomas McCormick, 2011. "Incentives for Transshipment in a Supply Chain with Decentralized Retailers," Manufacturing & Service Operations Management, INFORMS, vol. 13(3), pages 361-372, July.
    7. Muller, Alfred & Scarsini, Marco & Shaked, Moshe, 2002. "The Newsvendor Game Has a Nonempty Core," Games and Economic Behavior, Elsevier, vol. 38(1), pages 118-126, January.
    8. Serguei Netessine & Nils Rudi, 2003. "Centralized and Competitive Inventory Models with Demand Substitution," Operations Research, INFORMS, vol. 51(2), pages 329-335, April.
    9. Fiestras-Janeiro, M.G. & García-Jurado, I. & Meca, A. & Mosquera, M.A., 2011. "Cooperative game theory and inventory management," European Journal of Operational Research, Elsevier, vol. 210(3), pages 459-466, May.
    10. Gary D. Eppen, 1979. "Note--Effects of Centralization on Expected Costs in a Multi-Location Newsboy Problem," Management Science, INFORMS, vol. 25(5), pages 498-501, May.
    11. Hadar Amrani & Eugene Khmelnitsky, 2017. "Optimal division of inventory between depot and bases," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 3-18, February.
    12. Lingxiu Dong & Nils Rudi, 2004. "Who Benefits from Transshipment? Exogenous vs. Endogenous Wholesale Prices," Management Science, INFORMS, vol. 50(5), pages 645-657, May.
    13. Yigal Gerchak, 2017. "On the viability of partial inventory pooling," International Journal of Inventory Research, Inderscience Enterprises Ltd, vol. 4(1), pages 44-60.
    14. Ravi Anupindi & Yehuda Bassok & Eitan Zemel, 2001. "A General Framework for the Study of Decentralized Distribution Systems," Manufacturing & Service Operations Management, INFORMS, vol. 3(4), pages 349-368, February.
    15. Nils Rudi & Sandeep Kapur & David F. Pyke, 2001. "A Two-Location Inventory Model with Transshipment and Local Decision Making," Management Science, INFORMS, vol. 47(12), pages 1668-1680, December.
    16. Kwan Eng Wee & Maqbool Dada, 2005. "Optimal Policies for Transshipping Inventory in a Retail Network," Management Science, INFORMS, vol. 51(10), pages 1519-1533, October.
    17. Xinxin Hu & Izak Duenyas & Roman Kapuscinski, 2007. "Existence of Coordinating Transshipment Prices in a Two-Location Inventory Model," Management Science, INFORMS, vol. 53(8), pages 1289-1302, August.
    18. Hartman, Bruce C. & Dror, Moshe & Shaked, Moshe, 2000. "Cores of Inventory Centralization Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 26-49, April.
    19. Gemma Berenguer & Pinar Keskinocak & J. George Shanthikumar & Jayashankar M. Swaminathan & Luk Van Wassenhove & Fuminori Toyasaki & Emel Arikan & Lena Silbermayr & Ioanna Falagara Sigala, 2017. "Disaster Relief Inventory Management: Horizontal Cooperation between Humanitarian Organizations," Production and Operations Management, Production and Operations Management Society, vol. 26(6), pages 1221-1237, June.
    20. Steven A. Lippman & Kevin F. McCardle, 1997. "The Competitive Newsboy," Operations Research, INFORMS, vol. 45(1), pages 54-65, February.
    21. Mahmut Parlar, 1988. "Game theoretic analysis of the substitutable product inventory problem with random demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 397-409, June.
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