@conference {1502027,
	title = {Optimal Allocation of Police Patrol Resources Using a Continuous-Time Crime Model },
	booktitle = {Decision and Game Theory for Security (GameSec 2016)},
	year = {2016},
	abstract = {Police departments worldwide are eager to develop better patrolling methods to manage the complex and evolving crime landscape.
Surprisingly, the problem of spatial police patrol allocation to optimize
expected crime response time has not been systematically addressed in
prior research. We develop a bi-level optimization framework to address
this problem. Our framework includes novel linear programming patrol response formulations. Bender{\textquoteright}s decomposition is then utilized to solve the
underlying optimization problem. A key challenge we encounter is that
criminals may respond to police patrols, thereby shifting the distribution
of crime in space and time. To address this, we develop a novel iterative Bender{\textquoteright}s decomposition approach. Our validation involves a novel
spatio-temporal continuous-time model of crime based on survival analysis, which we learn using real crime and police patrol data for Nashville,
TN. We demonstrate that our model is more accurate, and much faster,
than state-of-the-art alternatives. Using this model in the bi-level optimization framework, we demonstrate that our decision theoretic approach
outperforms alternatives, including actual police patrol policies.},
	author = {Mukhopadhyay, Ayan and Zhang, Chao and Vorobeychik, Yevgeniy and Tambe, Milind and Pence, Kenneth and Speer, Paul}
}
