Geodesic
Upper bound procedure for dynamic competitive facility location problem with profit targeting
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 960-971 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a dynamic competitive facility location problem, where two competing parties (Leader and Follower) aim to capture customers in each time period of the planning horizon and get a profit from serving them. The Leader's objective function represents their regret composed of the cost of open facilities and a total shortage of income computed with respect to some predefined target income values set for each of the time periods. The Follower's goal is to maximize their profit on the whole planning horizon. In the model, the Leader makes their location decision once at the beginning of the planning horizon, while the Follower can open additional facilities at any time period. In the present work, a procedure computing upper bounds for the Leader's objective function is proposed. It is based on using a high-point relaxation of the initial bi-level mathematical program and strengthening it with additional constraints (cuts). New procedures of generating additional cuts in a form of c-cuts and d-cuts, which are stronger than the ones proposed in earlier works, are presented.
Keywords: Competitive facility location, dynamic decision-making model, bi-level programming. 
@article{SEMR_2024_21_2_a27,
     author = {V. L. Beresnev and A. A. Melnikov},
     title = {Upper bound procedure for dynamic competitive facility location problem with profit targeting},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {960--971},
     year = {2024},
     volume = {21},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a27/}
}
TY  - JOUR
AU  - V. L. Beresnev
AU  - A. A. Melnikov
TI  - Upper bound procedure for dynamic competitive facility location problem with profit targeting
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 960
EP  - 971
VL  - 21
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a27/
LA  - en
ID  - SEMR_2024_21_2_a27
ER  - 
%0 Journal Article
%A V. L. Beresnev
%A A. A. Melnikov
%T Upper bound procedure for dynamic competitive facility location problem with profit targeting
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 960-971
%V 21
%N 2
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a27/
%G en
%F SEMR_2024_21_2_a27
V. L. Beresnev; A. A. Melnikov. Upper bound procedure for dynamic competitive facility location problem with profit targeting. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 960-971. http://geodesic.mathdoc.fr/item/SEMR_2024_21_2_a27/

[1] V.L. Beresnev, A.A. Melnikov, “Additional constraints for dynamic competitive facility location problem”, J. Appl. Ind. Math., 17 (2023), 483–490 | DOI | MR

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

[3] M. Hemmati, J.C. Smith, “A mixed-integer bilevel programming approach for a competitive prioritized set covering problem”, Discrete Optim., 20 (2016), 105–134 | DOI | MR | Zbl

[4] M. Fischetti, I. Ljubić, M. Monaci, M. Sinnl, “A new general-purpose algorithm for mixed-integer bilevel linear programs”, Oper. Res., 65:6 (2017), 1615–1637 | DOI | MR | Zbl

[5] A. Rahmani, Y. Majid, “An effective branch-and-cut algorithm in order to solve the mixed integer bi-level programming”, Inter. J. Prod. Man. Eng., 5:1 (2017), 1–10 https://www.researchgate.net/publication/313258854_An_Effective_Branch-and-cut_algorithm_in_Order_to_Solve_the_Mixed_Integer_Bi-level_Programming | DOI

[6] S. Dempe, “Bilevel optimization: theory, algorithms, applications and a bibliography”, Bilevel optimization. Advances and next challenges, Springer Optim. Appl., 161, eds. Dempe S. et al., Springer, Cham, 2020 | DOI | MR | Zbl