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Models and Methods for Two-Level Facility Location Problems

In: Combinatorial Optimization and Applications

Author

Listed:
  • Bernard Gendron

    (Université de Montréal)

  • Paul-Virak Khuong

    (Université de Montréal)

  • Frédéric Semet

    (Univ. Lille, CNRS, Inria, Centrale Lille, UMR 9189 CRIStAL)

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.

Suggested Citation

  • Bernard Gendron & Paul-Virak Khuong & Frédéric Semet, 2024. "Models and Methods for Two-Level Facility Location Problems," International Series in Operations Research & Management Science, in: Teodor Gabriel Crainic & Michel Gendreau & Antonio Frangioni (ed.), Combinatorial Optimization and Applications, pages 59-75, Springer.
    • Handle: RePEc:spr:isochp:978-3-031-57603-4_4
    DOI: 10.1007/978-3-031-57603-4_4
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