Locating Obnoxious Facilities With Variable Capacities

The problem of locating facilities, such as garbage dumps or noisy factories, that have a negative impact on surrounding communities was initiated about 50 years ago, and intensively analyzed in the literature. In the models proposed in the literature, it is assumed that all facilities have the same capacity (size), and thus inflict the same negative impact. In this article, we propose to construct facilities of different capacities with a total given capacity. Facilities located in open areas are far from communities and can be larger without impacting the most affected community. This extra capacity allows facilities close to communities to be smaller without changing the total capacity and significantly reduces the negative impact on the most affected community. Such an important extension leads to a more complicated formulation that we were able to simplify and get much better solutions in shorter run times. In extensive computational experiments, we found in some cases that the negative impact on the most affected community is reduced by more than 50% when facilities of different capacities are established.