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arXiv · 2402.04328

Production-Inventory games: a new class of totally balanced combinatorial optimization games

Luis A. Guardiola·Ana Meca·Justo Puerto
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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.

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Luis A. Guardiola, Ana Meca, Justo Puerto. 2024-02-06. Production-Inventory games: a new class of totally balanced combinatorial optimization games. https://doi.org/10.1016/j.geb.2007.02.003

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