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An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective

Author

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  • Ľuboš Buzna
  • Michal Koháni
  • Jaroslav Janáček

Abstract

We present a new approximation algorithm to the discrete facility location problem providing solutions that are close to the lexicographic minimax optimum. The lexicographic minimax optimum is a concept that allows to find equitable location of facilities serving a large number of customers. The algorithm is independent of general purpose solvers and instead uses algorithms originally designed to solve the -median problem. By numerical experiments, we demonstrate that our algorithm allows increasing the size of solvable problems and provides high-quality solutions. The algorithm found an optimal solution for all tested instances where we could compare the results with the exact algorithm.

Suggested Citation

  • Ľuboš Buzna & Michal Koháni & Jaroslav Janáček, 2014. "An Approximation Algorithm for the Facility Location Problem with Lexicographic Minimax Objective," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-12, June.
    • Handle: RePEc:hin:jnljam:562373
    DOI: 10.1155/2014/562373
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    Cited by:

    1. Alexander Lam & Haris Aziz & Bo Li & Fahimeh Ramezani & Toby Walsh, 2023. "Proportional Fairness in Obnoxious Facility Location," Papers 2301.04340, arXiv.org, revised Nov 2024.
    2. Péter Egri & Balázs Dávid & Tamás Kis & Miklós Krész, 2023. "Robust facility location in reverse logistics," Annals of Operations Research, Springer, vol. 324(1), pages 163-188, May.

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