Sharing Costs in Some Distinguished Location Problems

Abstract

A location problem occurs whenever a set of users have to agree on the position of one or several facilities in order to provide some service for them. The goal is to minimize the overall service cost and depending on the framework space, nature of the service and the globalizing cost function many different models appear: median, center, ordered median, coverage, hub-location, etcetera. Any of these problems has produced a large body of literature in order to find optimal or approximate solutions to their corresponding optimization problems. However, even knowing the exact solution of those problems there is another interesting problem that deserves the attention of researchers: How to share the cost of implementing such an optimal solution among the users of that system? This chapter addresses this question for several well-known location problems that appears in location problems in the continuous setting.