The maximin-maxisum network location problem

In this paper, we consider the problem of finding a point on a general netw ork using two objectives, maximizing the minimum weighted distance from the point to the vertices (Maximin) and maximizing the sum of weighted distanc es between the point and the vertices (Maxisum). This bicriterion model can be used to locate an obnoxious facility on a network. We will identify the model properties, develop a polynomial algorithm for generating the effici ent set and provide a numerical example.