Degeneracy in the multi-source Weber problem

This study investigates a new phenomenon of degeneracy in the multi-source Weber problem. This phenomenon relates to the existence of solutions in whi ch one or more facilities are out of use; that is, no demands (or customers ) are allocated to these facilities. We show that a significant portion of solutions is degenerate when large numbers of new facilities are being cons idered. Computational result also reveal that the well-known Cooper algorit hm and the more recent projection method of Bongartz et al. tend to produce degenerate local minima of varying degree under these conditions, and that this tendancy adversely affects the quality of the solution. A simple modi fication of these algorithms involving insertion of out-of-use facilities p rovides a significant improvement in solution quality for larger problem si zes without affecting CPU time. Different insertion strategies are investig ated.