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
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
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.
under certain conditions on the input parameters,
the complexity decreases significantly
in some cases
the problem becomes polynomially solvable. Illustr. 3, bibliogr. 25.
bilevel problem, Stackelberg game, facility location, pricing, Bertrand model, nonuniform split of demand, complexity, polynomial hierarchy.
|Russian Science Foundation
|This research is supported by the Russian Science Foundation (Project 17Ц11Ц01021).
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Journal of Applied and Industrial Mathematics, 2019, 13:3, 500–510
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
\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.
\jour J. Appl. Industr. Math.
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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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