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Stability and monotonicity in newsvendor situations

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  • Özen, Ulaş
  • Erkip, Nesim
  • Slikker, Marco

Abstract

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers’ dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.

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Bibliographic Info

Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 218 (2012)
Issue (Month): 2 ()
Pages: 416-425

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Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:416-425

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: Supply chain management; Game theory; Newsvendor; Balancedness; Core-monotonicity;

References

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  1. 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.
  2. Ozen, U. & Norde, H.W. & Slikker, M., 2005. "On the Convexity of News Vendor Games," Discussion Paper 2005-103, Tilburg University, Center for Economic Research.
  3. David Housman & (*), Lori Clark, 1998. "Note Core and monotonic allocation methods," International Journal of Game Theory, Springer, vol. 27(4), pages 611-616.
  4. Ichiishi, T, 1990. "Comparative Cooperative Game Theory," International Journal of Game Theory, Springer, vol. 19(2), pages 139-52.
  5. Ozen, U. & Fransoo, J. & Norde, H.W. & Slikker, M., 2004. "Cooperation between Multiple Newsvendors with Warehouses," Discussion Paper 2004-34, Tilburg University, Center for Economic Research.
  6. 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.
  7. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  8. 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.
  9. 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.
  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. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer, vol. 24(4), pages 373-97.
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Cited by:
  1. Li, Jun & Feng, Hairong & Zeng, Yinlian, 2014. "Inventory games with permissible delay in payments," European Journal of Operational Research, Elsevier, vol. 234(3), pages 694-700.

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