A two-level evolutionary algorithm for solving the facility location and design (1|1)-centroid problem on the plane with variable demand

In this work, the problem of a company or chain (the leader) that considers the reaction of a competitor chain (the follower) is studied. In particular, the leader wants to set up a single new facility in a planar market where similar facilities of the follower, and possibly of its own chain, are al...

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Vydáno v:Journal of global optimization Ročník 56; číslo 3; s. 983 - 1005
Hlavní autoři: Redondo, J. L., Arrondo, A. G., Fernández, J., García, I., Ortigosa, P. M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.07.2013
Springer
Springer Nature B.V
Témata:
Algorithms
Attraction
Competition
Computer Science
Genetic algorithms
Heuristic
Industrial locations
Location analysis
Market shares
Mathematical models
Mathematics
Mathematics and Statistics
Operations research
Operations Research/Decision Theory
Optimization
Real Functions
Studies
Competition
Variable demand
Nonlinear bi-level programming problem
Multistart heuristic
Continuous location
Evolutionary algorithm
Grid search
Centroid (or Stackelberg) problem
ISSN:0925-5001, 1573-2916
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Shrnutí:In this work, the problem of a company or chain (the leader) that considers the reaction of a competitor chain (the follower) is studied. In particular, the leader wants to set up a single new facility in a planar market where similar facilities of the follower, and possibly of its own chain, are already present. The follower will react by locating another single facility after the leader locates its own facility. Both the location and the quality (representing design, quality of products, prices, etc.) of the new leader’s facility have to be found. The aim is to maximize the profit obtained by the leader considering the future follower’s entry. The demand is supposed to be concentrated at n demand points. Each demand point splits its buying power among the facilities proportionally to the attraction it feels for them. The attraction of a demand point for a facility depends on both the location and the quality of the facility. Usually, the demand is considered in the literature to be fixed or constant regardless the conditions of the market. In this paper, the demand varies depending on the attraction for the facilities. Taking variable demand into consideration makes the model more realistic. However, it increases the complexity of the problem and, therefore, the computational effort needed to solve it. Three heuristic methods are proposed to cope with this hard-to-solve global optimization problem, namely, a grid search procedure, a multistart algorithm and a two-level evolutionary algorithm. The computational studies show that the evolutionary algorithm is both the most robust algorithm and the one that provides the best results.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9893-4