Optimization in Positioning of Police Resources A case study of Asunción - Paraguay

Efficient attendance of 911 emergency calls is a significant challenge, mainly in cities with high rates of violence. This problem has been addressed by considering it as a coverage problem with violence rates but without guaranteeing maximum response time or minimizing response time without guaranteeing coverage. Consequently, in this work, we address this problem by considering a coverage maximization according to the violence index guaranteeing maximum response and coverage. For this purpose, we developed a tool that builds a weighted graph with the violence index, given a city map and the history of recorded incidents. Next, inspired by the previous works, we propose a new mathematical formulation that maximizes coverage according to the rate of violence subject to total coverage and guarantees maximum response time. Furthermore, we apply a Tabu Search to calculate the best solution. Considering actual data from the city of Asunción (Paraguay), a numerical simulation was performed using the strategy in the system 911, a state-of-theart algorithm based on coverage, and our contribution. The simulation results show that the proposed algorithm can find security coverage solutions with a better allocation for the areas with a high rate of violence than the other alternatives evaluated.