Allocation using a heterogeneous space Voronoi diagram

Abstract

Spatial allocation is a fundamentally important process reflecting customer behavior, efficient service assignment, districting, etc., and is at the heart of many spatial analytical methods and processes. The Voronoi diagram has proven to be an important mathematical and geometric construct and has been widely applied in various fields because it is intuitive and efficient in the allocation and/or partitioning of space. However, existing Voronoi diagram approaches rely on the assumption that the attribute(s) of continuous space (non-generator points) is homogenous, which often is not the case for many application contexts. This paper introduces the concept of spatial heterogeneity in allocation. A new Voronoi diagram is defined—the heterogeneous Voronoi diagram. A geographic information system-based method is developed to derive the heterogeneous Voronoi diagram using discretized spatial allocation properties. Application of the heterogeneous Voronoi diagram is reported for a planning problem involving emergency drone delivery. Results show that response potential is over- and underestimated when heterogeneity and travel obstacles are disregarded. Further, feasibility, usefulness, and significance are demonstrated for incorporating geographic heterogeneity in the allocation process.