Annals of Operations Research

, Volume 221, Issue 1, pp 9–31 | Cite as

Location-allocation models for traffic police patrol vehicles on an interurban network

  • Nicole Adler
  • Alfred Shalom Hakkert
  • Jonathan Kornbluth
  • Tal Raviv
  • Mali Sher


This research investigates the traffic police routine patrol vehicle (RPV) assignment problem on an interurban road network through a series of integer linear programs. The traffic police RPV’s main task, like other emergency services, is to handle calls-for-service. Emergency services allocation models are generally based on the shortest path algorithm however, the traffic police RPV also handles other roles, namely patrolling to create a presence that acts as a deterrence, and issuing tickets to offenders. The RPVs need to be located dynamically on both hazardous sections and on roads with heavy traffic in order to increase their presence and conspicuousness, in an attempt to prevent or reduce traffic offences, road accidents and traffic congestion. Due to the importance of the traffic patrol vehicle’s location with regard to their additional roles, allocation of the RPVs adheres to an exogenous, legal, time-to-arrival constraint. We develop location-allocation models and apply them to a case study of the road network in northern Israel. The results of the four models are compared to each other and in relation to the current chosen locations. The multiple formulations provide alternatives that jointly account for road safety and policing objectives which aid decision-makers in the selection of their preferred RPV assignments. The results of the models present a location-allocation configuration per RPV per shift with full call-for-service coverage whilst maximizing police presence and conspicuousness as a proxy for road safety.


Location Allocation Network Emergency services Traffic police 


  1. Araz, C., Selim, H., & Ozkaraham, I. (2007). A fuzzy multi-objective covering-based vehicle location model for emergency services. Computers & Operations Research, 34, 705–726. CrossRefGoogle Scholar
  2. Balas, E., & Jeroslow, R. (1972). Canonical cuts on the unit hypercube. SIAM Journal on Applied Mathematics, 23(1), 61–69. CrossRefGoogle Scholar
  3. Becker, G. S. (1968). Crime and punishment: an economic approach. Journal of Political Economy, 76(2), 169–217. CrossRefGoogle Scholar
  4. Beenstock, M., & Gafni, D. (2000). Globalization in road safety: explaining the downward trend in road accident rates in a single country (Israel). Accident Analysis and Prevention, 32(1), 71–84. CrossRefGoogle Scholar
  5. Berman, O., Drezner, Z., & Krass, D. (2010). Generalized coverage: new developments in covering location models. Computers & Operations Research, 37, 1675–1687. CrossRefGoogle Scholar
  6. Bester, C. J. (2001). Explaining national road fatalities. Accident Analysis and Prevention, 33(5), 663–672. CrossRefGoogle Scholar
  7. Birge, J. R., & Pollock, S. M. (1989). Modelling rural police patrol. Journal of the Operational Research Society, 40(1), 41–54. CrossRefGoogle Scholar
  8. Chaiken, J. M., & Dormont, P. (1978a). A patrol car allocation model: background. Management Science, 24(12), 1280–1290. CrossRefGoogle Scholar
  9. Chaiken, J. M., & Dormont, P. (1978b). A patrol car allocation model: capabilities and algorithms. Management Science, 24(12), 1291–1300. CrossRefGoogle Scholar
  10. Chang, L. Y., & Chen, W. C. (2005). Data mining of tree-based models to analyze freeway accident frequency. Journal of Safety Research, 36, 365–375. CrossRefGoogle Scholar
  11. Christensen, P., & Elvik, R. (2007). Effects on accidents of periodic motor vehicle inspection in Norway. Accident Analysis and Prevention, 39, 47–52. CrossRefGoogle Scholar
  12. Church, R., & Revelle, C. (1974). The maximal covering location problem. Papers in Regional Science, 32, 101–118. CrossRefGoogle Scholar
  13. Church, R., Sorensen, P., & Corrigan, W. (2001). Manpower deployment in emergency services. Fire Technology, 37, 219–234. CrossRefGoogle Scholar
  14. Coleman, T. F., & Moré, J. J. (1983). Estimation of sparse Jacobian matrices and graph coloring problems. SIAM Journal on Numerical Analysis, 20(1), 187–209. CrossRefGoogle Scholar
  15. Curtin, K. M., Qiu, F., Hayslett-McCall, K., & Bray, T. M. (2005). Integrating GIS and maximal covering models to determine optimal police patrol areas. In GIS and crime analysis (Chap. XIII). Google Scholar
  16. 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(1), 125–145. CrossRefGoogle Scholar
  17. Daskin, M. S. (1982). Application of an expected covering model to emergency medical service system design. Decision Sciences, 13(3), 416–439. CrossRefGoogle Scholar
  18. Daskin, M. S. (1995). Network and discrete location—models, algorithms and applications. New York: Wiley. CrossRefGoogle Scholar
  19. Daskin, M. S., Coullard, C. R., & Shen, Z. M. (2002). An inventory-location model: formulation, solution algorithm and computational results. Annals of Operations Research, 110, 83–106. CrossRefGoogle Scholar
  20. Dijkstra, E. W. (1959). A note on two problems in connection with graphs. Numerische Mathematik, 1, 269–271. CrossRefGoogle Scholar
  21. Elvik, R. (1997). Evaluations of road accident blackspot treatment: a case of the iron law of evaluation studies? Accident Analysis and Prevention, 29(2), 191–199. CrossRefGoogle Scholar
  22. Elvik, R., & Vaa, T. (2004). The handbook of road safety measurement. Oxford: Elsevier. Google Scholar
  23. ETSC (European Transport Safety Council) (May 1999). Police enforcement strategies to reduce traffic casualties in Europe, Brussels. Google Scholar
  24. Fell, J. C., Ferguson, S. A., Williams, A. F., & Fields, M. (2003). Why are sobriety checkpoints not widely adopted as an enforcement strategy in the United States? Accident Analysis and Prevention, 35(6), 897–902. CrossRefGoogle Scholar
  25. Francis, R. L., Lowe, T. J., Rayco, B., & Tamir, A. (2005). Aggregation error for location models: survey and analysis. Working paper, Department of Industrial and Systems Engineering, University of Florida, Gainesville.
  26. Garey, M. R., & Johnson, D. S. (1979). Computers and intractability: a guide to the theory of NP-completeness. New York: Freeman. Google Scholar
  27. Green, L. V., & Kolesar, P. J. (1989). Testing the validity of a queuing model of police patrol. Management Science, 35(2), 127–148. CrossRefGoogle Scholar
  28. Green, L. V., & Kolesar, P. J. (2004). Improving emergency responsiveness with management science. Management Science, 50(8), 1001–1014. CrossRefGoogle Scholar
  29. Hakkert, A. S., Yelinek, A., & Efrat, E. (1990). Police surveillance methods and police resource allocation models. In The international road safety symposium, Denmark. Google Scholar
  30. Hakkert, A. S., Gitelman, V., Cohen, A., Doveh, E., & Umansky, T. (2001). The evaluation of effects on driver behavior and accidents of concentrated general enforcement on interurban roads in Israel. Accident Analysis and Prevention, 33, 43–63. CrossRefGoogle Scholar
  31. Hauer, E. (2005). Fishing for safety information in murky waters. Journal of Transportation Engineering, 131(5), 340–344. CrossRefGoogle Scholar
  32. Hurley, W. J., Brimberg, J., & Pavlov, A. (2009). Optimal thresholds for fining speeders for a stationary speed-check operation when the traffic intensity is low. Journal of the Operational Research Society, 60, 1154–1159. CrossRefGoogle Scholar
  33. Israel Central Bureau of Statistics (2006). Traffic volumes. Google Scholar
  34. Larson, R. C. (1974). A hypercube queuing modeling for facility location and redistricting in urban emergency services. Computers & Operations Research, 50(1), 135–145. Google Scholar
  35. Larson, R. C., & McKnew, M. A. (1982). Police patrol-initiated activities within a systems queueing model. Management Science, 28(7), 759–774. CrossRefGoogle Scholar
  36. Ma, L. (2003). Integrating GIS and combinatorial optimization to determine police patrol areas. Master, GIS, supervised By Dr. Curtin Kevin, University of Texas at Dallas. Google Scholar
  37. Newstead, S. V., Cameron, M. H., & Leggett, L. M. W. (2001). The crash reduction effectiveness of a network-wide traffic police deployment system. Accident Analysis and Prevention, 33, 393–406. CrossRefGoogle Scholar
  38. OECD (Organisation for Economic Co-operation and Development) (1974). Research on traffic law enforcement. Paris, France. Google Scholar
  39. Owen, S. H. & Daskin, M. S. (1998). Strategic facility location: a review. European Journal of Operational Research, 111, 423–447. CrossRefGoogle Scholar
  40. Peleg, K. (2000). The effectiveness of Israel’s pre-hospital emergency medical services organization. PhD thesis, Ben-Gurion University, Beer-Sheba, Israel. Google Scholar
  41. Plastria, F., & Vanhaverbeke, L. (2007). Aggregation without loss of optimality in competitive location models. Networks and Spatial Economics, 7, 3–18. CrossRefGoogle Scholar
  42. ReVelle, C. S., & Eiselt, H. A. (2005). Location analysis: a synthesis and survey. European Journal of Operational Research, 165, 1–19. CrossRefGoogle Scholar
  43. Sacks, S. R. (2000). Optimal spatial deployment of police patrol cars. Social Science Computer Review, 18(1), 40–55. CrossRefGoogle Scholar
  44. Schrijver, A. (1998). Theory of linear and integer programming. New York: Wiley (Chap. 19, pp. 266–281). Google Scholar
  45. Simpson, N. C., & Hancock, P. G. (2009). Fifty years of operational research and emergency response. Journal of the Operational Research Society, 60, 126–139. CrossRefGoogle Scholar
  46. Tillyer, R., Engel, R. S., & Cherkauskas, J. C. (2010). Best practices in vehicle stop data collection and analysis. Policing: An International Journal of Police Strategies & Management, 33(1), 69–92. CrossRefGoogle Scholar
  47. Toregas, C., & ReVelle, C. (1973). Binary logic solutions to a class of location problem. Geographical Analysis, 5(2), 145–155. CrossRefGoogle Scholar
  48. Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971). The location of emergency service facilities. Operations Research, 19, 1363–1373. CrossRefGoogle Scholar
  49. Tsai, J. F., Lin, M. H., & Hu, Y. C. (2008). Finding multiple solutions to general integer linear programs. European Journal of Operational Research, 184, 802–809. CrossRefGoogle Scholar
  50. Vanlaar, W. (2008). Less is more: the influence of traffic count on drinking and driving behaviour. Accident Analysis and Prevention, 40, 1018–1022. CrossRefGoogle Scholar
  51. Walker, W., Chaiken, J., & Ignall, E. (1979). Fire department deployment analysis. The rand fire project. New York: Elsevier/North-Holland. Google Scholar
  52. 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. CrossRefGoogle Scholar
  53. Yin, Y. (2006). Optimal fleet allocation of freeway service patrols. Networks and Spatial Economics, 6, 221–234. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Nicole Adler
    • 1
  • Alfred Shalom Hakkert
    • 2
  • Jonathan Kornbluth
    • 1
  • Tal Raviv
    • 3
  • Mali Sher
    • 1
  1. 1.School of Business AdministrationHebrew University of JerusalemMount ScopusIsrael
  2. 2.Ran Naor Foundation for the Advancement of Road SafetyHodHasharonIsrael
  3. 3.Department of Industrial EngineeringTel Aviv UniversityTel AvivIsrael

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