A heuristic method for large-scale multi-facility location problems

Abstract

A heuristic method for solving large-scale multi-facility location problems is presented. The method is analogous to Cooper's method (SIAM Rev. 6 (1964) 37), using the authors’ single facility location method (Comput. Optim. Appl. 21 (2002) 213) as a parallel subroutine, and reassigning customers to facilities using the heuristic of nearest center reclassification. Numerical results are reported. Scope and purpose We study the multiple facility location problem (MFLP). The objective in MFLP is to locate facilities to serve optimally a given set of customers. MFLPs have many applications in Operations Research, and a rich literature, see Drezner (Location Sci. 3(4) (1995) 275) for a recent survey. MFLPs involve, in addition to the location decision, also the assignment of customers to facilities. The MFLP is therefore a special clustering problem, the clusters here are the sets of customers assigned to the same facility. We propose a parallel heuristic method for solving MFLPs, using ideas from cluster analysis (nearest mean reclassification (Cluster Analysis, 3rd Edition, Edward Arnold, London, 1993)), and the authors’ Newton bracketing method for convex minimization (Comput. Optim. Appl. 21 (2002) 213) as a subroutine. The method is suitable for large-scale problems, as illustrated by numerical examples.