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A minimum cost network flow model for the maximum covering and patrol routing problem

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  • Dewil, R.
  • Vansteenwegen, P.
  • Cattrysse, D.
  • Van Oudheusden, D.

Abstract

This paper shows how the maximum covering and patrol routing problem (MCPRP) can be modeled as a minimum cost network flow problem (MCNFP). Based on the MCNFP model, all available benchmark instances of the MCPRP can be solved to optimality in less than 0.4s per instance. It is furthermore shown that several practical additions to the MCPRP, such as different start and end locations of patrol cars and overlapping shift durations can be modeled by a multi-commodity minimum cost network flow model and solved to optimality in acceptable computational times given the sizes of practical instances.

Suggested Citation

  • 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, Elsevier, vol. 247(1), pages 27-36.
    • Handle: RePEc:eee:ejores:v:247:y:2015:i:1:p:27-36
    DOI: 10.1016/j.ejor.2015.05.067
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    References listed on IDEAS

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    Cited by:

    1. Paul A. Chircop & Timothy J. Surendonk & Menkes H. L. van den Briel & Toby Walsh, 2022. "On routing and scheduling a fleet of resource-constrained vessels to provide ongoing continuous patrol coverage," Annals of Operations Research, Springer, vol. 312(2), pages 723-760, May.
    2. Sukanya Samanta & Goutam Sen & Soumya Kanti Ghosh, 2022. "A literature review on police patrolling problems," Annals of Operations Research, Springer, vol. 316(2), pages 1063-1106, September.
    3. Xiuqiao Sun & Jian Wang & Weitiao Wu & Wenjia Liu, 2018. "Genetic Algorithm for Optimizing Routing Design and Fleet Allocation of Freeway Service Overlapping Patrol," Sustainability, MDPI, vol. 10(11), pages 1-15, November.
    4. Chen, Xinyuan & Wu, Shining & Liu, Yannick & Wu, Weiwei & Wang, Shuaian, 2022. "A patrol routing problem for maritime Crime-Fighting," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    5. Yuchen Luo & Bruce Golden & Rui Zhang, 2023. "The Hot Spot Coverage Patrol Problem: Formulations and Solution Approaches," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1286-1307, November.
    6. Timothy J. Surendonk & Paul A. Chircop, 2020. "On the computational complexity of the patrol boat scheduling problem with complete coverage," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(4), pages 289-299, June.

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