Spatiotemporal heterogeneous allocation to support service area response

Abstract

Uncertainty and error are inevitable when continuously varying geographic phenomena are approximated. Describing geography and spatial relationships is, therefore, challenging using analytics for planning and management. A critical aspect of spatial description has to do with allocation, a process of determining who is best served by which facility. Allocation is useful in reflecting customer behavior, efficient assignment, districting, etc. Even though spatial and temporal heterogeneity is part of assignment processes formalized in allocation problems, previous studies often assume a pre-specified network. The assumption is understandable since many service vehicles currently travel over road networks. However, there are some other vehicles, such as planes, unmanned aircraft vehicles, boats, ships, etc. Their access is not restricted to a network. How to structure and solve an allocation process is particularly challenging when heterogeneity must be taken into account across continuous space and through time. In this paper, a method is developed to construct service areas in order to minimize assignment cost in a continuous region where accessibility is spatially and temporally heterogeneous. Application findings are reported for planning problems involving emergency drone delivery since it is impacted by heterogeneity in the local environment. The travel accessibility of drones changes due to time-varying wind and airspace restrictions. Results show that the optimal allocation and service area of drone-based stations vary over time. The response time (or system costs) can be saved by taking into account wind and travel obstacles. Further, feasibility, practicality, and importance are demonstrated for incorporating spatial and temporal heterogeneity in continuous space allocation processes.