A new approach to cooperative competition in facility location problems: Mathematical formulations and an approximation algorithm

•This paper deals with cooperative competition in facility location problems.•A new game-theoretical multi-objective model is proposed that has efficient performance to achieve Nash equilibrium points.•Due to high computational complexity of the problem, a new approximation heuristic algorithm is pr...

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Bibliographic Details
Published in:Computers & operations research Vol. 83; pp. 45 - 53
Main Authors: Rohaninejad, Mohammad, Navidi, Hamidreza, Nouri, Behdin Vahedi, Kamranrad, Reza
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.07.2017
Pergamon Press Inc
Subjects:
Algorithms
Approximation
Approximation algorithm
Clients
Competition
Competitive facility location
Cooperative competition
Formulations
Game theory
Heuristic methods
Mathematical analysis
Mathematical programming
Multiple objective analysis
Nash equilibrium
Operations research
Players
Nash equilibrium
Cooperative competition
Approximation algorithm
Game theory
Competitive facility location
ISSN:0305-0548, 1873-765X, 0305-0548
Online Access:Get full text
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Summary:•This paper deals with cooperative competition in facility location problems.•A new game-theoretical multi-objective model is proposed that has efficient performance to achieve Nash equilibrium points.•Due to high computational complexity of the problem, a new approximation heuristic algorithm is proposed to solve large-sized problems.•The computational results show that the proposed algorithm has satisfactory performance in two criteria including computational time and the quality of final results. This paper deals with cooperative competition in facility location problems in which potential players (investors) are in competition (or conflict) over acquiring suitable sites and clients. In order to formulate the problem, a game-theoretical multi-objective model with the objective of maximizing investor utility is presented. In the proposed method, an acceptance threshold constraint is applied to facility allocation that is based on a combination of distance between a facility and clients, and investors’ product prices. Since the common solution methods for multi-objective optimization, such as weighted sums, ε-constraints, multi-objective meta-heuristic algorithms, etc. are not efficient enough, and cannot guarantee achieving Nash equilibrium points, a new approach is developed to solve the presented problem. Moreover, according to the computational complexity of the problem, an approximation algorithm is introduced for large-sized problems. Finally, the computational results demonstrate that the proposed algorithm performs efficiently in obtaining Nash equilibrium points.
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ISSN:0305-0548
1873-765X
0305-0548
DOI:10.1016/j.cor.2017.02.003