Kernel search for the capacitated facility location problem

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{NP}$\end{document}-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.