Additional constraints for computing upper bounds for (r|p) -centroid problem's objective function Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
||
|---|---|---|---|
| Output data | Year: 2025, Volume: 22, Number: 2, Pages: 1371-1381 Pages count : 11 DOI: 10.33048/semi.2025.22.082 | ||
| Tags | Competitive facility location, optimal solution, bilevel programming, high-point relaxation, cut generation. | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0019 |
Abstract:
We consider an (r|p)
-centroid problem formulated as a bilevel mathematical programming problem. In the problem, two competing parties open, respectively, r
and p
facilities aiming to attract customers' demand and maximize the market share. An approach for computing upper bounds for the first player's (Leader) objective function, is proposed based on generating additional constraints (cuts) for the high-point relaxation of the bi-level problem. New types of additional constraints are introduced, which take into account the specific of the (r|p)
-centroid problem.
A procedure of generating these constraints is discussed, which allows to improve sequentially the upper bound's quality.
Cite:
Beresnev V.L.
, Melnikov A.A.
Additional constraints for computing upper bounds for (r|p) -centroid problem's objective function
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.1371-1381. DOI: 10.33048/semi.2025.22.082
Additional constraints for computing upper bounds for (r|p) -centroid problem's objective function
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.1371-1381. DOI: 10.33048/semi.2025.22.082
Dates:
| Submitted: | Apr 17, 2025 |
| Published print: | Nov 25, 2025 |
| Published online: | Dec 25, 2025 |
Identifiers:
No identifiers
Citing:
Пока нет цитирований