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

• Published in: Games and economic behavior Vol. 65; no. 1; pp. 205 - 219
• Main Authors: Guardiola, Luis A., Meca, Ana, Puerto, Justo
• Format: Journal Article
• Language: English
• Published: Duluth Elsevier Inc 2009; Elsevier; Academic Press
• Series: Games and Economic Behavior
• Subjects: Allocations; Allocative efficiency; Cooperation; Core-allocations; Cost analysis; Game theory; Inventories; Monotonicity rules; Optimization; Owen-allocations; Production; Production costs; Production planning; Production-inventory games; Production-inventory games Totally balanced combinatorial optimization games Core-allocations Owen-allocations Monotonicity rules; Storage; Studies; Totally balanced combinatorial optimization games; Core-allocations; Production-inventory games; C71; Totally balanced combinatorial optimization games; Owen-allocations; Monotonicity rules
• ISSN: 0899-8256; 1090-2473
• DOI: 10.1016/j.geb.2007.02.003

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.