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A Stochastic Programming Duality Approach to Inventory Centralization Games

Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801
Stern School of Business, IOMS–Operations Management, New York University, New York, New York 10012
xinchen{at}uiuc.edu
jzhang{at}stern.nyu.edu

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.

Subject classifications: stochastic programming; inventory centralization; cooperative games.
History: Received February 2006; revision received December 2008; accepted December 2008.