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Diskretnyi Analiz i Issledovanie Operatsii, 2019, Volume 26, Issue 3, Pages 27–45
DOI: https://doi.org/10.33048/daio.2019.26.638 (Mi da929) 		 
This article is cited in 4 scientific papers (total in 4 papers)

A bilevel competitive location and pricing model with nonuniform split of demand

A. V. Kononovab, A. A. Paninab, A. V. Plyasunovab

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
b Novosibirsk State University, 1 Pirogov Street, 630090 Novosibirsk, Russia
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DOI: https://doi.org/10.33048/daio.2019.26.638
Abstract: Under study is the bilevel competitive facility location and pricing problem which is formulated in terms of the Stackelberg game. The problem involves the two producers: the Leader and the Competitor. They consistently place their facilities and set prices. The choice of prices is based on the Bertrand model of price competition and the possibility of dividing a client's demand if this will be profitable for both players. In this case, the demand is divided between the players in a given proportion.
The complexity is investigated of finding the optimal solution of the problem and its particular cases. It is shown that the problem is $\Sigma_2^P$-hard. However, under certain conditions on the input parameters, the complexity decreases significantly and in some cases the problem becomes polynomially solvable. Illustr. 3, bibliogr. 25.
Keywords: bilevel problem, Stackelberg game, facility location, pricing, Bertrand model, nonuniform split of demand, complexity, polynomial hierarchy.
Funding agency Grant number
Russian Science Foundation 17–11–01021
This research is supported by the Russian Science Foundation (Project 17–11–01021).
Received: 22.11.2018
Revised: 02.04.2019
Accepted: 05.06.2019
English version:
Journal of Applied and Industrial Mathematics, 2019, Volume 13, Issue 3, Pages 500–510
DOI: https://doi.org/10.1134/S1990478919030104
Bibliographic databases:
Document Type: Article
UDC: 519.8+518.25
Language: Russian
Citation: A. V. Kononov, A. A. Panin, A. V. Plyasunov, “A bilevel competitive location and pricing model with nonuniform split of demand”, Diskretn. Anal. Issled. Oper., 26:3 (2019), 27–45; J. Appl. Industr. Math., 13:3 (2019), 500–510
Citation in format AMSBIB
\Bibitem{KonPanPly19}
\by A.~V.~Kononov, A.~A.~Panin, A.~V.~Plyasunov
\paper A bilevel competitive location and pricing model with nonuniform split of demand
\jour Diskretn. Anal. Issled. Oper.
\yr 2019
\vol 26
\issue 3
\pages 27--45
\mathnet{http://mi.mathnet.ru/da929}
\crossref{https://doi.org/10.33048/daio.2019.26.638}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 3
\pages 500--510
\crossref{https://doi.org/10.1134/S1990478919030104}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067653979}
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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