Probabilistic location problems with discrete demand weights

In this article we consider four models for locating a facility on an undirected network with demand weights, which are independent discrete random variables. These problems include the probabilistic versions of two models for locating desirable facilities: the 1‐median and 1‐minimax problems and two problems for locating undesirable facilities: the 1‐antimedian and 1‐maximin problems. The article contains analysis of special cases where a solution is determined by solving deterministic versions of the problems and efficient algorithms to solve the problems in general. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(1), 47–57 2004