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Stability and monotonicity in newsvendor situations


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


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.

Suggested Citation

  • Özen, Ulaş & Erkip, Nesim & Slikker, Marco, 2012. "Stability and monotonicity in newsvendor situations," European Journal of Operational Research, Elsevier, vol. 218(2), pages 416-425.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:416-425
    DOI: 10.1016/j.ejor.2011.11.021

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    References listed on IDEAS

    1. Özen, Ulas & Norde, Henk & Slikker, Marco, 2011. "On the convexity of newsvendor games," International Journal of Production Economics, Elsevier, vol. 133(1), pages 35-42, September.
    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. David Housman & (*), Lori Clark, 1998. "Note Core and monotonic allocation methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(4), pages 611-616.
    4. 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.
    5. 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.
    6. Ichiishi, T, 1990. "Comparative Cooperative Game Theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(2), pages 139-152.
    7. 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.
    8. 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.
    9. Ulac{s} Özen & Jan Fransoo & Henk Norde & Marco Slikker, 2008. "Cooperation Between Multiple Newsvendors with Warehouses," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 311-324, February.
    10. Sasaki, Hiroo, 1995. "Consistency and Monotonicity in Assignment Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 373-397.
    11. 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.
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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.
    2. Uhan, Nelson A., 2015. "Stochastic linear programming games with concave preferences," European Journal of Operational Research, Elsevier, vol. 243(2), pages 637-646.


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