Integrated redistricting, location-allocation and service sharing with intra-district service transfer to reduce demand overload and its disparity

Service demand overload has been one of the main concerns in district-based service planning, because it strongly affects service quality. Moreover, the overload problem usually involves overload disparity among districts. The disparity often results from outdated district boundaries not reflecting up-to-date spatial demand distributions. A lack of systematic methodologies, however, has hindered solving such overload and disparity problems despite the increasing availability of information on spatial service demand and supply. This paper presents a novel mathematical programming model to address the service demand overload problem by reorganizing services in multiple spatial scales. The mathematical program optimizes simultaneously (1) redistricting service areas, (2) allocating multiple service resources into service-providing units in each district, and (3) sharing services between service-providing units within a district. Information on geographically distributed units is used as the spatial data of the model. This new model integrates districting and location-allocation problems as a combined problem. A heuristic solution approach is also presented to solve large problem instances. As a case study, a judicial service overload problem is examined for a state court system in the United States. This new integrated approach enables efficient utilization of the geographically distributed service capacity. In addition, these new features of the model allow for better utilization of spatial information for practical service planning.