Solution methods for the bi-objective (cost-coverage) unconstrained facility location problem with an illustrative example |
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Authors: | Juan G Villegas Fernando Palacios Andrés L Medaglia |
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Institution: | (1) Departamento de Ingeniería Industrial, Facultad de Ingeniería, Universidad de Antioquia, Medellín, Colombia;(2) Departamento de Ingeniería Industrial,Facultad de Ingeniería, Universidad de los Andes, Bogotá, D.C., A.A. 4976, Colombia |
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Abstract: | The Colombian coffee supply network, managed by the Federación Nacional de Cafeteros de Colombia (Colombian National Coffee-Growers
Federation), requires slimming down operational costs while continuing to provide a high level of service in terms of coverage
to its affiliated coffee growers. We model this problem as a biobjective (cost-coverage) uncapacitated facility location problem
(BOUFLP). We designed and implemented three different algorithms for the BOUFLP that are able to obtain a good approximation
of the Pareto frontier. We designed an algorithm based on the Nondominated Sorting Genetic Algorithm; an algorithm based on
the Pareto Archive Evolution Strategy; and an algorithm based on mathematical programming. We developed a random problem generator
for testing and comparison using as reference the Colombian coffee supply network with 29 depots and 47 purchasing centers.
We compared the algorithms based on the quality of the approximation to the Pareto frontier using a nondominated space metric
inspired on Zitzler and Thiele's. We used the mathematical programming-based algorithm to identify unique tradeoff opportunities
for the reconfiguration of the Colombian coffee supply network. Finally, we illustrate an extension of the mathematical programming-based
algorithm to perform scenario analysis for a set of uncapacitated location problems found in the literature. |
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Keywords: | Uncapacitated facility location Multi-objective optimization Multi-objective evolutionary algorithms Combinatorial optimization Integer programming Scenario analysis |
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