A flexible approach to location problems

In continuous location problems we are given a set of existing facilities and we are looking for the location of one or several new facilities. In the classical approaches weights are assigned to existing facilities expressing the importance of the new facilities for the existing ones. In this paper, we consider a pointwise deened objective function where the weights are assigned to the existing facilities depending on the location of the new facility. This approach is shown to be a generalization of the median, center and centdian objective functions. In addition, this approach allows to formulate completely new location models. EEcient algorithms as well as structural results for this algebraic approach for location problems are presented. A complexity analysis and extensions to the multifacility and restricted case are also considered.