- PII
- 10.31857/S2686954323700327-1
- DOI
- 10.31857/S2686954323700327
- Publication type
- Status
- Published
- Authors
- Volume/ Edition
- Volume 514 / Issue number 1
- Pages
- 20-25
- Abstract
- 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.
- Keywords
- двухуровневое программирование игра Штакельберга конкурентное размещение предприятий пессимистическое оптимальное решение
- Date of publication
- 01.01.2023
- Year of publication
- 2023
- Number of purchasers
- 0
- Views
- 40
References
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- 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
- 4. Aras N., Küçükaydın H. Bilevel Models on the Competitive Facility Location Problem. In: Mallozzi L., D’Amato E., Pardalos P. (eds) Spatial Interaction Models. Springer Optimization and Its Applications, vol 118. Springer, Cham. 2017. P. 1–19. https://doi.org/10.1007/978-3-319-52654-6_1
- 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
