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

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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.

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Correspondence to Nazlı Dolu.

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Dolu, N., Hastürk, U. & Tural, M.K. Solution methods for a min–max facility location problem with regional customers considering closest Euclidean distances. Comput Optim Appl 75, 537–560 (2020). https://doi.org/10.1007/s10589-019-00163-0

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  • Facility location
  • Min–max problem
  • Second order cone programming
  • Minkowski sum
  • Regional customer