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Solution methods for a min–max facility location problem with regional customers considering closest Euclidean distances

Author

Listed:
  • Nazlı Dolu

    (Middle East Technical University)

  • Umur Hastürk

    (Middle East Technical University)

  • Mustafa Kemal Tural

    (Middle East Technical University)

Abstract

We study a facility location problem where a single facility serves multiple customers each represented by a (possibly non-convex) region in the plane. The aim of the problem is to locate a single facility in the plane so that the maximum of the closest Euclidean distances between the facility and the customer regions is minimized. Assuming that each customer region is mixed-integer second order cone representable, we firstly give a mixed-integer second order cone programming formulation of the problem. Secondly, we consider a solution method based on the Minkowski sums of sets. Both of these solution methods are extended to the constrained case in which the facility is to be located on a (possibly non-convex) subset of the plane. Finally, these two methods are compared in terms of solution quality and time with extensive computational experiments.

Suggested Citation

  • Nazlı Dolu & Umur Hastürk & Mustafa Kemal Tural, 2020. "Solution methods for a min–max facility location problem with regional customers considering closest Euclidean distances," Computational Optimization and Applications, Springer, vol. 75(2), pages 537-560, March.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:2:d:10.1007_s10589-019-00163-0
    DOI: 10.1007/s10589-019-00163-0
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    References listed on IDEAS

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