Skip to main content

Advertisement

SpringerLink
Log in

A literature review on police patrolling problems

  • S.I.: CLAIO 2018
  • Published:
Annals of Operations Research Aims and scope Submit manuscript

A Correction to this article was published on 08 July 2021

This article has been updated

Abstract

Police patrol is an effective crime prevention tool and boosts public confidence in urban security. Many interesting decision making problems appear in route design, resource allocation and jurisdiction planning. Many cities across the world have adopted a structured and intelligent method of police patrol due to the presence of a variety of operational and resource constraints. In this paper, we present a comprehensive review of the state-of-the-art in this domain, especially from the practice of operations research (OR) point of view. This is the first-of-its-kind review on police patrol presenting a classification scheme based on the type of problem, objective and modelling approach. In this novel scheme, one can track any paper almost readily to find the specific contribution. The applicability of OR in this domain is set to grow significantly as the governments formulate policies related to smart city planning and urban security. This study reveals many practical challenges in police patrolling for future research.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Change history

References

  1. Adler, N., Hakkert, A. S., Kornbluth, J., Raviv, T., & Sher, M. (2014a). Location-allocation models for traffic police patrol vehicles on an interurban network. Annals of Operations Research, 221, 9–31.

    Google Scholar 

  2. Adler, N., Hakkert, A. S., Raviv, T., & Sher, M. (2014b). The traffic police location and schedule assignment problem. Journal of Multi-criteria Decision Analysis, 21, 315–333.

    Google Scholar 

  3. Aguirre, O., & Taboada, H. (2012). An evolutionary game theory approach for intelligent patrolling. Procedia Computer Science, 12, 140–145.

    Google Scholar 

  4. Alpern, S., Morton, A., & Papadaki, K. (2011). Patrolling games. Operations Research, 59, 1246–1257.

    Google Scholar 

  5. Amrutha, S., & Idicula, S. M. (2014). Agent based simulation of street robbery. International Journal of Computer Science and Information Technologies, 5, 6692–6696.

    Google Scholar 

  6. Andresen, M. A., & Lau, K. C. Y. (2014). An evaluation of police foot patrol in Lower Lonsdale, British Columbia. Police practice and research, 15, 476–489.

    Google Scholar 

  7. Andresen, M. A., & Malleson, N. (2014). Police foot patrol and crime displacement: a local analysis. Journal of Contemporary Criminal Justice, 30, 186–199.

    Google Scholar 

  8. Auad, R., & Batta, R. (2017). Location-coverage models for preventing attacks on interurban transportation networks. Annals of Operations Research, 258, 679–717.

    Google Scholar 

  9. Azimi, S. A. Z., & Bashiri, M. (2016). Modeling police patrol routing and its problem-solving technique based on the ant colony optimization algorithm (case study: Iran’s Police). Research Journal of Applied Sciences, 11, 536–546.

    Google Scholar 

  10. Baloian, N., Bassaletti, C. E., Fernández, M., Figueroa, O., Fuentes, P., Manasevich, R., Orchard, M., Peñafiel, S., Pino, J. A., & Vergara, M. (2017). Crime prediction using patterns and context. In 2017 IEEE 21st international conference on computer supported cooperative work in design (CSCWD), pp. 2–9.

  11. Birge, J. R., & Pollock, S. M. (1989). Modelling rural police patrol. Journal of the Operational Research Society, 40, 41–54.

    Google Scholar 

  12. Bishai, D., Asiimwe, B., Abbas, S., Hyder, A. A., & Bazeyo, W. (2008). Cost-effectiveness of traffic enforcement: case study from Uganda. Injury Prevention, 14, 223–227.

    Google Scholar 

  13. Bliss, T., Guria, J., Jones, W., & Rockliffe, N. (1999). A road safety resource allocation model. Transport Reviews, 19, 291–303.

    Google Scholar 

  14. Brown, D. E., & Oxford, R. B. (2001). Data mining time series with applications to crime analysis. In 2001 IEEE international conference on systems, man and cybernetics. e-Systems and e-Man for cybernetics in cyberspace, pp. 1453–1458.

  15. Brown, M., Saisubramanian, S., Varakantham, P. R., & Tambe, M. (2014). STREETS: Game-theoretic traffic patrolling with exploration and exploitation. Proceedings of the National Conference on Artificial Intelligence, 4, 2966–2971.

    Google Scholar 

  16. Bucarey, V., Casorrán, C., Labbé, M., Ordóñez, F., & Figueroa, O. (2019). Coordinated defender strategies for border patrols. European Journal of Operational Research.

  17. Bucarey, V., Ordóñez, F., & Bassaletti, E. (2015). Shape and balance in police districting. In H. Eiselt & V. Marianov (Eds.), Applications of location analysis (Vol. 232). Cham: Springer. https://doi.org/10.1007/978-3-319-20282-2_14.

    Chapter  Google Scholar 

  18. Camacho-Collados, M., & Liberatore, F. (2015). A decision support system for predictive police patrolling. Decision Support Systems, 75, 25–37.

    Google Scholar 

  19. Camacho-Collados, M., Liberatore, F., & Angulo, J. M. (2015). A multi-criteria police districting problem for the efficient and effective design of patrol sector. European Journal of Operational Research, 246, 674–684.

    Google Scholar 

  20. Çapar, I., Keskin, B. B., & Rubin, P. A. (2015). An improved formulation for the maximum coverage patrol routing problem. Computers & Operations Research, 59, 1–10.

    Google Scholar 

  21. Caskey, T. R., Wasek, J. S., & Franz, A. Y. (2018). Deter and protect: crime modeling with multi-agent learning. Complex & Intelligent Systems, 4, 155–169.

    Google Scholar 

  22. Chaiken, J. M., & Dormont, P. (1978). A patrol car allocation model: Capabilities and algorithms. Management Science, 24, 1291–1300.

    Google Scholar 

  23. Chamikara, M. A. P., Yapa, Y., Kodituwakku, S. R., & Gunathilake, J. (2012). SL-SecureNet: Intelligent policing using data mining techniques. International Journal of Soft Computing and Engineering, 2, 175–180.

    Google Scholar 

  24. Chawathe, S. S. (2007). Organizing hot-spot police patrol routes. In Intelligence and security informatics, IEEE, pp. 79–86.

  25. Chelst, K. (1978). An algorithm for deploying a crime directed (tactical) patrol force. Management Science, 24, 1314–1327.

    Google Scholar 

  26. Chelst, K. R. (1981). Deployment of one-vs. two-officer patrol units: A comparison of travel times. Management Science, 27, 213–230.

    Google Scholar 

  27. Chen, H., Cheng, T., & Shawe-Taylor, J. (2018). A balanced route design for min-max multiple-depot rural postman problem (MMMDRPP): A police patrolling case. International Journal of Geographical Information Science, 32, 169–190.

    Google Scholar 

  28. Chen, H., Cheng, T., & Wise, S. (2015). Designing daily patrol routes for policing based on ant colony algorithm. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2, 103–109.

    Google Scholar 

  29. Chen, H., Cheng, T., & Wise, S. (2017). Developing an online cooperative police patrol routing strategy. Computers, Environment and Urban Systems, 62, 19–29.

    Google Scholar 

  30. Chen, H., Cheng, T., & Ye, X. (2019). Designing efficient and balanced police patrol districts on an urban street network. International Journal of Geographical Information Science, 33, 269–290.

    Google Scholar 

  31. Chen, X. (2012). Fast patrol route planning in dynamic environments. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 42, 894–904.

    Google Scholar 

  32. Chen, X. (2013). Police patrol optimization with security level functions. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 43, 1042–1051.

    Google Scholar 

  33. Chen, X., & Yum, T.-S. P. (2010). Cross entropy approach for patrol route planning in dynamic environments. In 2010 IEEE international conference on intelligence and security informatics, pp. 114–119.

  34. Chevaleyre, Y. (2004). Theoretical analysis of the multi-agent patrolling problem. In Proceedings of IEEE/WIC/ACM international conference on intelligent agent technology, pp. 302–308.

  35. Chow, A. H. F., Cheung, C. Y., & Yoon, H. T. (2015). Optimization of police facility locationing. Transportation Research Record: Journal of the Transportation Research Board, 2528, 60–68.

    Google Scholar 

  36. Coupe, R. T., & Girling, A. J. (2001). Modelling police success in catching burglars in the act. Omega, 29, 19–27.

    Google Scholar 

  37. Curtin, K. M., Hayslett-McCall, K., & Qiu, F. (2010). Determining optimal police patrol areas with maximal covering and backup covering location models. Networks and Spatial Economics, 10, 125–145.

    Google Scholar 

  38. D’Amico, S. J., Wang, S.-J., Batta, R., & Rump, C. M. (2002). A simulated annealing approach to police district design. Computers & Operations Research, 29, 667–684.

    Google Scholar 

  39. Delle Fave, F. M., Jiang, A. X., Yin, Z., Zhang, C., Tambe, M., Kraus, S., & Sullivan, J. P. (2014). Game-theoretic patrolling with dynamic execution uncertainty and a case study on a real transit system. Journal of Artificial Intelligence Research, 50, 321–367.

    Google Scholar 

  40. Department of Justice US. (2009). Law enforcement officers killed & assaulted. https://ucr.fbi.gov/leoka/2009/leoka-2009.

  41. Dewil, R., Vansteenwegen, P., Cattrysse, D., & Van Oudheusden, D. (2015). A minimum cost network flow model for the maximum covering and patrol routing problem. European Journal of Operational Research, 247, 27–36.

    Google Scholar 

  42. Elmaliach, Y., Agmon, N., & Kaminka, G. A. (2009). Multi-robot area patrol under frequency constraints. Annals of Mathematics and Artificial Intelligence, 57, 293–320.

    Google Scholar 

  43. Eugene, & Memorandum. (2018). https://www.eugene-or.gov/DocumentCenter/View/9728.

  44. Fang, F., Jiang, A. X., & Tambe, M. (2013). Optimal patrol strategy for protecting moving targets with multiple mobile resources. In Proceedings of the 2013 international conference on autonomous agents and multi-agent systems, pp. 957–964.

  45. Furtado, V., Melo, A., Menezes, R., & Belchior, M. (2006). Using self-organization in an agent framework to model criminal activity in response to police patrol routes. In FLAIRS conference, pp. 68–73.

  46. Furtado, V., & Vasconcelos, E. (2006). A multiagent simulator for teaching police allocation. AI Magazine, 27, 63–74.

    Google Scholar 

  47. Geroliminis, N., Karlaftis, M. G., & Skabardonis, A. (2009). A spatial queuing model for the emergency vehicle districting and location problem. Transportation Research Part B: Methodological, 43, 798–811.

    Google Scholar 

  48. Geroliminis, N., Kepaptsoglou, K., & Karlaftis, M. G. (2011). A hybrid hypercube–genetic algorithm approach for deploying many emergency response mobile units in an urban network. European Journal of Operational Research, 210, 287–300.

    Google Scholar 

  49. Goldberg, J., & Paz, L. (1991). Locating emergency vehicle bases when service time depends on call location. Transportation Science, 25, 264–280.

    Google Scholar 

  50. Goldstein, H. (1990). Problem-oriented policing. New York: McGraw-Hill.

    Google Scholar 

  51. Gómez, J., Hernández, V., & Cobo, L. (2015). Urban security system based on quadrants. Procedia Computer Science, 52, 636–640.

    Google Scholar 

  52. Goss, C. W., Van Bramer, L. D., Gliner, J. A., Porter, T. R., Roberts, I. G., & DiGuiseppi, C. (2008). Increased police patrols for preventing alcohol-impaired driving. Cochrane Database of Systematic Reviews, 4, CD005242.

    Google Scholar 

  53. Graper, E. D. (1921). American police administration: A handbook on police organization and methods of administration in American cities. New York: Macmillan.

    Google Scholar 

  54. Green, L. (1984). A multiple dispatch queueing model of police patrol operations. Management Science, 30, 653–664.

    Google Scholar 

  55. Green, L., & Kolesar, P. (1984). A comparison of the multiple dispatch and M/M/c priority queueing models of police patrol. Management Science, 30, 665–670.

    Google Scholar 

  56. Green, L., & Kolesar, P. (1989). Testing the validity of a queueing model of police patrol. Management Science, 35, 127–148.

    Google Scholar 

  57. Grujičić, I., & Stanimirović, Z. (2012). Variable neighborhood search method for optimizing the emergency service network of police special forces units. Electronic Notes in Discrete Mathematics, 39, 185–192.

    Google Scholar 

  58. Guerette, R. T. (2009). Analyzing crime displacement and diffusion. US Department of Justice, Office of Community Oriented Policing Services Washington, DC. https://popcenter.asu.edu/sites/default/files/tools/pdfs/displacement.pdf.

  59. Gupta, M., Chandra, B., & Gupta, M. P. (2014). A framework of intelligent decision support system for Indian police. Journal of Enterprise Information Management, 27, 512–540.

    Google Scholar 

  60. Hochbaum, D. S., Lyu, C., & Ordóñez, F. (2014). Security routing games with multivehicle Chinese postman problem. Networks, 64(3), 181–191.

    Google Scholar 

  61. Junior, A. A., Cacho, N., Thome, A. C., Medeiros, A., & Borges, J. (2017). A predictive policing application to support patrol planning in smart cities. In 2017 International smart cities conference (ISC2), pp. 1–6.

  62. Kar, D., Nguyen, T. H., Fang, F., Brown, M., Sinha, A., Tambe, M., & Jiang, A. X. (2018). Trends and applications in Stackelberg Security Games. In T. Başar, & G. Zaccour (Eds.), Handbook of dynamic game theory, Springer , pp. 1223–1269.

  63. Karn, J. (2013). Policing and crime reduction: The evidence and its implications for practice. https://www.academia.edu/4282142/Policing_and_Crime_Reduction_The_evidence_and_its_implications_for_practice.

  64. Kennedy, L. W., Caplan, J. M., & Piza, E. (2011). Risk clusters, hotspots, and spatial intelligence: risk terrain modeling as an algorithm for police resource allocation strategies. Journal of Quantitative Criminology, 27, 339–362.

    Google Scholar 

  65. Keskin, B. B., Li, S. R., Steil, D., & Spiller, S. (2012). Analysis of an integrated maximum covering and patrol routing problem. Transportation Research Part E: Logistics and Transportation Review, 48, 215–232.

    Google Scholar 

  66. Kiekintveld, C., Jain, M., Tsai, J., Pita, J., Ordóñez, F., & Tambe, M. (2009). Computing optimal randomized resource allocations for massive security games. In Proceedings of the 8th international conference on autonomous agents and multiagent systems, Vol.1, pp. 689–696.

  67. Kolesar, P. J., Rider, K. L., Crabill, T. B., & Walker, W. E. (1975). A queuing-linear programming approach to scheduling police patrol cars. Operations Research, 23, 1045–1062.

    Google Scholar 

  68. Kong, Y., Zhu, Y., & Wang, Y. (2019). A center-based modeling approach to solve the districting problem. International Journal of Geographical Information Science, 33, 368–384.

    Google Scholar 

  69. Kratcoski, P. C., & Das, D. K. (2002). Traffic policing: an international perspective. Policing: An International Journal of Police Strategies & Management, 25, 619–630.

    Google Scholar 

  70. Kuo, P.-F., Lord, D., & Walden, T. D. (2013). Using geographical information systems to organize police patrol routes effectively by grouping hotspots of crash and crime data. Journal of Transport Geography, 30, 138–148.

    Google Scholar 

  71. Kwak, N. K., & Leavitt, M. B. (1984). Police patrol beat design: Allocation of effort and evaluation of expected performance. Decision Sciences, 15, 421–433.

    Google Scholar 

  72. Larson, R. C. (1972). Urban police patrol analysis. Cambridge: The MIT Press.

    Google Scholar 

  73. Larson, R. C. (1974). A hypercube queuing model for facility location and redistricting in urban emergency services. Computers & Operations Research, 1, 67–95.

    Google Scholar 

  74. Larson, R. C. (1975). Approximating the performance of urban emergency service systems. Operations Research, 23, 845–868.

    Google Scholar 

  75. Larson, R. C., & Mcknew, M. A. (1982). Police patrol-initiated activities within a systems queueing model. Management Science, 28, 759–774.

    Google Scholar 

  76. Larson, R. C., & Stevenson, K. A. (1972). On insensitivities in urban redistricting and facility location. Operations Research, 20, 595–612.

    Google Scholar 

  77. Lau, H. C. W., Ho, G. T. S., Zhao, Y., & Hon, W. T. (2010). Optimizing patrol force deployment using a genetic algorithm. Expert Systems with Applications, 37, 8148–8154.

    Google Scholar 

  78. Lau, H. C., Yuan, Z., & Gunawan, A. (2016). Patrol scheduling in urban rail network. Annals of Operations Research, 239, 317–342.

    Google Scholar 

  79. Leahy, F., Jr. (1968). A literature review of police planning and research. Hartford: The Travelers Research Center.

    Google Scholar 

  80. Lee, S. M., Franz, L. S., & Wynne, A. J. (1979). Optimizing state patrol manpower allocation. Journal of the Operational Research Society, 30, 885–896.

    Google Scholar 

  81. Leigh, J., Dunnett, S., & Jackson, L. (2017). Predictive police patrolling to target hotspots and cover response demand. Annals of Operations Research. https://doi.org/10.1007/s10479-017-2528-x.

    Article  Google Scholar 

  82. Li, L., Jiang, Z., Duan, N., Dong, W., Hu, K., & Sun, W. (2011). Police patrol service optimization based on the spatial pattern of hotspots. In Proceedings of 2011 IEEE international conference on service operations, logistics and informatics, pp. 45–50.

  83. Liberatore, F., & Camacho-Collados, M. (2016). A comparison of local search methods for the multicriteria police districting problem on graph. Mathematical Problems in Engineering, 2016, 1–13.

    Google Scholar 

  84. Liberatore, F., Camacho-Collados, M., & Vitoriano, B. (2020). Police districting problem: Literature review and annotated bibliography. Optimal districting and territory design (pp. 9–29). Cham: Springer.

    Google Scholar 

  85. Lin, K. Y., Atkinson, M. P., Chung, T. H., & Glazebrook, K. D. (2013). A graph patrol problem with random attack times. Operations Research, 61, 694–710.

    Google Scholar 

  86. Major Cities Chiefs Association (MCCA). (2006). More policing does matter–Recent findings from objective empirical research. https://www.majorcitieschiefs.com/pdf/news/more_policing_does_matter.pdf.

  87. Malik, A., Maciejewski, R., Towers, S., McCullough, S., & Ebert, D. S. (2014). Proactive spatiotemporal resource allocation and predictive visual analytics for community policing and law enforcement. IEEE transactions on visualization and computer graphics, 20, 1863–1872.

    Google Scholar 

  88. Mohler, G. O., Short, M. B., Malinowski, S., Johnson, M., Tita, G. E., Bertozzi, A. L., & Brantingham, P. J. (2015). Randomized controlled field trials of predictive policing. Journal of the American Statistical Association, 110, 1399–1411.

    Google Scholar 

  89. Moonen, M., Cattrysse, D., & Van Oudheusden, D. (2007). Organising patrol deployment against violent crimes. Operational Research, 7, 401–417.

    Google Scholar 

  90. Muaafa, M., & Ramirez-Marquez, J. E. (2017). Engineering management models for urban security. IEEE Transactions on Engineering Management, 64, 29–41.

    Google Scholar 

  91. Mukhopadhyay, A., Zhang, C., Vorobeychik, Y., Tambe, M., Pence, K., & Speer, P. (2016). Optimal allocation of police patrol resources using a continuous-time crime model. In International conference on decision and game theory for security, pp. 139–158.

  92. Novak, K. J., Fox, A. M., Carr, C. M., & Spade, D. A. (2016). The efficacy of foot patrol in violent places. Journal of Experimental Criminology, 12, 465–475.

    Google Scholar 

  93. Oghovese, O., & Olaniyi, O. S. (2014). On optimal allocation of crime preventing patrol team using dynamic programming. International Journal of Mathematics and Statistics Invention, 2, 7–17.

    Google Scholar 

  94. Olson, D. G., & Wright, G. P. (1975). Models for allocating police preventive patrol effort. Journal of the Operational Research Society, 26, 703–715.

    Google Scholar 

  95. Ordónez, F., Tambe, M., Jara, J. F., Jain, M., Kiekintveld, C., & Tsai, J. (2013). Deployed security games for patrol planning. In Handbook of operations research for homeland security, Springer, pp. 45–72.

  96. Papadaki, K., Alpern, S., Lidbetter, T., & Morton, A. (2016). Patrolling a border. Operations Research, 64, 1256–1269.

    Google Scholar 

  97. Paruchuri, P., Pearce, J. P., Marecki, J., Tambe, M., Ordonez, F., & Kraus, S. (2008). Efficient algorithms to solve Bayesian stackelberg games for security applications. In AAAI, pp. 1559–1562.

  98. Pasqualetti, F., Durham, J. W., & Bullo, F. (2012a). Cooperative patrolling via weighted tours: Performance analysis and distributed algorithms. IEEE Transactions on Robotics, 28, 1181–1188.

    Google Scholar 

  99. Pasqualetti, F., Franchi, A., & Bullo, F. (2012b). On cooperative patrolling: Optimal trajectories, complexity analysis, and approximation algorithms. IEEE Transactions on Robotics, 28, 592–606.

    Google Scholar 

  100. Pita, J., Jain, M., Marecki, J., Ordóñez, F., Portway, C., Tambe, M., Western, C., Paruchuri, P., & Kraus, S. (2008). Deployed ARMOR protection: The application of a game theoretic model for security at the Los Angeles International Airport. In Proceedings of the 7th international joint conference on autonomous agents and multiagent systems: industrial track, pp. 125–132.

  101. Porras, C., Fajardo, J., & Rosete, A. (2019). Multi-coverage dynamic maximal covering location problem. Investigación Operacional, 40, 140–150.

    Google Scholar 

  102. Portugal, D., & Rocha, R. (2010). Msp algorithm: Multi-robot patrolling based on territory allocation using balanced graph partitioning. In Proceedings of the 2010 ACM symposium on applied computing, pp. 1271–1276.

  103. Portugal, D., & Rocha, R. P. (2012). Decision methods for distributed multi-robot patrol. In 2012 IEEE international symposium on safety, security, and rescue robotics (SSRR), pp. 1–6.

  104. Portugal, D., & Rocha, R. P. (2013a). Distributed multi-robot patrol: A scalable and fault-tolerant framework. Robotics and Autonomous Systems, 61, 1572–1587.

    Google Scholar 

  105. Portugal, D., & Rocha, R. P. (2013b). Multi-robot patrolling algorithms: Examining performance and scalability. Advanced Robotics, 27, 325–336.

    Google Scholar 

  106. Reis, D., Melo, A., Coelho, A., & Furtado, V. (2006). GAPatrol: An evolutionary multiagent approach for the automatic definition of hotspots and patrol routes. In Advances in artificial intelligence-IBERAMIA-SBIA 2006, pp. 118–127.

  107. Reppetto, T. A. (1974). Residential crime. MA: Ballinger Publishing Company Cambridge.

    Google Scholar 

  108. Rosenshine, M. (1970). Contributions to a theory of patrol scheduling. Operational Research Quarterly, 21, 99–106.

    Google Scholar 

  109. Sacks, S. R. (2000). Optimal spatial deployment of police patrol cars. Social Science Computer Review, 18, 40–55.

    Google Scholar 

  110. Saladin, B. A. (1982). Goal programming applied to police patrol allocation. Journal of Operations Management, 2, 239–249.

    Google Scholar 

  111. Santana, H., Ramalho, G., Corruble, V., & Ratitch, B. (2004). Multi-agent patrolling with reinforcement learning. In Proceedings of the third international joint conference on autonomous agents and multiagent systems, Vol. 3, pp. 1122–1129.

  112. Sathyadevan, S., & Gangadharan, S. S. (2014). Crime analysis and prediction using data mining. In 2014 First international conference on networks & soft computing (ICNSC2014), pp. 406–412.

  113. Shapiro, A. (2017). Reform predictive policing. Nature, 541, 458–460.

    Google Scholar 

  114. Smith, D. K. (1997). Police patrol policies on motorways with unequal patrol lengths. Journal of the Operational Research Society, 48, 996–1000.

    Google Scholar 

  115. Steil, D. A., Pate, J. R., Kraft, N. A., Smith, R. K., Dixon, B., Ding, L., & Parrish, A. (2011). Patrol routing expression, execution, evaluation, and engagement. IEEE Transactions on Intelligent Transportation Systems, 12, 58–72.

    Google Scholar 

  116. Stranders, R., De Cote, E. M., Rogers, A., & Jennings, N. R. (2013). Near-optimal continuous patrolling with teams of mobile information gathering agents. Artificial intelligence, 195, 63–105.

    Google Scholar 

  117. Taylor, B., Koper, C. S., & Woods, D. J. (2011). A randomized controlled trial of different policing strategies at hot spots of violent crime. Journal of Experimental Criminology, 7, 149–181.

    Google Scholar 

  118. Taylor, B. W. III, Moore, L. J., Clayton, E. R., Davis, K. R., & Rakes, T. R. (1985). An integer nonlinear goal programming model for the deployment of state highway patrol units. Management Science, 31, 1335–1347.

    Google Scholar 

  119. Taylor, P. E., & Huxley, S. J. (1989). A break from tradition for the San Francisco police: Patrol officer scheduling using an optimization-based decision support system. Interfaces, 19, 4–24.

    Google Scholar 

  120. Trojanowicz, R., & Bucqueroux, B. (1990). Community policing: A contemporary perspective, Anderson, Cincinnati, OH.

  121. Uk Police. (2011). The effectiveness of visible police patrol. https://whatworks.college.police.uk/Research/overview/Documents/WW_overview_Visible_patrol.pdf.

  122. Vollmer, A. (1930). Survey of the Police Department. Minneapolis Police Department.

  123. Weisburd, S. (2018). Police presence, rapid response rates, and crime prevention, pp. 1–59. https://saritw.weebly.com/uploads/2/8/7/9/28790127/police_aej_feb26.pdf.

  124. Wenger, D. E., Quarantelli, E. L., & Dynes, R. R. (1989). Disaster analysis: Police and fire departments. The Disaster Research Center, University of Delaware, Newark, DE. http://udspace.udel.edu/handle/19716/1141.

  125. White, R. D., Bunch, T. J., & Hankins, D. G. (2005). Evolution of a community-wide early defibrillation programme: experience over 13 years using police/fire personnel and paramedics as responders. Resuscitation, 65, 279–283.

    Google Scholar 

  126. Willemse, E. J., & Joubert, J. W. (2012). Applying min–max k postmen problems to the routing of security guards. Journal of the Operational Research Society, 63, 245–260.

    Google Scholar 

  127. Wilson, J. Q., & Kelling, G. L. (1982). Broken windows. Atlantic monthly, 249, 29–38.

    Google Scholar 

  128. Wright, P. D., Liberatore, M. J., & Nydick, R. L. (2006). A survey of operations research models and applications in homeland security. Interfaces, 36(6), 514–529.

    Google Scholar 

  129. Zarandi, M. H. F., Davari, S., & Sisakht, S. A. H. (2011). The large scale maximal covering location problem. Scientia Iranica, 18, 1564–1570.

    Google Scholar 

  130. Zhang, Y., & Brown, D. E. (2013). Police patrol districting method and simulation evaluation using agent-based model & GIS. Security Informatics, 2, 1–13.

    Google Scholar 

  131. Zhang, Y., & Brown, D. (2014). Simulation optimization of police patrol districting plans using response surfaces. Simulation, 90, 687–705.

    Google Scholar 

  132. Zhang, C., Bucarey, V., Mukhopadhyay, A., Sinha, A., Yundi, Q., Vorobeychik, Y., & Tambe, M. (2016a). Using abstractions to solve opportunistic crime security games at scale. In Proceedings of 15th international conference on autonomous agents and multiagent systems (AAMAS), Research Collection School Of Information Systems.

  133. Zhang, C., Sinha, A., & Tambe, M. (2015). Keeping pace with criminals: Designing patrol allocation against adaptive opportunistic criminals. In Proceedings of the 2015 international conference on autonomous agents and multiagent systems, pp. 1351–1359.

  134. Zhang, H., Tako, A. A., Jackson, L. M., & Liu, J. (2016b). Simulation combined approach to police patrol services staffing. In 5th Student conference on operational research (SCOR 2016b), pp. 1–11.

  135. Zhang, Y., Xiao, Y., Wang, Y., & Mosca, P. (2017). Bio-inspired patrolling scheme design in wireless and mobile sensor and robot networks. Wireless Personal Communications, 92, 1303–1332.

    Google Scholar 

  136. Zhao, K. Q., Luo, L., & Xia, Y. M. (2012). The optimal dispatch of traffic and patrol police service platforms. Journal of Applied Mathematics.  https://doi.org/10.1155/2012/292415.

  137. Zipkin, J. R., Short, M. B., & Bertozzi, A. L. (2014). Cops on the dots in a mathematical model of urban crime and police response. Discrete and Continuous Dynamical Systems: Series B, 19, 1479–1506.

    Google Scholar 

  138. Zoroa, N., Fernández-Sáez, M. J., & Zoroa, P. (2012). Patrolling a perimeter. European Journal of Operational Research, 222, 571–582.

    Google Scholar 

Download references

Funding

The funding was provided by Science and Engineering Research Board, Department of Science and Technology (Grand No. SRG/2020/001887).

Author information

Authors and Affiliations

  1. Advanced Technology Development Centre, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

    Sukanya Samanta

  2. Department of Industrial and Systems Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, 721302, India

    Goutam Sen

  3. Department of Computer Science and Engineering, Indian Institute of Technology, Kharagpur, Kharagpur, West Bengal, 721302, India

    Soumya Kanti Ghosh

Authors
  1. Sukanya Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Goutam Sen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Soumya Kanti Ghosh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Goutam Sen.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Samanta, S., Sen, G. & Ghosh, S.K. A literature review on police patrolling problems. Ann Oper Res 316, 1063–1106 (2022). https://doi.org/10.1007/s10479-021-04167-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-021-04167-0

Keywords

Search

Navigation