The problem considered in this talk is to locate some dimensional facilities in a general planar demand region minimizing the installation, congestion and lost demand costs. For a location of the facilities, a partition of the demand region that determines the allocation of the customers to the facilities has to be done minimizing the access cost of the customers to the facilities and the distribution cost in the resulting subregions (see e.g. [1] for similar partitions in a different context). These assumptions impose to the problem a hierarchical structure of bilevel problem. We approximate the problem by a discrete bilevel problem and present two methods to solve this last approximation: an exact mixed-integer linear programming model and a GRASP heuristic.
[1] Mallozzi, L., Puerto, J.: The geometry of optimal partitions in location problems. Optim Lett 12, 203-220 (2018). https://doi.org/10.1007/s11590-017-1156-3.
