Classical median location problem under uncertain environment

In this paper, we investigate the classical p-median location problem on a network in which the vertex weights and the distances between vertices are uncertain variables. The aim is to locate p facilities on vertices of the network such that the sum of the weighted distances from each vertex to its closest facility becomes minimum. We show that the uncertain p-median problem is Np-hard on general networks. Then we present a method for solving the uncertain 1-median problem on tree networks.