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Lagrangian Bounds and a Heuristic for the Two-Stage Capacitated Facility Location Problem

Author

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  • Igor Litvinchev

    (Nuevo Leon State University, Mexico)

  • Edith L. Ozuna

    (Nuevo Leon State University, Mexico)

Abstract

In the two-stage capacitated facility location problem, a single product is produced at some plants in order to satisfy customer demands. The product is transported from these plants to some depots and then to the customers. The capacities of the plants and depots are limited. The aim is to select cost minimizing locations from a set of potential plants and depots. This cost includes fixed cost associated with opening plants and depots, and variable cost associated with both transportation stages. In this work, two different mixed integer linear programming formulations are considered for the problem. Several Lagrangian relaxations are analyzed and compared, and a Lagrangian heuristic producing feasible solutions is presented. The results of a computational study are reported.

Suggested Citation

  • Igor Litvinchev & Edith L. Ozuna, 2012. "Lagrangian Bounds and a Heuristic for the Two-Stage Capacitated Facility Location Problem," International Journal of Energy Optimization and Engineering (IJEOE), IGI Global, vol. 1(1), pages 59-71, January.
    • Handle: RePEc:igg:jeoe00:v:1:y:2012:i:1:p:59-71
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    Cited by:

    1. Romanova, Tatiana & Stoyan, Yurij & Pankratov, Alexander & Litvinchev, Igor & Plankovskyy, Sergiy & Tsegelnyk, Yevgen & Shypul, Olga, 2021. "Sparsest balanced packing of irregular 3D objects in a cylindrical container," European Journal of Operational Research, Elsevier, vol. 291(1), pages 84-100.
    2. Yang, Zhen & Chen, Haoxun & Chu, Feng & Wang, Nengmin, 2019. "An effective hybrid approach to the two-stage capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 467-480.
    3. Lu Yang & Leishan Zhou & Hanxiao Zhou & Chang Han & Wenqiang Zhao, 2023. "A Lagrangian Method for Calculation of Passing Capacity on a Railway Hub Station," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    4. Ortiz-Astorquiza, Camilo & Contreras, Ivan & Laporte, Gilbert, 2018. "Multi-level facility location problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 791-805.
    5. Liu, Zhimin & Wu, Zhong & Ji, Ying & Qu, Shaojian & Raza, Hassan, 2021. "Two-stage distributionally robust mixed-integer optimization model for three-level location–allocation problems under uncertain environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).

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