Optimal Allocation of Police Patrol Resources Using a Continuous-Time Crime Model

  • Ayan Mukhopadhyay
  • Chao Zhang
  • Yevgeniy Vorobeychik
  • Milind Tambe
  • Kenneth Pence
  • Paul Speer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9996)


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’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’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.


Decision theoretic policing Crime modeling Survival analysis Bender’s decomposition 



This research was partially supported by the NSF (IIS-1526860), ONR (N00014-15-1-2621), ARO (W911NF-16-1-0069), ARO MURI (W911NF-111-0332), and Vanderbilt University.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Ayan Mukhopadhyay
    • 1
  • Chao Zhang
    • 2
  • Yevgeniy Vorobeychik
    • 1
  • Milind Tambe
    • 2
  • Kenneth Pence
    • 1
  • Paul Speer
    • 1
  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.University of Southern CaliforniaLos AngelesUSA

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