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New models for the location of controversial facilities: A bilevel programming approach

Martine Labbé 1, 2 Marina Leal 3 Justo Puerto 3 
1 INOCS - Integrated Optimization with Complex Structure
Inria Lille - Nord Europe, ULB - Université libre de Bruxelles, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : Motivated by recent real-life applications in Location Theory in which the location decisions generate controversy, we propose a novel bilevel location model in which, on the one hand, there is a leader that chooses among a number of fixed potential locations which ones to establish. Next, on the second hand, there is one or several followers that, once the leader location facilities have been set, chooses his location points in a continuous framework. The leader's goal is to maximize some proxy to the weighted distance to the follower's location points, while the follower(s) aim is to locate his location points as close as possible to the leader ones. We develop the bilevel location model for one follower and for any polyhedral distance, and we extend it for several followers and any p-norm, p ∈ Q, p ≥ 1. We prove the NP-hardness of the problem and propose different mixed integer linear programming formulations. Moreover, we develop alternative Benders decomposition algorithms for the problem. Finally, we report some computational results comparing the formulations and the Benders decompositions on a set of instances.
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Submitted on : Friday, November 23, 2018 - 6:27:26 PM
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Martine Labbé, Marina Leal, Justo Puerto. New models for the location of controversial facilities: A bilevel programming approach. Computers and Operations Research, 2019, 107, pp.95 -106. ⟨10.1016/j.cor.2019.03.003⟩. ⟨hal-01933601⟩



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