ARTICLE IN PRESS Computers & Operations Research ( ) – www.elsevier.com/locate/cor A generalized model of equality measures in network location problems M.C. López-de-los-Mozos a, b, ∗ , Juan A. Mesa a, b , Justo Puerto c a Departamento de Matemática Aplicada I. Universidad de Sevilla, Spain b Departamento de Matemática Aplicada II. Universidad de Sevilla, Spain c Departamento de Estadística e Investigación Operativa. Universidad de Sevilla, Spain Abstract In this paper, the concept of the ordered weighted averaging operator is applied to define a model which unifies and generalizes several inequality measures. For a location x, the value of the new objective function is the ordered weighted average of the absolute deviations from the average distance from the facilities to the location x. Several kinds of networks are studied: cyclic, tree and path networks and, for each of them, the properties of the objective function are analyzed in order to identify a finite dominating set for optimal locations. Polynomial-time algorithms are proposed for these problems, and the corresponding complexity is discussed.  2006 Elsevier Ltd. All rights reserved. Keywords: Location; Networks; Equality measures 1. Introduction Recent studies in network location problems have been focused on designing new objective functions which general- ize different location measures. The incorporation of several problems in a globalized model enables the exploration of the incidence of the geometrical structure of the network with respect to different criteria. In this way, several unifying location models have been introduced, the most recent of which is based on the concept of an ordered averaging oper- ator. The global model obtained by means of such a concept generalizes the most important location criteria according to the vector to be sorted. When such a vector is the classic weighted distance vector, the ordered median model is obtained. This model provides a unified framework which includes both the center and the median as special cases, as well as several related measures (such as the cent-dian and the k-centrum). The single ordered median problem has been studied in several types of cyclic networks and tree networks, both from the theoretical and algorithmic points of view, and also recent studies have focused on the multifacility version and other related instances of this problem in several kinds of spaces (see [1–4] and references therein). However, the ordered median model does not generalize a group of objective functions: the equality measures, whose formulation and behavior present structural differences with respect to the center and median measures. Nevertheless, the equality measures (and more generally, the issue of equity) are relevant in facility location problems in the public ∗ Corresponding author. Tel.: +34 954554387; fax: +34 954557878. E-mail addresses: mclopez@us.es (M.C. López-de-los-Mozos), jmesa@us.es (J.A. Mesa), puerto@us.es (J. Puerto). 0305-0548/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2006.05.016