A generalized model of equality measures in network location problems

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.Future and Emerging Technologies Unit (European Commission)Ministerio de Educación y Cienci

Unreliable point facility location problems on networks

In this paper we study facility location problems on graphs under the most common criteria, such as, median, center and centdian, but we incorporate in the objective function some reliability aspects. Assuming that facilities may become unavailable with a certain probability, the problem consists of locating facilities minimizing the overall or the maximum expected service cost in the long run, or a convex combination of the two. We show that the k-facility problem on general networks is NP-hard. Then, we provide efficient algorithms for these problems for the cases of k = 1, 2, both on general networks and on trees. We also explain how our methodology extends to handle a more general class of unreliable point facility location problems related to the ordered median objective function.Ministerio de Ciencia y TecnologíaJunta de Andalucí