Improving Law Enforcement Daily Deployment Through Machine
Learning-Informed Optimization under Uncertainty
Abstract
Urban law enforcement agencies are under great
pressure to respond to emergency incidents effectively while operating within restricted budgets.
Minutes saved on emergency response times can
save lives and catch criminals, and a responsive
police force can deter crime and bring peace of
mind to citizens. To efficiently minimize the response times of a law enforcement agency operating in a dense urban environment with limited
manpower, we consider in this paper the problem
of optimizing the spatial and temporal deployment
of law enforcement agents to predefined patrol regions in a real-world scenario informed by machine
learning. To this end, we develop a mixed integer
linear optimization formulation (MIP) to minimize
the risk of failing response time targets. Given the
stochasticity of the environment in terms of incident numbers, location, timing, and duration, we
use Sample Average Approximation (SAA) to find
a robust deployment plan. To overcome the sparsity of real data, samples are provided by an incident generator that learns the spatio-temporal distribution and demand parameters of incidents from
a real world historical dataset and generates sets
of training incidents accordingly. To improve runtime performance across multiple samples, we implement a heuristic based on Iterated Local Search
(ILS), as the solution is intended to create deployment plans quickly on a daily basis. Experimental
results demonstrate that ILS performs well against
the integer model while offering substantial gains
in execution time