Models and Methods for Two-Level Facility Location Problems

Bernard Gendron, Paul-Virak Khuong () and Frédéric Semet ()
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Bernard Gendron: Université de Montréal
Paul-Virak Khuong: Université de Montréal
Frédéric Semet: Univ. Lille, CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL

A chapter in Combinatorial Optimization and Applications, 2024, pp 59-75 from Springer

Abstract: Abstract We consider the two-level uncapacitated facility location problems with single-assignment constraints (TUFLP-S), a problem that arises in industrial applications in freight transportation and telecommunications. First, we recall the real-life application that motivates this research work. Then, we present an integer programming formulation for this variant with modular costs of the TUFLP-S, and we describe an adaptation of variable neighborhood search to the classical TUFLP-S and the variant with modular costs. Focusing on the TUFLP-S, we introduce mathematical programming models based on reformulation techniques and on the relaxation of the integrality of some of the variables associated with location decisions. We then present a Lagrangian relaxation approach for the TUFLP-S, based on solving a single-level uncapacitated facility location problem (UFLP) as the Lagrangian subproblem. We also describe a matheuristic based on a mixed-integer programming-based large neighborhood search. Synthetic computational results on instances derived from the industrial application as well as on large, hard, artificial instances are reported throughout the chapter.

Keywords: Location analysis; Two-level facility location problem; Mathematical modeling; Lagrangian relaxation; Large neighborhood search (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-57603-4_4

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