a graph theoretic-based approach for optimizing location-routing and crew assignment in police patrols

Ensuring urban safety and preventing crime are paramount responsibilities of municipal managers. police patrolling plays a crucial role in securing urban areas, yet limited resources and budget constraints necessitate an efficient patrolling system. this study introduces a multi-objective mathematical programming model aimed at maximizing the total effectiveness of a police patrolling system while minimizing associated costs. the approach utilizes a two-stage bi-objective mixed integer linear programming based on the k-windy postman problem. in the first stage, the model determines optimal locations for constructing police stations, while in the second stage, it allocates vehicle modes, plans patrolling routes, and assigns crew members to each vehicle. for small-size problems, the model is solved using the ε-constraint method, whereas a cluster-based algorithm is proposed for tackling medium- and large-size problems. to illustrate the model’s applicability, a real-world case study involving various city zones in tehran, iran is examined. the proposed model offers a practical tool for optimizing police patrolling systems in similar urban settings.