Pareto Locations on Networks

Abstract

In an effort to improve the performance of facility systems, planners have developed a host of operational models to deal with the location of a facility on a network (see [LPT95] for a recent survey). A large number of these models focuses on the minimization of a unique objective function which is increasing with the distance to travel. However, in many location problems, especially in the public sector, the decision must be made by a group of decision makers, e.g. when a group of small communities wants to build and share a public facility. Then, each decision maker is endowed with a specific objective function but different decision makers have different objectives. In this paper, we consider the median (or minisum) location problem in this context of several decision makers. Specifically, the goal of all decision makers is the same: to locate a facility in order to minimize the total weighted distance to the potential users but the value of weights assigned to those potential users varies from one decision maker to another, hence yielding different objective functions. Some help might be provided to the group through the set of efficient or Pareto locations, i.e. solutions such that there exists no other location which is not worse for all decision makers and better for at least one of them. More details about the material presented in the following, as well as a discussion of the tree case can be found in [HNL96] and [HN96] for the planar case.