The mean-value-at-risk median problem on a network with random demand weights

Abstract

Dr. Zvi Drezner’s research career has touched on many areas of location analysis. We devote the first part of this chapter to summarizing Zvi’s vast contributions to the studies of the minimax and the maximum facility location problems. His relevant publications are grouped in terms of the characteristics of the problems investigated, including space, the number of facilities to locate, and completeness of information. In particular, we provide an overview of Zvi’s work in the deterministic planar minimax problems. The second part of the chapter is our own paper on a network median problem when demand weights are independent random variables. The objective of the model proposed is to locate a single facility so as to minimize the expected total demand-weighted distance subject to a constraint on the value-at-risk (VaR). The study integrates the expectation criterion with the VaR measure and links different median models with random demand weights. Methods are suggested to identify dominant points for the optimal solution. An algorithm is developed for solving the problem.