A stochastic programming duality approach to inventory centralization games

A stochastic programming duality approach to inventory centralization games

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Article ID: iaor200970263
Country: United States
Volume: 57
Issue: 4
Start Page Number: 840
End Page Number: 851
Publication Date: Jul 2009
Journal: Operations Research
Authors: ,
Keywords: programming: probabilistic, game theory
Abstract:

In this paper, we present a unified approach to study a class of cooperative games arising from inventory centralization. The optimization problems corresponding to the inventory games are formulated as stochastic programs. We observe that the strong duality of stochastic linear programming not only directly leads to a series of recent results concerning the nonemptiness of the core of such games, but also suggests a way to find an element in the core. The proposed approach is also applied to inventory games with concave ordering cost. In particular, we show that the newsvendor game with concave ordering cost has a nonempty core. Finally, we prove that it is NP-hard to determine whether a given allocation is in the core of the inventory games even in a very simple setting.

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