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The capacity constrained facility location problem

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  • Aziz, Haris
  • Chan, Hau
  • Lee, Barton E.
  • Parkes, David C.

Abstract

We initiate the study of the capacity constrained facility location problem from a mechanism design perspective. In the capacity constrained setting, the facility can serve only a subset of the population, assumed to be the k-closest with respect to agents' true locations (this can be justified as the essentially unique equilibrium outcome of a first-come-first game induced by the facility location). The main result is a complete characterization of dominant-strategy incentive compatible (DIC) mechanisms via the family of generalized median mechanisms (GMMs). Thus, the framework we introduce surprisingly provides a new characterization of GMMs, and is responsive to gaps in the current social choice literature highlighted by Border and Jordan (1983) and Barberà et al. (1998). We also provide algorithmic results and study the performance of DIC mechanisms in optimizing welfare. Adopting a worst-case approximation measure, we attain tight lower bounds on the approximation ratio of any DIC mechanism.

Suggested Citation

  • Aziz, Haris & Chan, Hau & Lee, Barton E. & Parkes, David C., 2020. "The capacity constrained facility location problem," Games and Economic Behavior, Elsevier, vol. 124(C), pages 478-490.
    • Handle: RePEc:eee:gamebe:v:124:y:2020:i:c:p:478-490
    DOI: 10.1016/j.geb.2020.09.001
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    Cited by:

    1. Qi Zhao & Wenjing Liu & Qingqin Nong & Qizhi Fang, 2023. "Constrained heterogeneous facility location games with max-variant cost," Journal of Combinatorial Optimization, Springer, vol. 45(3), pages 1-20, April.
    2. Yingyi Huang & Xinyu Wang & Hongyan Chen, 2022. "Location Selection for Regional Logistics Center Based on Particle Swarm Optimization," Sustainability, MDPI, vol. 14(24), pages 1-10, December.
    3. Haris Aziz & Alexander Lam & Barton E. Lee & Toby Walsh, 2021. "Strategyproof and Proportionally Fair Facility Location," Papers 2111.01566, arXiv.org, revised Nov 2023.
    4. Andrew Jennings & Rida Laraki & Clemens Puppe & Estelle Varloot, 2021. "New Characterizations of Strategy-Proofness under Single-Peakedness," Papers 2102.11686, arXiv.org, revised Jun 2022.

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