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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.

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

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    1. 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.
    2. 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.
    3. Xin Chen & Jiawei Zhang, 2009. "A Stochastic Programming Duality Approach to Inventory Centralization Games," Operations Research, INFORMS, vol. 57(4), pages 840-851, August.
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