A Study of the Threshold Stability of the Bilevel Problem of Facility Location and Discriminatory Pricing

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A Study of the Threshold Stability of the Bilevel Problem of Facility Location and Discriminatory Pricing. / Vodyan, M. E.; Panin, A. A.; Plyasunov, A. V.

In: Journal of Applied and Industrial Mathematics, Vol. 18, No. 3, 06.2024, p. 558-574.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{b571eb498ef24f16866aca9aa39f9138,

title = "A Study of the Threshold Stability of the Bilevel Problem of Facility Location and Discriminatory Pricing",

abstract = "The problem of threshold stability for a bilevel problem with a median type of facilitylocation and discriminatory pricing is considered. When solving such a problem, it is necessary tofind the threshold stability radius and a semifeasible solution of the original bilevel problem suchthat the leader{\textquoteright}s revenue is not less than a predetermined value (threshold) for any deviation ofbudgets that does not exceed the threshold stability radius and which preserves its semifeasibility.Thus, the threshold stability radius determines the limit of disturbances of consumer budgets withwhich these conditions are satisfied. Two approximate algorithms for solving the threshold stability problem based onthe heuristic of descent with alternating neighborhoods are developed. These algorithms are basedon finding a good approximate location of facilities as well as on calculating the optimal set ofprices for the found location of facilities. The algorithms differ in the way they compare variouslocations of facilities; this ultimately leads to different estimates of threshold stability radius. Anumerical experiment has shown the efficiency of the chosen approach both in terms of therunning time of the algorithms and the quality of the solutions obtained.",

keywords = "bilevel optimization, discriminatory pricing, facility location, threshold stability problem, threshold stability radius, variable neighborhood descent",

author = "Vodyan, {M. E.} and Panin, {A. A.} and Plyasunov, {A. V.}",

note = "This work was financially supported by the Russian Science Foundation, project no. 23-201321-201300424.",

year = "2024",

month = jun,

doi = "10.1134/S1990478924030165",

language = "English",

volume = "18",

pages = "558--574",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - A Study of the Threshold Stability of the Bilevel Problem of Facility Location and Discriminatory Pricing

AU - Vodyan, M. E.

AU - Panin, A. A.

AU - Plyasunov, A. V.

N1 - This work was financially supported by the Russian Science Foundation, project no. 23-201321-201300424.

PY - 2024/6

Y1 - 2024/6

N2 - The problem of threshold stability for a bilevel problem with a median type of facilitylocation and discriminatory pricing is considered. When solving such a problem, it is necessary tofind the threshold stability radius and a semifeasible solution of the original bilevel problem suchthat the leader’s revenue is not less than a predetermined value (threshold) for any deviation ofbudgets that does not exceed the threshold stability radius and which preserves its semifeasibility.Thus, the threshold stability radius determines the limit of disturbances of consumer budgets withwhich these conditions are satisfied. Two approximate algorithms for solving the threshold stability problem based onthe heuristic of descent with alternating neighborhoods are developed. These algorithms are basedon finding a good approximate location of facilities as well as on calculating the optimal set ofprices for the found location of facilities. The algorithms differ in the way they compare variouslocations of facilities; this ultimately leads to different estimates of threshold stability radius. Anumerical experiment has shown the efficiency of the chosen approach both in terms of therunning time of the algorithms and the quality of the solutions obtained.

AB - The problem of threshold stability for a bilevel problem with a median type of facilitylocation and discriminatory pricing is considered. When solving such a problem, it is necessary tofind the threshold stability radius and a semifeasible solution of the original bilevel problem suchthat the leader’s revenue is not less than a predetermined value (threshold) for any deviation ofbudgets that does not exceed the threshold stability radius and which preserves its semifeasibility.Thus, the threshold stability radius determines the limit of disturbances of consumer budgets withwhich these conditions are satisfied. Two approximate algorithms for solving the threshold stability problem based onthe heuristic of descent with alternating neighborhoods are developed. These algorithms are basedon finding a good approximate location of facilities as well as on calculating the optimal set ofprices for the found location of facilities. The algorithms differ in the way they compare variouslocations of facilities; this ultimately leads to different estimates of threshold stability radius. Anumerical experiment has shown the efficiency of the chosen approach both in terms of therunning time of the algorithms and the quality of the solutions obtained.

KW - bilevel optimization

KW - discriminatory pricing

KW - facility location

KW - threshold stability problem

KW - threshold stability radius

KW - variable neighborhood descent

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85211228158&origin=inward&txGid=702effb6d3360d3981f8c229081d2a1f

UR - https://www.mendeley.com/catalogue/2b937b34-b32e-358a-8d6b-ba21a3b13b71/

U2 - 10.1134/S1990478924030165

DO - 10.1134/S1990478924030165

M3 - Article

VL - 18

SP - 558

EP - 574

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 3

ER -

ID: 61285776