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


DOLU HASTÜRK N., HASTÜRK U., TURAL M. K.

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, vol.75, no.2, pp.537-560, 2020 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 75 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1007/s10589-019-00163-0
  • Journal Name: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.537-560

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.