We study the problem of locating p facilities to serve clients residing at the nodes of a network with discrete probabilistic demand weights. The objective is to maximize the probability that the total weighted distance from a client to the closest facility does not exceed a given threshold value. The problem is formulated as an integer program but can be solved only for very small instances because of the exponential number of decision variables and constraints. We analyze the problem and, using a normal approximation of the total weighted distance we develop branch and bound solution procedures for various cases of the problem. We also develop heuristics and meta-heuristics to solve the problem. Based on our computational experiments we make recommendations on which approach to use and when.
