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Production-inventory games: A new class of totally balanced combinatorial optimization games

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  • Guardiola, Luis A.
  • Meca, Ana
  • Puerto, Justo

Abstract

In this paper we introduce a new class of cooperative games that arise from production-inventory problems. Several agents have to cover their demand over a finite time horizon and shortages are allowed. Each agent has its own unit production, inventory-holding and backlogging cost. Cooperation among agents is given by sharing production processes and warehouse facilities: agents in a coalition produce with the cheapest production cost and store with the cheapest inventory cost. We prove that the resulting cooperative game is totally balanced and the Owen set reduces to a singleton: the Owen point. Based on this type of allocation we find a population monotonic allocation scheme for this class of games. Finally, we point out the relationship of the Owen point with other well-known allocation rules such as the nucleolus and the Shapley value.

Suggested Citation

  • Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2009. "Production-inventory games: A new class of totally balanced combinatorial optimization games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 205-219, January.
    • Handle: RePEc:eee:gamebe:v:65:y:2009:i:1:p:205-219
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