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Kernel search for the capacitated facility location problem

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Abstract

The Capacitated Facility Location Problem (CFLP) is among the most studied problems in the OR literature. Each customer demand has to be supplied by one or more facilities. Each facility cannot supply more than a given amount of product. The goal is to minimize the total cost to open the facilities and to serve all the customers. The problem is \(\mathcal{NP}\)-hard. The Kernel Search is a heuristic framework based on the idea of identifying subsets of variables and in solving a sequence of MILP problems, each problem restricted to one of the identified subsets of variables. In this paper we enhance the Kernel Search and apply it to the solution of the CFLP. The heuristic is tested on a very large set of benchmark instances and the computational results confirm the effectiveness of the Kernel Search framework. The optimal solution has been found for all the instances whose optimal solution is known. Most of the best known solutions have been improved for those instances whose optimal solution is still unknown.

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Acknowledgements

The authors would like to express their appreciation for the valuable comments made by the associate editor and two anonymous reviewers.

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Authors and Affiliations

  1. Department of Quantitative Methods, University of Brescia, C. da S. Chiara 50, Brescia, Italy

    G. Guastaroba & M. G. Speranza

Authors
  1. G. Guastaroba
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  2. M. G. Speranza
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Correspondence to G. Guastaroba.

Appendix: Detailed computational results

Appendix: Detailed computational results

Table 13 Computational results for OR-Library data set
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Table 14 Computational results for TBED1 data set
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Table 15 Computational results for Test Bed A data set
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Table 16 Computational results for Test Bed B data set
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Table 17 Computational results for Test Bed C data set
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Guastaroba, G., Speranza, M.G. Kernel search for the capacitated facility location problem. J Heuristics 18, 877–917 (2012). https://doi.org/10.1007/s10732-012-9212-8

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