A Trajectory Method for the Optimization of the Multi-Facility Location Problem With lp Distances

We consider the multi-facility location problem of placing m new facilities optimally among n demand points (or existing facilities) so that the sum of all weighted lp distance pairs (facility to facility and facility to demand point) is minimized. A method involving the solution of differential equations by numerical integration is presented. This method is computationally comparable to many existing heuristic and iterative methods. It avoids the frequent convergence difficulties associated with many iterative methods for p > 1 and has no difficulties in dealing with Targe "clusters" of facilities of p = 1.