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This article is cited in 1 scientific paper (total in 1 paper)
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
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). |
DOI:
https://doi.org/10.33048/daio.2019.26.638
Full text:
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English version:
Journal of Applied and Industrial Mathematics, 2019, 13:3, 500–510
UDC:
519.8+518.25 Received: 22.11.2018 Revised: 02.04.2019 Accepted:05.06.2019
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
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\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}
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Linking options:
http://mi.mathnet.ru/eng/da929 http://mi.mathnet.ru/eng/da/v26/i3/p27
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This publication is cited in the following articles:
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Cvokic D.D., Kochetov Yu.A., Plyasunov A.V., Savic A., “the Competitive Hub Location Under the Price War”, Mathematical Optimization Theory and Operations Research, Lecture Notes in Computer Science, 11548, eds. Khachay M., Kochetov Y., Pardalos P., Springer International Publishing Ag, 2019, 133–146
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