RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Diskretn. Anal. Issled. Oper.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Diskretn. Anal. Issled. Oper., 2019, Volume 26, Number 3, Pages 27–45 (Mi da929)  

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 17Ц11Ц01021
This research is supported by the Russian Science Foundation (Project 17Ц11Ц01021).


DOI: https://doi.org/10.33048/daio.2019.26.638

Full text: PDF file (366 kB)
References: PDF file   HTML file

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
\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}


Linking options:
  • http://mi.mathnet.ru/eng/da929
  • http://mi.mathnet.ru/eng/da/v26/i3/p27

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. 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  crossref  zmath  isi  scopus
  • ƒискретный анализ и исследование операций
    Number of views:
    This page:99
    Full text:12
    References:8
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021