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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 6, Pages 1055–1066 (Mi zvmmf4705)  
This article is cited in 31 scientific papers (total in 31 papers)

New lower bounds for the facility location problem with clients' preferences

I. L. Vasilievab, K. B. Klimentovaab, Yu. A. Kochetovba

a Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, Russia
b Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
Full-text PDF (1387 kB) Citations (31)
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Abstract: A bilevel facility location problem in which the clients choose suppliers based on their own preferences is studied. It is shown that the coopertative and anticooperative statements can be reduced to a particular case in which every client has a linear preference order on the set of facilities to be opened. For this case, various reductions of the bilevel problem to integer linear programs are considered. A new statement of the problem is proposed that is based on a family of valid inequalities that are related to the problem on a pair of matrices and the set packing problem. It is shown that this formulation is stronger than the other known formulations from the viewpoint of the linear relaxation and the integrality gap.
Key words: bilevel facility location problems, bilevel programming, valid inequalities, lower bounds.
Received: 12.03.2008
Revised: 24.12.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 6, Pages 1010–1020
DOI: https://doi.org/10.1134/S0965542509060098
Bibliographic databases:
Document Type: Article
UDC: 519.6:519.866.6
Language: Russian
Citation: I. L. Vasiliev, K. B. Klimentova, Yu. A. Kochetov, “New lower bounds for the facility location problem with clients' preferences”, Zh. Vychisl. Mat. Mat. Fiz., 49:6 (2009), 1055–1066; Comput. Math. Math. Phys., 49:6 (2009), 1010–1020
Citation in format AMSBIB
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\paper New lower bounds for the facility location problem with clients' preferences
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    • This publication is cited in the following 31 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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