Production-inventory games: A new class of totally balanced combinatorial optimization games |
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| Authors: | Luis A. Guardiola Ana Meca Justo Puerto |
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| Affiliation: | 1. Operations Research Center, Universidad Miguel Hernández, Avda. de la Universidad s/n, Elche, 03202 Alicante, Spain;2. Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain;1. Department of Economics, University of Windsor, 401 Sunset Avenue, Windsor, Ontario, Canada;2. ECOSOT (Economics, Society and Territory) and Departamento de Estatistica e IO, Universidade de Vigo, 36200 Vigo (Pontevedra), Spain;1. Department of Mathematics Education, Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Chungbuk, 28644, Republic of Korea;2. Department of Mathematics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, 02841, Republic of Korea;1. Decision Sciences & Systems, TU München, Boltzmannstr. 3, 85748 Garching, Munich, Germany;2. ESEI Center for Market Design, University of Zürich, Blümlisalpstrasse 10, CH-8006 Zürich, Switzerland |
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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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