TY - JOUR

T1 - Additional Constraints for Dynamic Competitive Facility Location Problem

AU - Beresnev, V. L.

AU - Melnikov, A. A.

N1 - This work was financially supported by the Russian Science Foundation, project no. 23–21–00082, https://rscf.ru/en/project/23-21-00082/. Публикация для корректировки.

PY - 2023/9

Y1 - 2023/9

N2 - We consider a competitive facility location model where competing parties (Leader andFollower) make decisions considering changes of the set of customers happening during the planinghorizon consisting a known number of time periods. It is assumed that the Leader makes adecision on opening their facilities at the beginning of the planning horizon, while the Follower canrevise their decision in each time period. In the present paper, we study perspectives to apply amethod for finding the best solution that is based on using HP-relaxation of the bilevel problemconsidered. The key element of this method is construction of additional inequalitiesstrengthening the HP-relaxation and computation of upper bounds for the objective function ofthe problem. In the paper, we propose new families of additional constraints to strengthen theHP-relaxation that allow computing nontrivial upper bounds.

AB - We consider a competitive facility location model where competing parties (Leader andFollower) make decisions considering changes of the set of customers happening during the planinghorizon consisting a known number of time periods. It is assumed that the Leader makes adecision on opening their facilities at the beginning of the planning horizon, while the Follower canrevise their decision in each time period. In the present paper, we study perspectives to apply amethod for finding the best solution that is based on using HP-relaxation of the bilevel problemconsidered. The key element of this method is construction of additional inequalitiesstrengthening the HP-relaxation and computation of upper bounds for the objective function ofthe problem. In the paper, we propose new families of additional constraints to strengthen theHP-relaxation that allow computing nontrivial upper bounds.

KW - Stackelberg game

KW - bilevel programming

KW - competitive location

KW - valid inequalities

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85175826713&origin=inward&txGid=a701d490aba1a02576fc29020497e1ab

UR - https://www.mendeley.com/catalogue/77fb8b02-ea43-3b0f-8c4d-9b82e0c8e040/

U2 - 10.1134/S199047892303002X

DO - 10.1134/S199047892303002X

M3 - Article

VL - 17

SP - 483

EP - 490

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -