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Data-driven distributionally robust capacitated facility location problem

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  • Saif, Ahmed
  • Delage, Erick

Abstract

We study a distributionally robust version of the classical capacitated facility location problem with a distributional ambiguity set defined as a Wasserstein ball around an empirical distribution constructed based on a small data sample. Both single- and two-stage problems are addressed, with customer demands being the uncertain parameter. For the single-stage problem, we provide a direct reformulation into a mixed-integer program. For the two-stage problem, we develop two iterative algorithms, based on column generation, for solving the problem exactly. We also present conservative approximations based on support set relaxation for the single- and two-stage problems, an affine decision rule approximation of the two-stage problem, and a relaxation of the two-stage problem based on support set restriction. Numerical experiments on benchmark instances show that the exact solution algorithms are capable of solving large scale problems efficiently. The different approximation schemes are numerically compared and the performance guarantee of the two-stage problem’s solution on out-of-sample data is analyzed.

Suggested Citation

  • Saif, Ahmed & Delage, Erick, 2021. "Data-driven distributionally robust capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 291(3), pages 995-1007.
    • Handle: RePEc:eee:ejores:v:291:y:2021:i:3:p:995-1007
    DOI: 10.1016/j.ejor.2020.09.026
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    Citations

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    Cited by:

    1. Zhang, Guowei & Jia, Ning & Zhu, Ning & He, Long & Adulyasak, Yossiri, 2023. "Humanitarian transportation network design via two-stage distributionally robust optimization," Transportation Research Part B: Methodological, Elsevier, vol. 176(C).
    2. Raoul Fonkoua Fofou & Zhigang Jiang & Qingshan Gong & Yihua Yang, 2022. "A Decision-Making Model for Remanufacturing Facility Location in Underdeveloped Countries: A Capacitated Facility Location Problem Approach," Sustainability, MDPI, vol. 14(22), pages 1-18, November.
    3. Bellè, Andrea & Abdin, Adam F. & Fang, Yi-Ping & Zeng, Zhiguo & Barros, Anne, 2023. "A data-driven distributionally robust approach for the optimal coupling of interdependent critical infrastructures under random failures," European Journal of Operational Research, Elsevier, vol. 309(2), pages 872-889.
    4. Erick Delage & Ahmed Saif, 2022. "The Value of Randomized Solutions in Mixed-Integer Distributionally Robust Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 333-353, January.
    5. Qinxiao Yu & Chun Cheng & Ning Zhu, 2022. "Robust Team Orienteering Problem with Decreasing Profits," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3215-3233, November.
    6. Saldanha-da-Gama, Francisco, 2022. "Facility Location in Logistics and Transportation: An enduring relationship," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 166(C).
    7. Tianqi Liu & Francisco Saldanha-da-Gama & Shuming Wang & Yuchen Mao, 2022. "Robust Stochastic Facility Location: Sensitivity Analysis and Exact Solution," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2776-2803, September.
    8. Ariel Neufeld & Matthew Ng Cheng En & Ying Zhang, 2024. "Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems," Papers 2403.09532, arXiv.org.
    9. Aakil M. Caunhye & Douglas Alem, 2023. "Practicable robust stochastic optimization under divergence measures with an application to equitable humanitarian response planning," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 759-806, September.
    10. Lu, Xiaohan & Cheng, Chun, 2021. "Locating facilities with resiliency to capacity failures and correlated demand uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    11. Tsang, Man Yiu & Shehadeh, Karmel S., 2023. "Stochastic optimization models for a home service routing and appointment scheduling problem with random travel and service times," European Journal of Operational Research, Elsevier, vol. 307(1), pages 48-63.

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