Proactive Policing : A Resource Allocation Model for Crime Prevention with Deterrence Effect

This paper addresses police resource allocation across multiple locations, aiming to minimize the overall cost of potential crimes. Unlike previous literature focused on reactive police tasks, we propose a proactive approach that emphasizes crime prevention through deterrence. To account for the deterrence effect of police resources on crime, we employ the multinomial logit model to calibrate the distribution of crime locations. Our model sheds light on two facets of the deterrence effect in proactive policing - crime control diffusion and crime displacement - relevant to modern crime patterns from both criminology and economics perspectives. We also investigate the structural properties of our problem and its relation to mixture-of-logits assortment optimization. Additionally, we provide reformulations for mixed-integer linear/conic programs that can be solved directly using conventional optimization software. Finally, we showcase the efficacy of our model through a data-driven case study on the allocation of surveillance cameras in New York City