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Diskretn. Anal. Issled. Oper., 2019, Volume 26, Number 2, Pages 5–29 (Mi da921)  

This article is cited in 1 scientific paper (total in 1 paper)

A cut generation algorithm of finding an optimal solution in a market competition

V. L. Beresnevab, A. A. Melnikovab

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
b Novosibirsk State University, 1 Pirogov Street, 630090 Novosibirsk, Russia

Abstract: We consider a mathematical model of market competition between two parties. The parties sequentially bring their products to the market while aiming to maximize profit. The model is based on the Stackelberg game and formulated as a bilevel integer mathematical program. The problem can be reduced to the competitive facility location problem (CompFLP) with a prescribed choice of suppliers which belongs to a family of bilevel models generalizing the classical facility location problem. For the CompFLP with a prescribed choice of suppliers, we suggest an algorithm of finding a pessimistic optimal solution. The algorithm is an iterative procedure that successively strengthens an estimating problem with additional constraints. The estimating problem provides an upper bound for the objective function of the CompFLP and is resulted from the bilevel model by excluding the lower-level objective function. To strengthen the estimating problem, we suggest a new family of constraints. Numerical experiments with randomly generated instances of the CompFLP with prescribed choice of suppliers demonstrate the effectiveness of the algorithm. Tab. 2, bibliogr. 17.

Keywords: market competition, Stackelberg game, bilevel programming, estimating problem.

Funding Agency Grant Number
Russian Science Foundation 17Ц11Ц01021


DOI: https://doi.org/10.33048/daio.2019.26.642

Full text: PDF file (400 kB)
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English version:
Journal of Applied and Industrial Mathematics, 2019, 13:2, 194–207

UDC: 519.8+518.25
Received: 17.12.2018
Revised: 11.01.2019
Accepted:27.02.2019

Citation: V. L. Beresnev, A. A. Melnikov, “A cut generation algorithm of finding an optimal solution in a market competition”, Diskretn. Anal. Issled. Oper., 26:2 (2019), 5–29; J. Appl. Industr. Math., 13:2 (2019), 194–207

Citation in format AMSBIB
\Bibitem{BerMel19}
\by V.~L.~Beresnev, A.~A.~Melnikov
\paper A cut generation algorithm of finding an~optimal~solution in a market competition
\jour Diskretn. Anal. Issled. Oper.
\yr 2019
\vol 26
\issue 2
\pages 5--29
\mathnet{http://mi.mathnet.ru/da921}
\crossref{https://doi.org/10.33048/daio.2019.26.642}
\transl
\jour J. Appl. Industr. Math.
\yr 2019
\vol 13
\issue 2
\pages 194--207
\crossref{https://doi.org/10.1134/S1990478919020029}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85067414381}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Kononov, A. A. Panin, A. V. Plyasunov, “A bilevel competitive location and pricing model with nonuniform split of demand”, J. Appl. Industr. Math., 13:3 (2019), 500–510  mathnet  crossref  crossref
  • ƒискретный анализ и исследование операций
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