UC Santa Barbara

Location-allocation decisions are extremely important and directly influence the efficiency of the investment and operation of a given service. The efficiency of the service system results from the geographical arrangement of a given set of facilities, the manner in which their services are provided, and the spatial distribution of demand. However, there are often unrealistic assumptions of spatial and temporal homogeneity in associated location and allocation processes. For example, one assumption is that service assignment cost is fixed over space and time, not impacted by instantaneous travel movement changes caused by topography, time, direction, slope, weather, etc. Even though heterogeneity has been formalized in assignment processes, previous studies assume a pre-specified road network. Without the restriction of a network, how to structure and solve an allocation process is particularly challenging when heterogeneity must be taken into account across continuous space over time. Both raster and vector base methods are developed in this dissertation to construct service areas in order to minimize assignment cost. Generalized location-allocation models are proposed to improve planning and decision-making processes with an appropriate description of travel accessibility and distributed demand. Emergency medical service delivery is utilized to demonstrate the feasibility, usefulness, and significance of incorporating spatial and temporal heterogeneity in location and allocation processes across a continuous terrain. A primary question to be answered for this specific case study is how to locate medical drone base stations and allocate service in order to optimize the overall response, especially given the spatiotemporal heterogeneity in distributed demand and varying service response times/costs. Results show that response potential is over- and under-estimated when heterogeneity and travel obstacles are disregarded. More importantly, travel times to patients across a region can be significantly reduced through better location and allocation decision making.