Multi-Type, Multi-Zone Facility Location

The placement of facilities according to spatial and/or geographic requirements is a popular problem within the domain of location science. Objectives that are typically considered in this class of problems include dispersion, median, center, and covering objectivesand are generally defined in terms of distance or service-related criteria. With few exceptions, the existing models in the literature for these problems only accommodate one type of facility. Furthermore, the literature on these problems does not allow for the possibility of multiple placement zones within which facilities may be placed. Due to the unique placement requirements of different facility typessuch as suitable terrain that may be considered for placement and specific placement objectives for each facility typeit is expected that different suitable placement zones for each facility type, or groups of facility types, may differ. In this article, we introduce a novel mathematical treatment for multi-type, multi-zone facility location problems. We derive multi-type, multi-zone extensions to the classical integer-linear programming formulations involving dispersion, centering and maximal covering. The complexity of these formulations leads us to follow a heuristic solution approach, for which a novel multi-type, multi-zone variation of the non-dominated sorting genetic algorithm-II algorithm is proposed and employed to solve practical examples of multi-type, multi-zone facility location problems.