A simulated annealing approach to police district design |
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| Affiliation: | 1. Blasland, Bouck & Lee, Inc. 6723 Towpath Road, Syracuse, NY 13214, USA;2. First USA Bank, DE1-1027, 201 North Walnut Street, Wilmington, DE 19801, USA;3. Department of Industrial Engineering, University at Buffalo, State University of New York, 342 Lawrence D. Bell Hall, Box 602050 Buffalo, NY 14260, USA;1. Department of Epidemiology and Environmental Health, School of Public Health and Health Professions, University at Buffalo, The State University of New York, Buffalo, NY, USA;2. Biostatistics and Epidemiology Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Centers for Disease Control and Prevention, Morgantown, WV, USA;3. Toxicology and Molecular Biology Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Centers for Disease Control and Prevention, Morgantown, WV, USA;1. Monash University Accident Research Centre, Monash University, Australia;2. Centre for Health Policy, Melbourne School of Population and Global Health, University of Melbourne, Australia;1. Department of Information Systems, Statistics, and Management Science, The University of Alabama, Tuscaloosa, AL 35487-0226, United States;2. Broad College of Business, Michigan State University, East Lansing, MI 48824, United States;1. Faculty of Technology, Policy and Management, Safety and Security Science Group (S3G), TU Delft, 2628 BX Delft, The Netherlands;2. Faculty of Applied Economics, Antwerp Research Group on Safety and Security (ARGoSS), University Antwerp, 2000 Antwerp, Belgium;3. CEDON, KULeuven, Campus Brussels, 1000 Brussels, Belgium;4. Research Center of Computational Experiments and Parallel System Technology, College of Information System and Management, National University of Defense Technology, Changsha 410073, China;1. LISES – Dipartimento di Ingegneria Civile, Chimica, Ambientale e dei Materiali, Alma Mater Studiorum – Università di Bologna, via Terracini n.28, 40131 Bologna, Italy;2. Safety and Security Science Group (S3G), Faculty of Technology, Policy and Management, TU Delft, 2628 BX Delft, Netherlands;3. Faculty of Applied Economics, Research Groups ANT/OR, University of Antwerp, Prinsstraat 13, 2000 Antwerp, Belgium;4. CEDON, KULeuven, Campus Brussels, 1000, Brussels, Belgium |
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| Abstract: | This paper considers the problem of redistricting or redrawing police command boundaries. We model this problem as a constrained graph-partitioning problem involving the partitioning of a police jurisdiction into command districts subject to constraints of contiguity, compactness, convexity and size. Since the districting affects urban emergency services, there also exist quality-of-service constraints, which limit the response time (queue time plus travel time) to calls for service. Confronted with the combinatorial challenge of the districting problem, we propose a simulated annealing algorithm to search for a “good” partitioning of the police jurisdiction. At each iteration of the algorithm, we employ a variant of the well-known PCAM model to optimally assign the patrol cars and assess the “goodness” of a particular district design with respect to some prescribed performance measures. This approach differs from the well-known Hypercube queuing model, which simply evaluates the performance of a user-specified district design and allocation. A computational case study using data from the Buffalo, New York, Police Department reveals the merits of this approach.Scope and purposeTwo of the primary concerns of urban police departments are the effective use of patrol cars and the workload balance between officers in different geographical districts. In recent years, a well known, public domain software package based on the Patrol Car Allocation Model (PCAM) has been developed. PCAM was designed to help police management specify the number of patrol cars that should be on duty at various times of the day on each day of the week in each district. For long-term planning, police management also faces the thorny problem of designing these districts. To address this problem, we employ a simulated annealing search method to determine the geographic boundaries between the police districts. PCAM is used to evaluate the “goodness” of each district design encountered in this search, where “goodness” involves minimizing the disparity between the maximum workload and the minimum workload of the police officers. Working with the Buffalo, New York, Police Department, we were able to significantly reduce officer workload disparity while maintaining current levels of response time. |
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