{"title":"A Study of the Threshold Stability of the Bilevel Problem\nof Facility Location and Discriminatory Pricing","authors":"M. E. Vodyan, A. A. Panin, A. V. Plyasunov","doi":"10.1134/S1990478924030165","DOIUrl":null,"url":null,"abstract":"<p> The problem of threshold stability for a bilevel problem with a median type of facility\nlocation and discriminatory pricing is considered. When solving such a problem, it is necessary to\nfind the threshold stability radius and a semifeasible solution of the original bilevel problem such\nthat the leader’s revenue is not less than a predetermined value (threshold) for any deviation of\nbudgets that does not exceed the threshold stability radius and which preserves its semifeasibility.\nThus, the threshold stability radius determines the limit of disturbances of consumer budgets with\nwhich these conditions are satisfied.\n</p><p>Two approximate algorithms for solving the threshold stability problem based on\nthe heuristic of descent with alternating neighborhoods are developed. These algorithms are based\non finding a good approximate location of facilities as well as on calculating the optimal set of\nprices for the found location of facilities. The algorithms differ in the way they compare various\nlocations of facilities; this ultimately leads to different estimates of threshold stability radius. A\nnumerical experiment has shown the efficiency of the chosen approach both in terms of the\nrunning time of the algorithms and the quality of the solutions obtained.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"558 - 574"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030165","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
The problem of threshold stability for a bilevel problem with a median type of facility
location and discriminatory pricing is considered. When solving such a problem, it is necessary to
find the threshold stability radius and a semifeasible solution of the original bilevel problem such
that the leader’s revenue is not less than a predetermined value (threshold) for any deviation of
budgets 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 with
which these conditions are satisfied.
Two approximate algorithms for solving the threshold stability problem based on
the heuristic of descent with alternating neighborhoods are developed. These algorithms are based
on finding a good approximate location of facilities as well as on calculating the optimal set of
prices for the found location of facilities. The algorithms differ in the way they compare various
locations of facilities; this ultimately leads to different estimates of threshold stability radius. A
numerical experiment has shown the efficiency of the chosen approach both in terms of the
running time of the algorithms and the quality of the solutions obtained.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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