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A mixed integer formulation and an efficient metaheuristic procedure for the k-Travelling Repairmen Problem

Author

Listed:
  • Samuel Nucamendi-Guillén

    (Universidad Panamericana)

  • Iris Martínez-Salazar

    (Universidad Autónoma de Nuevo León)

  • Francisco Angel-Bello

    (Tecnologico de Monterrey)

  • J Marcos Moreno-Vega

    (Universidad de La Laguna)

Abstract

In this paper, we study a k-Travelling Repairmen Problem where the objective is to minimize the sum of clients waiting time to receive service. This problem is relevant in applications that involve distribution of humanitarian aid in disaster areas, delivery and collection of perishable products and personnel transportation, where reaching demand points to perform service, fast and fair, is a priority. This paper presents a new mixed integer formulation and a simple and efficient metaheuristic algorithm. The proposed formulation consumes less computational time and allows solving to optimality more than three times larger data instances than the previous formulation published in literature, even outperforming a recently published Branch and Price and Cut algorithm for this problem. The proposed metaheuristic algorithm solved to optimality 386 out of 389 tested instances in a very short computational time. For larger instances, the algorithm was assessed using the best results reported in the literature for the Cumulative Capacitated Vehicle Routing Problem.

Suggested Citation

  • Samuel Nucamendi-Guillén & Iris Martínez-Salazar & Francisco Angel-Bello & J Marcos Moreno-Vega, 2016. "A mixed integer formulation and an efficient metaheuristic procedure for the k-Travelling Repairmen Problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(8), pages 1121-1134, August.
    • Handle: RePEc:pal:jorsoc:v:67:y:2016:i:8:d:10.1057_jors.2015.113
    DOI: 10.1057/jors.2015.113
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    References listed on IDEAS

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    1. Lysgaard, Jens & Wøhlk, Sanne, 2014. "A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 800-810.
    2. Luo, Zhixing & Qin, Hu & Lim, Andrew, 2014. "Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints," European Journal of Operational Research, Elsevier, vol. 234(1), pages 49-60.
    3. Silva, Marcos Melo & Subramanian, Anand & Vidal, Thibaut & Ochi, Luiz Satoru, 2012. "A simple and effective metaheuristic for the Minimum Latency Problem," European Journal of Operational Research, Elsevier, vol. 221(3), pages 513-520.
    4. Potvin, Jean-Yves & Rousseau, Jean-Marc, 1993. "A parallel route building algorithm for the vehicle routing and scheduling problem with time windows," European Journal of Operational Research, Elsevier, vol. 66(3), pages 331-340, May.
    5. SALEHIPOUR, Amir & SÖRENSEN, Kenneth & GOOS, Peter & BRÄYSY, Olli, 2008. "An efficient GRASP+VND metaheuristic for the traveling repairman problem," Working Papers 2008008, University of Antwerp, Faculty of Business and Economics.
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    Citations

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    Cited by:

    1. Timo Gschwind & Stefan Irnich & Simon Emde & Christian Tilk, 2018. "Branch-Cut-and-Price for the Scheduling Deliveries with Time Windows in a Direct Shipping Network," Working Papers 1805, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    2. Bruni, M.E. & Khodaparasti, S. & Beraldi, P., 2020. "The selective minimum latency problem under travel time variability: An application to post-disaster assessment operations," Omega, Elsevier, vol. 92(C).
    3. F. Angel-Bello & Y. Cardona-Valdés & A. Álvarez, 2019. "Mixed integer formulations for the multiple minimum latency problem," Operational Research, Springer, vol. 19(2), pages 369-398, June.
    4. Albert Einstein Fernandes Muritiba & Tibérius O. Bonates & Stênio Oliveira Da Silva & Manuel Iori, 2021. "Branch-and-Cut and Iterated Local Search for the Weighted k -Traveling Repairman Problem: An Application to the Maintenance of Speed Cameras," Transportation Science, INFORMS, vol. 55(1), pages 139-159, 1-2.
    5. Timo Gschwind & Stefan Irnich & Christian Tilk & Simon Emde, 2020. "Branch-cut-and-price for scheduling deliveries with time windows in a direct shipping network," Journal of Scheduling, Springer, vol. 23(3), pages 363-377, June.
    6. Ajam, Meraj & Akbari, Vahid & Salman, F. Sibel, 2019. "Minimizing latency in post-disaster road clearance operations," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1098-1112.
    7. Vahid Akbari & İhsan Sadati & F. Sibel Salman & Davood Shiri, 2023. "Minimizing total weighted latency in home healthcare routing and scheduling with patient prioritization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 807-852, September.
    8. Ajam, Meraj & Akbari, Vahid & Salman, F. Sibel, 2022. "Routing multiple work teams to minimize latency in post-disaster road network restoration," European Journal of Operational Research, Elsevier, vol. 300(1), pages 237-254.

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