Models and algorithms for competitive facility location problems with different customer behavior

Competitive facility location problems arise in the context of two non-cooperating companies, a leader and a follower, competing for market share from a given set of customers. We assume that the firms place a given number of facilities on locations taken from a discrete set of possible points. For...

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Bibliographic Details
Published inAnnals of mathematics and artificial intelligence Vol. 76; no. 1-2; pp. 93 - 119
Main Authors Biesinger, Benjamin, Hu, Bin, Raidl, Günther
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2016
Springer Nature B.V
Subjects
Algorithms
Artificial Intelligence
Competition
Complex Systems
Computer Science
Customers
Evolutionary algorithms
Expert systems
Followers
Integer programming
Linear programming
Markets
Mathematical models
Mathematics
Mixed integer
Operations research
Site selection
Solution archive
68T20
Bi-level optimization
Evolutionary algorithm
90B80
90C27
Competitive facility location
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Summary:Competitive facility location problems arise in the context of two non-cooperating companies, a leader and a follower, competing for market share from a given set of customers. We assume that the firms place a given number of facilities on locations taken from a discrete set of possible points. For this bi-level optimization problem we consider six different customer behavior scenarios from the literature: binary, proportional and partially binary, each combined with essential and unessential demand. The decision making for the leader and the follower depends on these scenarios. In this work we present mixed integer linear programming models for the follower problem of each scenario and use them in combination with an evolutionary algorithm to optimize the location selection for the leader. A complete solution archive is used to detect already visited candidate solutions and convert them efficiently into similar, not yet considered ones. We present numerical results of our algorithm and compare them to so far state-of-the-art approaches from the literature. Our method shows good performance in all customer behavior scenarios and is able to outperform previous solution procedures on many occasions.
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ISSN:1012-2443
1573-7470
DOI:10.1007/s10472-014-9448-0