Grey Median Problem and Vertex Optimality

The median problem is a basic model in location theory and transportation sciences. This problem deals with locating a facility on a network, to minimize the sum of weighted distances between the facility and the vertices of the network. In this paper, the cases that weights of vertices, edge lengths or both of them are grey numbers, are considered. For all these cases, we show that the set of vertices of network contains a solution of the median problem. This property is called vertex optimality. Median problem with grey parameters and its properties are first considered in this paper.