Spatial organization of multi-level services: A modeling framework for Hierarchical Districting

In this paper, novel, general and tractable optimization models are introduced for the spatial organization of multi-level services. Specifically, a hierarchically-structured districting plan is to be designed for geographical areas composed of multiple territorial units. This gives rise to a hierarchical districting problem. Different variants are analyzed accounting for features of practical relevance in real-world contexts, notably nestedness and coherency. The applicability of the proposed models is evidenced on small-to-mid-sized instances. Furthermore, the implications of incorporating multiple (often conflicting) planning criteria within different hierarchical structures are investigated. The results suggest that decision-makers may benefit from treating coherency as a “soft” requirement. This observation motivates the introduction of partial coherency, whereby a solution is deemed acceptable if it satisfies a prescribed minimum degree of coherency. The earlier formulations are accordingly extended to incorporate this concept, resulting in a unified model that subsumes the previous variants as special cases. Additional experiments demonstrate that partial coherency enables a flexible range of solutions that effectively address the inherent multi-criteria nature of hierarchical districting.