{"type":"ScholarlyArticle","title":"Facility Location Problems with Capacity Constraints: Two Facilities and Beyond","authors":[{"name":"Gennaro Auricchio","slug":"gennaro-auricchio","given":"Gennaro","family":"Auricchio","affiliation":"University of Bath , Department of Computer Science"},{"name":"Zihe Wang","slug":"zihe-wang","given":"Zihe","family":"Wang","affiliation":"Renmin University of China"},{"name":"Jie Zhang","slug":"jie-zhang","given":"Jie","family":"Zhang","affiliation":"University of Bath , Department of Computer Science"}],"abstract":"In this paper, we investigate the Mechanism Design aspects of the m-Capacitated Facility Location Problem (m-CFLP) on a line. We focus on two frameworks. In the first framework, the number of facilities is arbitrary, all facilities have the same capacity, and the number of agents is equal to the total capacity of all facilities. In the second framework, we aim to place two facilities, each with a capacity of at least half of the total agents. For both of these frameworks, we propose truthful mechanisms with bounded approximation ratios with respect to the Social Cost (SC) and the Maximum Cost (MC). When m>2, the result sharply contrasts with the impossibility results known for the classic m-Facility Location Problem, where capacity constraints are not considered. Furthermore, all our mechanisms are optimal with respect to the MC and optimal or nearly optimal with respect to the SC among anonymous mechanisms. For both frameworks, we provide a lower bound on the approximation ratio that any truthful and deterministic mechanism can achieve with respect to the SC and MC.","doi":"10.24963/ijcai.2024/293","url":"https://ijcai.org/proceedings/2024/293","pdf":"https://ijcai.org/proceedings/2024/0293.pdf","markdown":"https://ijcai.org/proceedings/2024/293.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/293","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":293,"pages":{"first":2651,"last":2659},"keywords":["Game Theory and Economic Paradigms: GTEP: Mechanism design","Agent-based and Multi-agent Systems: MAS: Resource allocation","Agent-based and Multi-agent Systems: MAS: Agent theories and models","Agent-based and Multi-agent Systems: MAS: Coordination and cooperation"],"videos":[],"references":[{"position":1,"raw":"[Aardal et al., 2015] Karen Aardal, Pieter L van den Berg, Dion Gijswijt, and Shanfei Li. 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