Production-Inventory games: a new class of totally balanced combinatorial optimization games
<|reference_start|>Production-Inventory games: a new class of totally balanced combinatorial optimization games: 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.<|reference_end|>
@article{guardiola2024production-inventory,
    title={Production-Inventory games: a new class of totally balanced
  combinatorial optimization games},
    author={Luis A. Guardiola, Ana Meca and Justo Puerto},
    journal={arXiv preprint arXiv:2402.04328},
    year={2024},
    doi={10.1016/j.geb.2007.02.003},
    archivePrefix={arXiv},
    eprint={2402.04328},
    primaryClass={cs.GT}
}