Advertisement

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)

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’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.

Keywords

Decision theoretic policing Crime modeling Survival analysis Bender’s decomposition 

Notes

Acknowledgments

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.

References

  1. 1.
    Bertsimas, D., Tsitsiklis, J.N.: Linear Optimization, 3rd edn. Athena Scientific, Belmont (1997)Google Scholar
  2. 2.
    Brantingham, P.J., Brantingham, P.L.: Patterns in Crime. Macmillan, New York (1984)zbMATHGoogle Scholar
  3. 3.
    Chrobak, M., Karloof, H., Payne, T., Vishwnathan, S.: New results on server problems. SIAM J. Discrete Math. 4(2), 172–181 (1991)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cohen, J., Gorr, W.L., Olligschlaeger, A.M.: Leading indicators and spatial interactions: a crime-forecasting model for proactive police deployment. Geogr. Anal. 39(1), 105–127 (2007)CrossRefGoogle Scholar
  5. 5.
    Cohn, E.G.: Weather and crime. Br. J. Criminol. 30(1), 51–64 (1990)Google Scholar
  6. 6.
    Cox, D.R., Oakes, D.: Analysis of Survival Data, vol. 21. CRC Press, Cleveland (1984)Google Scholar
  7. 7.
    Felson, M., Poulsen, E.: Simple indicators of crime by time of day. Int. J. Forecast. 19(4), 595–601 (2003)CrossRefGoogle Scholar
  8. 8.
    Hope, T.: Problem-oriented policing and drug market locations: three case studies. Crime Prev. Stud. 2(1), 5–32 (1994)Google Scholar
  9. 9.
    Ivaha, C., Al-Madfai, H., Higgs, G., Ware, J.A.: The dynamic spatial disaggregation approach: a spatio-temporal modelling of crime. In: World Congress on Engineering, pp. 961–966 (2007)Google Scholar
  10. 10.
    Kennedy, L.W., Caplan, J.M., Piza, E.: Risk clusters, hotspots, and spatial intelligence: risk terrain modeling as an algorithm for police resource allocation strategies. J. Quant. Criminol. 27(3), 339–362 (2011)CrossRefGoogle Scholar
  11. 11.
    Kleemans, E.R.: Repeat burglary victimisation: results of empirical research in the Netherlands. Crime Prev. Stud. 12, 53–68 (2001)Google Scholar
  12. 12.
    Koper, C.S.: Just enough police presence: reducing crime and disorderly behavior by optimizing patrol time in crime hot spots. Justice Q. 12(4), 649–672 (1995)CrossRefGoogle Scholar
  13. 13.
    Landau, S.F., Fridman, D.: The seasonality of violent crime: the case of robbery and homicide in Israel. J. Res. Crime Delinquency 30(2), 163–191 (1993)CrossRefGoogle Scholar
  14. 14.
    Lauritsen, J.L., White, N.: Seasonal Patterns in Criminal Victimization Trends, vol. 245959. US DOJ, Office of Justice Program, Bureau of Justice Statistics (2014)Google Scholar
  15. 15.
    Levine, N., et al.: Crimestat III: a spatial statistics program for the analysis of crime incident locations (version 3.0). Houston (TX): Ned Levine & Associates/Washington, DC: National Institute of Justice (2004)Google Scholar
  16. 16.
    Mohler, G.O., Short, M.B., Brantingham, P.J., Schoenberg, F.P., Tita, G.E.: Self-exciting point process modeling of crime. J. Am. Stat. Assoc. 106(493), 100–108 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Murray, A.T., McGuffog, I., Western, J.S., Mullins, P.: Exploratory spatial data analysis techniques for examining urban crime implications for evaluating treatment. Br. J. Criminol. 41(2), 309–329 (2001)CrossRefGoogle Scholar
  18. 18.
    Short, M.B., D’Orsogna, M.R., Pasour, V.B., Tita, G., Brantingham, P.J., Bertozzi, A.L., Chayes, L.B.: A statistical model of criminal behavior. Math. Models Methods Appl. Sci. 18, 1249–1267 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Short, M.B., D’Orsogna, M.R., Pasour, V.B., Tita, G.E., Brantingham, P.J., Bertozzi, A.L., Chayes, L.B.: A statistical model of criminal behavior. Math. Models Methods Appl. Sci. 18(supp01), 1249–1267 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Speer, P.W., Gorman, D.M., Labouvie, E.W., Ontkush, M.J.: Violent crime and alcohol availability: relationships in an urban community. J. Public Health Policy 19(3), 303–318 (1998)CrossRefGoogle Scholar
  21. 21.
    Toomey, T.L., Erickson, D.J., Carlin, B.P., Quick, H.S., Harwood, E.M., Lenk, K.M., Ecklund, A.M.: Is the density of alcohol establishments related to nonviolent crime? J. Stud. Alcohol Drugs 73(1), 21–25 (2012)CrossRefGoogle Scholar
  22. 22.
    Zhang, C., Bucarey, V., Mukhopadhyay, A., Sinha, A., Qian, Y., Vorobeychik, Y., Tambe, M.: Using abstractions to solve opportunistic crime security games at scale. In: International Conference on Autonomous Agents and Multiagent Systems, 196–204. ACM (2016)Google Scholar
  23. 23.
    Zhang, C., Sinha, A., Tambe, M.: Keeping pace with criminals: designing patrol allocation against adaptive opportunistic criminals. In: International Conference on Autonomous Agents and Multiagent Systems. pp. 1351–1359 (2015)Google Scholar

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

Personalised recommendations