Additional constraints for dynamic competitive facility location problem
Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 43-56.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a competitive facility location model, where competing parties (Leader and Follower) make decisions considering changes of the set of customers happening during the planing horizon, having known number of time periods. It is supposed that the Leader makes a decision on opening their facilities at the beginning of the planning horizon, while the Follower can revise their decision in each time period. In the present paper, we study perspectives to apply a method for finding the best solution which is based on using HP-relaxation of the bi-level problem considered. The key element of this method is construction of additional inequalities strengthening the HP-relaxation and computation of upper bounds for the objective function of the problem. In the work, new families of additional constraints are proposed to strengthen the HP-relaxation, that allow us to compute non-trivial upper bounds. Bibliogr. 13.
Keywords: Stackelberg game, bi-level programming, competitive location, valid inequalities.
@article{DA_2023_30_3_a1,
     author = {V. L. Beresnev and A. A. Melnikov},
     title = {Additional constraints for dynamic competitive facility location problem},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {43--56},
     publisher = {mathdoc},
     volume = {30},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2023_30_3_a1/}
}
TY  - JOUR
AU  - V. L. Beresnev
AU  - A. A. Melnikov
TI  - Additional constraints for dynamic competitive facility location problem
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2023
SP  - 43
EP  - 56
VL  - 30
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2023_30_3_a1/
LA  - ru
ID  - DA_2023_30_3_a1
ER  - 
%0 Journal Article
%A V. L. Beresnev
%A A. A. Melnikov
%T Additional constraints for dynamic competitive facility location problem
%J Diskretnyj analiz i issledovanie operacij
%D 2023
%P 43-56
%V 30
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2023_30_3_a1/
%G ru
%F DA_2023_30_3_a1
V. L. Beresnev; A. A. Melnikov. Additional constraints for dynamic competitive facility location problem. Diskretnyj analiz i issledovanie operacij, Tome 30 (2023) no. 3, pp. 43-56. http://geodesic.mathdoc.fr/item/DA_2023_30_3_a1/

[1] Aras N., Kü{ç}ükayd{\i}n H., “Bilevel models on the competitive facility location problem”, Spatial interaction models: Facility location using game theory, Springer, Cham, 2017, 1–19 | Zbl

[2] Ashtiani M. G., Makui A., Ramezanian R., “A robust model for a leader-follower competitive facility location problem in a discrete space”, Appl. Math. Model., 37:1–2 (2013), 62–71 | DOI | MR | Zbl

[3] Drezner T., “A review of competitive facility location in the plane”, Logist. Res., 7:1 (2014), 114, 12 pp. | DOI | MR

[4] Karakitsiou A., Modeling discrete competitive facility location, Springer, Cham, 2015, 54 pp. | MR

[5] Kress D., Pesch E., “Sequential competitive location on networks”, Eur. J. Oper. Res., 217:3 (2012), 483–499 | DOI | MR | Zbl

[6] Mishra M., Singh S. P., Gupta M. P., “Location of competitive facilities: A comprehensive review and future research agenda”, Benchmarking, 30:4 (2022), 1171–1230 | DOI

[7] Current J., Ratick S., ReVelle C., “Dynamic facility location when the total number of facilities is uncertain: A decision analysis approach”, Eur. J. Oper. Res., 110:3 (1998), 597–609 | DOI

[8] Eiselt H. A., Marianov V., Drezner T., “Competitive location models”, Location science, Springer, Cham, 2019, 391–429 | DOI | MR

[9] Castro J., Nasini S., Saldanha-da-Gama F., “A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method”, Math. Program., 163:1 (2017), 411–444 | DOI | MR | Zbl

[10] V. L. Beresnev, “On the competitive facility location problem with a free choice of suppliers”, Autom. Remote Control, 75:4 (1997), 668–676 | DOI | MR | Zbl

[11] Beresnev V. L., Melnikov A. A., “Approximation of the competitive facility location problem with MIPs”, Comput. Oper. Res., 104 (2019), 139–148 | DOI | MR | Zbl

[12] Santos-Peñate D. R., Suárez-Vega R., Dorta-González P., “The leader-follower location model”, Netw. Spat. Econ., 7:1 (2007), 45–61 | DOI | MR | Zbl

[13] Dempe S., “Bilevel optimization: Theory, algorithms, applications and a bibliography”, Bilevel optimization: Advances and next challenges, Springer, Cham, 2020, 581–672 | DOI | MR | Zbl