Annals of Operations Research

, Volume 258, Issue 2, pp 679–717 | Cite as

Location-coverage models for preventing attacks on interurban transportation networks

  • Ramon Auad
  • Rajan BattaEmail author


Interurban roads are constantly used by transient vehicles. In some places, however, network users are subject to attacks, resulting in assaults to drivers and cargo theft. In an attempt to solve this problem, a binary integer programming model is developed, whose objective is to maximize the expected vehicle coverage across the network. The model dynamically locates patrol units through a fixed time horizon, subject to movement and location constraints, considering a probability of not being able to attend to an attack, due to a distance factor. A chronological decomposition heuristic is developed, and achieves an optimality gap of less than 1 %, in less than 5 min. The problem is also solved by developing a geographical decomposition heuristic. To introduce a measure of equity, two sets of constraints are proposed. Three measures are considered: total vehicle coverage, inequity and network coverage. A trade-off between these three measures is observed and discussed. Finally, scalability of the model is explored, using decomposition in terms of patrolling units, until we obtain subproblems of equal size as the original instance. All of these features are applied to a case study in Northern Israel. In the last section, some adaptations and additions to the model that can be made in further research are discussed.


Location Patrolling Coverage Transportation  Traffic police Routing 



The authors would like to thank the Associate Editor and anonymous referees for their comments on earlier versions of this paper. This proved to be of great help, specially for improving many explanations in this work.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.


  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(1), 9–31.CrossRefGoogle 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(5–6), 315–333.CrossRefGoogle Scholar
  3. Anderson, B. (2007). Securing the supply chain-prevent cargo theft. Security, 44(5), 56–59.Google Scholar
  4. Badri, M. A., Mortagy, A. K., & Alsayed, C. A. (1998). A multi-objective model for locating fire stations. European Journal of Operational Research, 110(2), 243–260.CrossRefGoogle Scholar
  5. Barth, S., & White, M. (1998). Hazardous cargo. World, 11(11), 46–48.Google Scholar
  6. Bassett, M. H., Pekny, J. F., & Reklaitis, G. V. (1996). Decomposition techniques for the solution of large-scale scheduling problems. AIChE Journal, 42(12), 3373–3387.CrossRefGoogle Scholar
  7. Batta, R., Dolan, J. M., & Krishnamurthy, N. N. (1989). The maximal expected covering location problem: Revisited. Transportation Science, 23(4), 277–287.CrossRefGoogle Scholar
  8. Berman, O., & Krass, D. (2002). The generalized maximal covering location problem. Computers & Operations Research, 29(6), 563–581.CrossRefGoogle Scholar
  9. Brotcorne, L., Laporte, G., & Semet, F. (2003). Ambulance location and relocation models. European Journal of Operational Research, 147(3), 451–463.CrossRefGoogle Scholar
  10. Capar, I., Keskin, B. B., & Rubin, P. A. (2015). An improved formulation for the maximum coverage patrol routing problem. Computers & Operations Research, 59, 1–10.CrossRefGoogle Scholar
  11. Capar, I., & Kuby, M. (2012). An efficient formulation of the flow refueling location model for alternative-fuel stations. IIE Transactions, 44(8), 622–636.CrossRefGoogle Scholar
  12. Chapman, S., & White, J. (1974). Probabilistic formulations of emergency service facilities location problems. In ORSA/TIMS conference, San Juan, Puerto Rico.Google Scholar
  13. Church, R., & ReVelle, C. (1974). The maximal covering location problem. Papers in Regional Science, 32(1), 101–118.CrossRefGoogle Scholar
  14. Cox, A., Prager, F., & Rose, A. (2011). Transportation security and the role of resilience: A foundation for operational metrics. Transport Policy, 18(2), 307–317.CrossRefGoogle Scholar
  15. Current, J., Min, H., & Schilling, D. (1990). Multiobjective analysis of facility location decisions. European Journal of Operational Research, 49(3), 295–307.CrossRefGoogle Scholar
  16. Current, J. R., Velle, C. R., & Cohon, J. L. (1985). The maximum covering/shortest path problem: A multiobjective network design and routing formulation. European Journal of Operational Research, 21(2), 189–199.CrossRefGoogle Scholar
  17. 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
  18. 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 F. Wang (Ed.), Geographic information systems and crime analysis (Chap. 13, pp. 214–235). Hershey: IDEA Group Publishing.Google Scholar
  19. Daskin, M. S. (1983). A maximum expected covering location model: Formulation, properties and heuristic solution. Transportation Science, 17(1), 48–70.CrossRefGoogle Scholar
  20. Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische Mathematik, 1(1), 269–271.CrossRefGoogle Scholar
  21. Ekwall, D. (2010). On analysing the official statistics for antagonistic threats against transports in EU: A supply chain risk perspective. Journal of Transportation Security, 3(4), 213–230.CrossRefGoogle Scholar
  22. Hodgson, M. J. (1990). A flow-capturing location-allocation model. Geographical Analysis, 22(3), 270–279.CrossRefGoogle Scholar
  23. International Road Transport Union. (2008). Attacks on drivers of international heavy goods vehicles. Technical report, 3, rue de Varembé B.P. 44 CH-1211 Geneva 20 Switzerland.
  24. Kaza, S., Xu, J., Marshall, B., & Chen, H. (2009). Topological analysis of criminal activity networks: Enhancing transportation security. IEEE Transactions on Intelligent Transportation Systems, 10(1), 83–91.CrossRefGoogle Scholar
  25. Kelly, J. D. (2002). Chronological decomposition heuristic for scheduling: Divide and conquer method. AIChE Journal, 48(12), 2995–2999.CrossRefGoogle Scholar
  26. 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(1), 215–232.CrossRefGoogle Scholar
  27. Kuby, M., & Lim, S. (2005). The flow-refueling location problem for alternative-fuel vehicles. Socio-Economic Planning Sciences, 39(2), 125–145.CrossRefGoogle Scholar
  28. Kuby, M., & Lim, S. (2007). Location of alternative-fuel stations using the flow-refueling location model and dispersion of candidate sites on arcs. Networks and Spatial Economics, 7(2), 129–152.CrossRefGoogle Scholar
  29. Marianov, V., & Revelle, C. (1994). The queuing probabilistic location set covering problem and some extensions. Socio-Economic Planning Sciences, 28(3), 167–178.CrossRefGoogle Scholar
  30. Marshall, B., Kaza, S., Xu, J., Atabakhsh, H., Petersen, T., Violette, C., & Chen, H. (2004). Cross-jurisdictional criminal activity networks to support border and transportation security. In The 7th international IEEE conference on intelligent transportation systems, 2004. Proceedings (pp. 100–105). IEEE.Google Scholar
  31. Patel, D. J., Batta, R., & Nagi, R. (2005). Clustering sensors in wireless ad hoc networks operating in a threat environment. Operations Research, 53(3), 432–442.CrossRefGoogle Scholar
  32. Rajagopalan, H. K., Saydam, C., & Xiao, J. (2008). A multiperiod set covering location model for dynamic redeployment of ambulances. Computers & Operations Research, 35(3), 814–826.CrossRefGoogle Scholar
  33. Revelle, C., & Hogan, K. (1989). The maximum reliability location problem and \(\alpha \)-reliablep-center problem: Derivatives of the probabilistic location set covering problem. Annals of Operations Research, 18(1), 155–173.CrossRefGoogle Scholar
  34. ReVelle, C. S., & Eiselt, H. A. (2005). Location analysis: A synthesis and survey. European Journal of Operational Research, 165(1), 1–19.CrossRefGoogle Scholar
  35. Sahinidis, N., & Grossmann, I. E. (1991). Reformulation of multiperiod milp models for planning and scheduling of chemical processes. Computers & Chemical Engineering, 15(4), 255–272.CrossRefGoogle Scholar
  36. Secretariado Ejecutivo del Sistema Nacional de Seguridad Pública. (2015). Incidencia delictiva del fuero común 2014. Technical report, Gral. Mariano Escobedo 456, Anzures, Miguel Hidalgo, 11590 Ciudad de México, D.F., Mexico.
  37. Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971). The location of emergency service facilities. Operations Research, 19(6), 1363–1373.CrossRefGoogle Scholar
  38. Vaa, T. (1997). Increased police enforcement: Effects on speed. Accident Analysis & Prevention, 29(3), 373–385.CrossRefGoogle Scholar
  39. Van den Engel, A., & Prummel, E. (2007). Organised theft of commercial vehicles and their loads in the european union. European Parliament. Directorate General Internal Policies of the Union. Policy Department Structural and Cohesion Policies. Transport and Tourism, Brussels.Google Scholar
  40. Welch, T. F., & Mishra, S. (2013). A measure of equity for public transit connectivity. Journal of Transport Geography, 33, 29–41.CrossRefGoogle Scholar
  41. 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
  42. Yan, T., Gu, Y., He, T., & Stankovic, J. A. (2008). Design and optimization of distributed sensing coverage in wireless sensor networks. ACM Transactions on Embedded Computing Systems (TECS), 7(3), 33.CrossRefGoogle Scholar
  43. Yoon, S. W., Velasquez, J. D., Partridge, B., & Nof, S. Y. (2008). Transportation security decision support system for emergency response: A training prototype. Decision Support Systems, 46(1), 139–148.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departamento de Ingenieria IndustrialUniversidad Catolica del NorteAntofagastaChile
  2. 2.Department of Industrial and Systems EngineeringUniversity at Buffalo (SUNY)BuffaloUSA

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