Hierarchical Location-Allocation with Spatial Choice Interaction Modeling

Abstract

We combine concepts and methods from hierarchical spatial systems, spatial interaction modeling, and location-allocation modeling to derive optimal hierarchical facility systems. We consider models of increasing realism in how spatial interaction is dealt with—the first two are from past literature, the third is new. The p-median model assumes that patrons always travel to the closest facility and that distance minimization best serves them. Several researchers have observed, however, that patients in the developing world frequently bypass lower level facilities to attend more distant higher level ones. Previous location-allocation models have incorporated spatial interaction models attributing attendance and benefits to facility size and distance. In this article, we present a new model that incorporates a spatial choice interaction model attributing attendance and benefits to facility size, distance, and neighborhood accessibility. We demonstrate our approach with 150-node, three-level Oppong's problem of locating healthcare facilities in Suhum District, Ghana. This approach reacts intuitively to changes in accessibility patterns and deals realistically with the bypassing problem.