Police service district planning

We propose a new framework to address the territory design problem of emergency services in collaboration with two police authorities in Europe. Our framework serves as a strategic decision support system to assess different districting layouts, department locations, staffing decisions and dispatching strategies. First, we introduce a novel modification of the p-median problem with a combined approach to the contiguity and compactness of district layouts solvable by a commercial solver. Second, we utilize a new discrete event simulation that accounts for the variability of spatial and temporal incident patterns and driving times to evaluate the district layouts according to several criteria based upon up to 1.8 million historical incidents. Our simulation results demonstrate that our proposed district layouts can lead to a reduction of the response time by up to 14.52% while also lowering the dispatch time, the overall driving time, and the number of unanswered calls for service. Additionally, we examine the computational complexity of optimally locating district centers and analyze the more restricted problem of optimally reassigning districts to fixed district centers.