Book Sections Year : 2024

Models and Methods for Two-Level Uncapacitated Facility Location problems

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 paper.
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hal-04384267 , version 1 (10-01-2024)

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Bernard Gendron, Paul-Virak Khuong, Frédéric Semet. Models and Methods for Two-Level Uncapacitated Facility Location problems. Springer. Contributions to Combinatorial Optimization and Applications, 358, Springer Nature Switzerland, pp.59-75, 2024, International Series in Operations Research & Management Science, ⟨10.1007/978-3-031-57603-4_4⟩. ⟨hal-04384267⟩
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