An Exact Column Generation Approach to the Capacitated Facility Location Problem

Abstract

The Capacitated Facility Location Problem (CFLP) is a well-known combinatorial optimization problem with applications in distribution and production planning. It consists in selecting plant sites from a finite set of potential sites and in allocating customer demands in such a way as to minimize operating and transportation costs. A variety of lower bounds based on Lagrangean relaxation and subgradient optimization has been proposed for this problem. However, in order to solve large or difficult problem instances information about a primal (fractional) solution is important. Therefore, we employ column generation in order to solve a corresponding master problem exactly. The algorithm uses different strategies for stabilizing the column generation process. Furthermore, the column generation method is employed within a branch-and-price procedure for computing optimal solutions to the CFLP. Computational results are reported for a set of larger and difficult problem instances. The results are compared with computational results obtained from a branch-and-bound procedure based on Lagrangean relaxation and subgradient optimization and a branch-and-bound method that uses the LP relaxation and polyhedral cuts