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 Avtomat. i Telemekh., 2014, Issue 4, Pages 94–105 (Mi at7534)

Two-level programming problems

On the competitive facility location problem with a free choice of suppliers

V. L. Beresnev

Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Abstract: We consider a mathematical model from the class of competitive sequential facility location problems. In these problems, the competitors sequentially open their facilities, and each side aims to “capture” the consumers and maximize its profits. In the proposed model, we consider a situation of a “free” choice by each side of an open facility to service a customer. The model is formulated as a bilevel integer programming problem. We show that the problem of finding an optimal noncooperative solution can be represented as a maximization problem for a pseudo-Boolean function. We propose an algorithm for constructing an admissible noncooperative solution for fixed values of the variables in this pseudo-Boolean function. We also propose a method for constructing an upper bound on the maximal value of the pseudo-Boolean function on subsets of solutions defined by partial $(0,1)$-vectors.

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English version:
Automation and Remote Control, 2014, 75:4, 668–676

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Presented by the member of Editorial Board: À. È. Êèáçóí

Citation: V. L. Beresnev, “On the competitive facility location problem with a free choice of suppliers”, Avtomat. i Telemekh., 2014, no. 4, 94–105; Autom. Remote Control, 75:4 (2014), 668–676

Citation in format AMSBIB
\Bibitem{Ber14} \by V.~L.~Beresnev \paper On the competitive facility location problem with a~free choice of suppliers \jour Avtomat. i Telemekh. \yr 2014 \issue 4 \pages 94--105 \mathnet{http://mi.mathnet.ru/at7534} \transl \jour Autom. Remote Control \yr 2014 \vol 75 \issue 4 \pages 668--676 \crossref{https://doi.org/10.1134/S0005117914040079} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000334423100007} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899577060} 

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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. S. M. Lavlinskii, A. A. Panin, A. V. Plyasunov, “A bilevel planning model for public-private partnership”, Autom. Remote Control, 76:11 (2015), 1976–1987
2. A. Karakitsiou, “Discrete competitive facility location: modeling and optimization approaches”, Optimization, Control, and Applications in the Information Age: in Honor of Panos M. Pardalos'S 60Th Birthday, Springer Proceedings in Mathematics & Statistics, 130, eds. A. Migdalas, A. Karakitsiou, Springer, 2015, 153–169
3. V. L. Beresnev, A. A. Melnikov, “A capacitated competitive facility location problem”, J. Appl. Industr. Math., 10:1 (2016), 61–68
4. V. Beresnev, A. Melnikov, “Facility location in unfair competition”, Discrete Optimization and Operations Research, Lecture Notes in Computer Science, 9869, eds. Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski, P. Pardalos, Springer Int Publishing Ag, 2016, 325–335
5. A. Melnikov, V. Beresnev, “Upper bound for the competitive facility location problem with quantile criterion”, Discrete Optimization and Operations Research, Lecture Notes in Computer Science, 9869, eds. Y. Kochetov, M. Khachay, V. Beresnev, E. Nurminski, P. Pardalos, Springer Int Publishing Ag, 2016, 373–387
6. 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
7. L.-Ch. Kung, W.-H. Liao, “An approximation algorithm for a competitive facility location problem with network effects”, Eur. J. Oper. Res., 267:1 (2018), 176–186
8. V. Beresnev, A. Melnikov, “Exact method for the capacitated competitive facility location problem”, Comput. Oper. Res., 95 (2018), 73–82
9. M. M. Nasiri, V. Mahmoodian, A. Rahbari, Sh. Farahmand, “A modified genetic algorithm for the capacitated competitive facility location problem with the partial demand satisfaction”, Comput. Ind. Eng., 124 (2018), 435–448
10. Beresnev V., Melnikov A., “Approximation of the Competitive Facility Location Problem With Mips”, Comput. Oper. Res., 104 (2019), 139–148
11. V. L. Beresnev, A. A. Melnikov, “A cut generation algorithm of finding an optimal solution in a market competition”, J. Appl. Industr. Math., 13:2 (2019), 194–207
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