Solving nonlinear multiple‐facility network location problems

We show how to locate optimally p new facilities (servers) on a network so as to minimize cost, where cost can be any convex function of the distances between demand points (nodes) and a closest server. The algorithm is generally practical only for small p (perhaps 2, 3, or 4), but it admits a large number of servers with locations fixed beforehand. The classical p ‐median, p ‐center, and p ‐facility cent‐dian problems are special cases. Other problems of this form include a large number of obnoxious facility problems, problems in which the objective is to minimize an L k norm of distances, and a wide variety of problems, problems in which the objective is to minimize an L k norm of distances, and a wide variety of problems in which equity or social welfare is a a factor.