Advances and applications in continuous location and related problems

Abstract

This thesis focuses on the family of the continuous location problems. A location problem arises whenever a question of where to locate something is raised. This kind of problems belongs to one of the research areas of Operations Research which has had a greatest development since the 1960s, the Location Science. This discipline is mainly defined by the facility location problems which consist of finding the optimal locations for a set of facilities with respect a set of demand nodes and a given objective function. There are many classifications of location problems, one of them is the one that considers the location space as a classifier. In a discrete location problem, facilities can be located in a finite set of potential locations; the continuous space consider the space where the problem is defined and there are infinite positions to locate; and when we consider a network as a location space, facilities can be located at the nodes or at the arcs of the network. The use of each space will be given by the real application of the problem. We usually use the discrete case when we locate physical services such as schools or ATMs; the continuous one when the location can be more flexible, as in routers or sensors; and the network when the elements to be located are used in applications with networks such as bus stops or gas stations.