Formulations and Approximation Algorithms for Multilevel Uncapacitated Facility Location

This paper studies multilevel uncapacitated p -location problems, a general class of facility location problems. We use a combinatorial representation of the general problem where the objective function satisfies the submodular property, and we exploit this characterization to derive worst-case bounds for a greedy heuristic. We also obtain sharper bounds when the setup cost for opening facilities is zero and the allocation profits are nonnegative. Moreover, we introduce a mixed integer linear programming formulation for the problem based on the submodularity property. We present results of computational experiments to assess the performance of the greedy heuristic and that of the formulation. We compare the models with previously studied formulations.