TY - JOUR

T1 - Upper Bound for the Competitive Facility Location Problem with Demand Uncertainty

AU - Береснев, Владимир Леонидович

AU - Мельников, Андрей Андреевич

N1 - This work was supported by the Russian Science Foundation, project no. 21-41-09017. Публикация для корректировки.

PY - 2023/12

Y1 - 2023/12

N2 - We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenarios. The problem of finding the best solutions for the parties is formulated as a discrete bilevel mathematical programming problem. A procedure for computing an upper bound for the objective function on solution subsets is suggested. The procedure could be employed in implicit enumeration schemes capable of computing an optimal solution for the problem under study. Within the procedure, additional constraints (cuts) iteratively augment the high-point relaxation of the initial bilevel problem, which strengthens the relaxation and improves the upper bound’s quality. A new procedure for generating such cuts is proposed, which allows us to construct the strongest cuts without enumerating the parameters encoding them.

AB - We consider a competitive facility location problem with two competing parties operating in a situation of uncertain demand scenarios. The problem of finding the best solutions for the parties is formulated as a discrete bilevel mathematical programming problem. A procedure for computing an upper bound for the objective function on solution subsets is suggested. The procedure could be employed in implicit enumeration schemes capable of computing an optimal solution for the problem under study. Within the procedure, additional constraints (cuts) iteratively augment the high-point relaxation of the initial bilevel problem, which strengthens the relaxation and improves the upper bound’s quality. A new procedure for generating such cuts is proposed, which allows us to construct the strongest cuts without enumerating the parameters encoding them.

KW - Stackelberg game

KW - bilevel programming

KW - competitive facility location

KW - pessimistic optimal solution

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187910747&origin=inward&txGid=3ab4c093e6e8a95a499ee09316668bee

UR - https://www.mendeley.com/catalogue/3050679f-70b7-3795-9231-4e315a9c840b/

U2 - 10.1134/S1064562423600318

DO - 10.1134/S1064562423600318

M3 - Article

VL - 108

SP - 438

EP - 442

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 3

ER -