On Location-Allocation Problems for Dimensional Facilities

This paper deals with a bilevel approach of the location-allocation problem with dimen- sional facilities. We present a general model that allows us to consider very general shapes of domains for the dimensional facilities, and we prove the existence of opti- mal solutions under mild assumptions. To achieve these results, we borrow tools from optimal transport mass theory that allow us to give explicit solution structure of the considered lower level problem. We also provide a discretization approach that can approximate, up to any degree of accuracy, the optimal solution of the original prob- lem. This discrete approximation can be optimally solved via a mixed-integer linear program. To address very large instance sizes, we also provide a GRASP heuristic that performs rather well according to our experimental results. The paper also reports some experiments run on test data.