UPPER BOUND FOR THE COMPETITIVE FACILITY LOCATION PROBLEM WITH DEMAND UNCERTAINTY

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详细

We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenario. The problem to find the best solutions for the parties is formulated as a discrete bi-level mathematical programming problem. In the paper, we suggest a procedure to compute an upper bound for the objective function on subsets. The procedure could be employed in implicit enumeration schemes capable to compute an optimal solution for the problem under study. Within the procedure, additional constraints iteratively augment the high-point relaxation of the initial bi-level problem, what strengthens the relaxation and improves the upper bound’s quality. New procedure to generate such cuts allows to construct the strongest cuts without enumerating the parameters encoding them.

作者简介

V. Beresnev

Sobolev Institute of Mathematics; Novosibirsk State University

编辑信件的主要联系方式.
Email: beresnev@math.nsc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk

A. Melnikov

Sobolev Institute of Mathematics; Novosibirsk State University

编辑信件的主要联系方式.
Email: melnikov@math.nsc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk

参考

  1. Береснев В.Л., Мельников А.А. Алгоритм генерации отсечений для дискретной задачи конкурентного размещения предприятий. Доклады Академии наук. 2018. V. 480. № 5. P. 515–518. https://doi.org/10.1134/S1064562418030183
  2. Beresnev V., Melnikov A. Approximation of the competitive facility location problem with MIPs. Computers & Operations Research. 2019. V. 104. P. 139–148, https://doi.org/10.1016/j.cor.2018.12.010
  3. Ashtiani M. Competitive location: A state-of-art review. International Journal of Industrial Engineering Computations. 2016. V. 7. № 1. P. 1–18.https://doi.org/10.5267/j.ijiec.2015.8.002
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  5. Karakitsiou A. Modeling discrete competitive facility location. Springer Cham, 2015, SpringerBriefs in Optimization, 54.
  6. Mishra M., Singh S.P., Gupta M.P. Location of competitive facilities: a comprehensive review and future research agenda. Benchmarking, 2022.https://doi.org/10.1108/BIJ-11-2021-0638
  7. Dempe S. Bilevel Optimization: Theory, Algorithms, Applications and a Bibliography, In: S. Dempe, A. Zemkoho (eds) Bilevel Optimization: Advances and Next Challenges, Springer International Publishing, Cham. 2020. P. 581–672. https://doi.org/10.1007/978-3-030-52119-6_20

版权所有 © В.Л. Береснев, А.А. Мельников, 2023

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