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Applying min–max k postmen problems to the routing of security guards

Author

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  • E J Willemse

    (Logistics and Quantitative Methods, CSIR: Built Environment, Pretoria, South Africa)

  • J W Joubert

    (Optimisation Group, Department of Industrial and System Engineering, University of Pretoria, Pretoria, South Africa)

Abstract

The most essential and alluring characteristic of a security estate is the estate's ability to provide 24-h security to its residents, of which the continual patrolling of roads and paths is vital. The objective of this paper is to address the lack of sufficient patrol route design procedures by presenting a tabu search algorithm capable of generating multiple patrol routes for an estate's security guards. The paper shows that the problem of designing these routes can be modelled as an Arc Routing Problem, specifically as min–max k postmen problems. The algorithm is illustrated with a real problem instance from an estate in Gauteng, South Africa. The patrol routes generated by the algorithm provide a significant improvement in the even patrolling of the road network, and a more balanced work distribution among guards. The algorithm is also tested on several benchmark problems from literature.

Suggested Citation

  • E J Willemse & J W Joubert, 2012. "Applying min–max k postmen problems to the routing of security guards," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(2), pages 245-260, February.
    • Handle: RePEc:pal:jorsoc:v:63:y:2012:i:2:p:245-260
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    Citations

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    Cited by:

    1. Jesica Armas & Peter Keenan & Angel A. Juan & Seán McGarraghy, 2019. "Solving large-scale time capacitated arc routing problems: from real-time heuristics to metaheuristics," Annals of Operations Research, Springer, vol. 273(1), pages 135-162, February.
    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. Wei Yu, 2023. "Improved approximation algorithms for some min–max postmen cover problems with applications to the min–max subtree cover," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(1), pages 135-157, February.
    4. Elena Fernández & Jessica Rodríguez-Pereira, 2017. "Multi-depot rural postman problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 340-372, July.
    5. 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).

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