A flexible approach to location problems

When dealing with location problems we are usually 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 defined 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 the formulation of completely new location models. Efficient algorithms as well as structural results for this algebraic approach to location problems are presented. A complexity analysis and extensions to the multifacility and restricted case are also considered.