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Outer approximation and submodular cuts for maximum capture facility location problems with random utilities

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  • Ljubić, Ivana
  • Moreno, Eduardo

Abstract

We consider a family of competitive facility location problems in which a “newcomer” company enters the market and has to decide where to locate a set of new facilities so as to maximize its market share. The multinomial logit model is used to estimate the captured customer demand. We propose a first branch-and-cut approach for this family of difficult mixed-integer non-linear problems. Our approach combines two types of cutting planes that exploit particular properties of the objective function: the first one are the outer-approximation cuts and the second one are the submodular cuts.

Suggested Citation

  • Ljubić, Ivana & Moreno, Eduardo, 2018. "Outer approximation and submodular cuts for maximum capture facility location problems with random utilities," European Journal of Operational Research, Elsevier, vol. 266(1), pages 46-56.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:1:p:46-56
    DOI: 10.1016/j.ejor.2017.09.023
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    Cited by:

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    6. Georg Bechler & Claudius Steinhardt & Jochen Mackert, 2021. "On the Linear Integration of Attraction Choice Models in Business Optimization Problems," SN Operations Research Forum, Springer, vol. 2(1), pages 1-13, March.
    7. Yun Hui Lin & Qingyun Tian & Yanlu Zhao, 2022. "Locating facilities under competition and market expansion: Formulation, optimization, and implications," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3021-3042, July.
    8. Mai, Tien & Lodi, Andrea, 2020. "A multicut outer-approximation approach for competitive facility location under random utilities," European Journal of Operational Research, Elsevier, vol. 284(3), pages 874-881.
    9. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2022. "Submodularity and local search approaches for maximum capture problems under generalized extreme value models," European Journal of Operational Research, Elsevier, vol. 300(3), pages 953-965.
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    11. Dam, Tien Thanh & Ta, Thuy Anh & Mai, Tien, 2023. "Robust maximum capture facility location under random utility maximization models," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1128-1150.
    12. Basciftci, Beste & Ahmed, Shabbir & Shen, Siqian, 2021. "Distributionally robust facility location problem under decision-dependent stochastic demand," European Journal of Operational Research, Elsevier, vol. 292(2), pages 548-561.
    13. Steven Lamontagne & Margarida Carvalho & Emma Frejinger & Bernard Gendron & Miguel F. Anjos & Ribal Atallah, 2023. "Optimising Electric Vehicle Charging Station Placement Using Advanced Discrete Choice Models," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1195-1213, September.
    14. Méndez-Vogel, Gonzalo & Marianov, Vladimir & Lüer-Villagra, Armin & Eiselt, H.A., 2023. "Store location with multipurpose shopping trips and a new random utility customers’ choice model," European Journal of Operational Research, Elsevier, vol. 305(2), pages 708-721.
    15. Kyosang Hwang & Tooba Binte Asif & Taesik Lee, 2022. "Choice-driven location-allocation model for healthcare facility location problem," Flexible Services and Manufacturing Journal, Springer, vol. 34(4), pages 1040-1065, December.
    16. Lin, Yun Hui & Tian, Qingyun, 2021. "Branch-and-cut approach based on generalized benders decomposition for facility location with limited choice rule," European Journal of Operational Research, Elsevier, vol. 293(1), pages 109-119.
    17. Ngan Ha Duong & Tien Thanh Dam & Thuy Anh Ta & Tien Mai, 2022. "Joint Location and Cost Planning in Maximum Capture Facility Location under Multiplicative Random Utility Maximization," Papers 2205.07345, arXiv.org, revised Feb 2023.
    18. Lin, Yun Hui & Wang, Yuan & Lee, Loo Hay & Chew, Ek Peng, 2022. "Omnichannel facility location and fulfillment optimization," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 187-209.
    19. Lin, Yunhui & Wang, Yuan & Lee, Loo Hay & Chew, Ek Peng, 2022. "Profit-maximizing parcel locker location problem under threshold Luce model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    20. Ralf Krohn & Sven Müller & Knut Haase, 2021. "Preventive healthcare facility location planning with quality-conscious clients," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(1), pages 59-87, March.
    21. Ren, Xiyuan & Chow, Joseph Y.J., 2022. "A random-utility-consistent machine learning method to estimate agents’ joint activity scheduling choice from a ubiquitous data set," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 396-418.
    22. Méndez-Vogel, Gonzalo & Marianov, Vladimir & Lüer-Villagra, Armin, 2023. "The follower competitive facility location problem under the nested logit choice rule," European Journal of Operational Research, Elsevier, vol. 310(2), pages 834-846.
    23. Kübra Tanınmış & Markus Sinnl, 2022. "A Branch-and-Cut Algorithm for Submodular Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2634-2657, September.
    24. Teodora Dan & Andrea Lodi & Patrice Marcotte, 2020. "Joint location and pricing within a user-optimized environment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(1), pages 61-84, March.
    25. Liu, Kanglin & Zhang, Hengliang & Zhang, Zhi-Hai, 2021. "The efficiency, equity and effectiveness of location strategies in humanitarian logistics: A robust chance-constrained approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 156(C).

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