Standard

A Cut Generation Algorithm of Finding an Optimal Solution in a Market Competition. / Beresnev, V. L.; Melnikov, A. A.

In: Journal of Applied and Industrial Mathematics, Vol. 13, No. 2, 01.04.2019, p. 194-207.

Research output: Contribution to journal › Article › peer-review

Harvard

Beresnev, VL & Melnikov, AA 2019, 'A Cut Generation Algorithm of Finding an Optimal Solution in a Market Competition', Journal of Applied and Industrial Mathematics, vol. 13, no. 2, pp. 194-207. https://doi.org/10.1134/S1990478919020029

APA

Beresnev, V. L., & Melnikov, A. A. (2019). A Cut Generation Algorithm of Finding an Optimal Solution in a Market Competition. Journal of Applied and Industrial Mathematics, 13(2), 194-207. https://doi.org/10.1134/S1990478919020029

Vancouver

Beresnev VL, Melnikov AA. A Cut Generation Algorithm of Finding an Optimal Solution in a Market Competition. Journal of Applied and Industrial Mathematics. 2019 Apr 1;13(2):194-207. doi: 10.1134/S1990478919020029

Author

Beresnev, V. L. ; Melnikov, A. A. / A Cut Generation Algorithm of Finding an Optimal Solution in a Market Competition. In: Journal of Applied and Industrial Mathematics. 2019 ; Vol. 13, No. 2. pp. 194-207.

BibTeX

@article{e285bc2c87fb4426a0f5b72ca25a57b8,
title = "A Cut Generation Algorithm of Finding an Optimal Solution in a Market Competition",
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.",
keywords = "bilevel programming, estimating problem, market competition, Stackelberg game",
author = "Beresnev, {V. L.} and Melnikov, {A. A.}",
year = "2019",
month = apr,
day = "1",
doi = "10.1134/S1990478919020029",
language = "English",
volume = "13",
pages = "194--207",
journal = "Journal of Applied and Industrial Mathematics",
issn = "1990-4789",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - A Cut Generation Algorithm of Finding an Optimal Solution in a Market Competition

AU - Beresnev, V. L.

AU - Melnikov, A. A.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

KW - bilevel programming

KW - estimating problem

KW - market competition

KW - Stackelberg game

UR - http://www.scopus.com/inward/record.url?scp=85067414381&partnerID=8YFLogxK

U2 - 10.1134/S1990478919020029

DO - 10.1134/S1990478919020029

M3 - Article

AN - SCOPUS:85067414381

VL - 13

SP - 194

EP - 207

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 2

ER -

ID: 20643221