{"title":"Additional Constraints for Dynamic Competitive Facility Location Problem","authors":"V. L. Beresnev, A. A. Melnikov","doi":"10.1134/S199047892303002X","DOIUrl":null,"url":null,"abstract":"<p> We consider a competitive facility location model where competing parties (Leader and\nFollower) make decisions considering changes of the set of customers happening during the planing\nhorizon consisting a known number of time periods. It is assumed that the Leader makes a\ndecision on opening their facilities at the beginning of the planning horizon, while the Follower can\nrevise their decision in each time period. In the present paper, we study perspectives to apply a\nmethod for finding the best solution that is based on using HP-relaxation of the bilevel problem\nconsidered. The key element of this method is construction of additional inequalities\nstrengthening the HP-relaxation and computation of upper bounds for the objective function of\nthe problem. In the paper, we propose new families of additional constraints to strengthen the\nHP-relaxation that allow computing nontrivial upper bounds.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 3","pages":"483 - 490"},"PeriodicalIF":0.5800,"publicationDate":"2023-11-04","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/S199047892303002X","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
We consider a competitive facility location model where competing parties (Leader and
Follower) make decisions considering changes of the set of customers happening during the planing
horizon consisting a known number of time periods. It is assumed that the Leader makes a
decision on opening their facilities at the beginning of the planning horizon, while the Follower can
revise their decision in each time period. In the present paper, we study perspectives to apply a
method for finding the best solution that is based on using HP-relaxation of the bilevel problem
considered. The key element of this method is construction of additional inequalities
strengthening the HP-relaxation and computation of upper bounds for the objective function of
the problem. In the paper, we propose new families of additional constraints to strengthen the
HP-relaxation that allow computing nontrivial upper bounds.
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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