On the development and analysis of a comprehensive police patrolling model

Abstract

Police patrolling is a combination of proactive and reactive tasks. The initial focus is on the development and analysis of a deterministic model which has proactive patrolling tasks consisting of hot spot and general patrolling duties. Two different formulations are developed to address the problem: a compact arc-based and an extensive path-based formulation embedded in a column generation procedure. These formulations incorporate three metrics of efficiency and fairness: density, equity, and dispersion. Our model has discrete time steps and seeks to make a balance between hot spot and general patrolling duties by defining details of patrolling routes. The model allows a patrol unit to be at a hot spot for multiple consecutive time steps, thereby allowing foot patrolling to be used at a hot spot. We embed the deterministic model in a simulation environment for the purpose of defining proactive patrolling routes while responding to the calls for service. Numerical experiments are conducted to (a) evaluate the computational efficiency of the proposed methods, and (b) explore sensitivity analysis with respect to key parameters. A crime-data based case study is developed to illustrate the utility of the models and methods in a practical situation.