Range minimization problems in path-facility location on trees

Abstract

In location analysis, the issue of equity among clients has become a relevant criterion especially when locating public facilities. Equity refers to the distribution of the clients' demand in a geographical area and the objective is to locate facilities in order to ensure a low variability of the distribution of the distances from the demand points (clients) to a facility. In this paper we study the problem of locating path-shaped facilities on a tree network with nonnegative weights associated to the vertices and positive lengths associated to the edges.We consider the maximum and the minimum weighted distances of a client to a facility and minimize the Range function which is defined as the difference between the maximum and the minimum weighted distance from the vertices of the network to a facility. This problem arises, for example, when locating a transit line for commuters on a network with the aim of making the line easily accessible to all the clients scattered in a given territory.