The geometry of optimal partitions in location problems

Given the position of some facilities, we study the shape of optimal par- titions of the customers’ area in a general planar demand region minimizing total average cost that depends on a set up cost plus some function of the travelling dis- tances. By taking into account different norms, according to the considered situation of the location problem, we characterize optimal consumers’ partitions and describe their geometry. The case of dimensional facilities is also investigated.