NETWORK LOCATION-PROBLEMS WITH CONTINUOUS LINK DEMANDS - P-MEDIANS ON A CHAIN AND 2-MEDIANS ON A TREE

This paper is concerned with minisum location-allocation problems on undirected networks in which demands can occur on links with uniform probability distributions. Two types of networks are considered. The first type considered is simply a chain graph. It is shown that except for the 1-median case, the problem is generally non-convex. However, for the p-median case, a discrete set of potential optimal facility locations may be identified, and hence it is shown that all local and global minima to the problem may be discovered by solving a series of trivial linear programming problems.