A Kernel Search Matheuristic to Solve The Discrete Leader-Follower Location Problem

Abstract

In the leader-follower, (r|p)-centroid or Stackelberg location problem, two players sequentially enter the market and compete to provide goods or services. This paper considers this competitive facility location problem in a discrete space. To solve it, the linear programming formulations for the leader and the follower are integrated into an algorithm which, in an iterative process, finds a solution by solving a sequence of these linear problems. We propose a matheuristic procedure that provides solutions for the leader via a kernel search algorithm. Taking into account binary and S-shaped customer choice rules, we present the computational results obtained and compare the exact algorithm with two versions of the kernel search procedure.

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Acknowledgements

This study was partially funded by Ministerio de Economía y Competitividad (Spanish Government) with FEDER funds, through grants ECO2014-59067-P and TIN2015-70226-R, and also by Fundación Cajacanarias (grant 2016TUR19).

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Correspondence to Dolores R. Santos-Peñate.

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Santos-Peñate, D.R., Campos-Rodríguez, C.M. & Moreno-Pérez, J.A. A Kernel Search Matheuristic to Solve The Discrete Leader-Follower Location Problem. Netw Spat Econ 20, 73–98 (2020). https://doi.org/10.1007/s11067-019-09472-7

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Keywords

  • Competitive location
  • Leader-follower problem
  • (r|p)-centroid
  • (r|Xp)-medianoid
  • Linear programming
  • Kernel search