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Diskretn. Anal. Issled. Oper., 2016, Volume 23, Number 1, Pages 35–50 (Mi da837)  

This article is cited in 2 scientific papers (total in 2 papers)

A capacitated competitive facility location problem

V. L. Beresnevab, A. A. Melnikovab

a Sobolev Institute of Mathematics, 4 Koptyug Ave., 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov St., 630090 Novosibirsk, Russia

Abstract: We consider a mathematical model relative to competitive location problems. In such problems, there are two competing sides which subsequently open their facilities aiming to “capture” clients and maximize profit. In our model, we assume that capacitiy of facilities are bounded. The model is formulated as a bi-level integer mathematical program and we study the problem of obtaining its optimal (cooperative) solution. It is shown that the problem can be reformulated as a problem of maximization of a pseudo-Boolean function with the number of arguments equal to the number of places available for facility opening. We propose an algorithm for calculation of an upper bound for values that the function takes on subsets which are specified by partial $(0,1)$-vectors. Bibl. 15.

Keywords: bi-level programming, upper bound, competitive facility location.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-01446


DOI: https://doi.org/10.17377/daio.2016.23.493

Full text: PDF file (287 kB)
References: PDF file   HTML file

English version:
Journal of Applied and Industrial Mathematics, 2016, 10:1, 61–68

Bibliographic databases:

UDC: 519.85
Received: 20.05.2015
Revised: 22.06.2015

Citation: V. L. Beresnev, A. A. Melnikov, “A capacitated competitive facility location problem”, Diskretn. Anal. Issled. Oper., 23:1 (2016), 35–50; J. Appl. Industr. Math., 10:1 (2016), 61–68

Citation in format AMSBIB
\Bibitem{BerMel16}
\by V.~L.~Beresnev, A.~A.~Melnikov
\paper A capacitated competitive facility location problem
\jour Diskretn. Anal. Issled. Oper.
\yr 2016
\vol 23
\issue 1
\pages 35--50
\mathnet{http://mi.mathnet.ru/da837}
\crossref{https://doi.org/10.17377/daio.2016.23.493}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3555674}
\elib{http://elibrary.ru/item.asp?id=25792211}
\transl
\jour J. Appl. Industr. Math.
\yr 2016
\vol 10
\issue 1
\pages 61--68
\crossref{https://doi.org/10.1134/S1990478916010075}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84961674893}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. L. Beresnev, A. A. Melnikov, “An upper bound for the competitive location and capacity choice problem with multiple demand scenarios”, J. Appl. Industr. Math., 11:4 (2017), 472–480  mathnet  crossref  crossref  elib
    2. V. Beresnev, A. Melnikov, “Exact method for the capacitated competitive facility location problem”, Comput. Oper. Res., 95 (2018), 73–82  crossref  mathscinet  zmath  isi  scopus
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