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Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints

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  • Luo, Zhixing
  • Qin, Hu
  • Lim, Andrew

Abstract

In this paper, we extend the multiple traveling repairman problem by considering a limitation on the total distance that a vehicle can travel; the resulting problem is called the multiple traveling repairmen problem with distance constraints (MTRPD). In the MTRPD, a fleet of identical vehicles is dispatched to serve a set of customers. Each vehicle that starts from and ends at the depot is not allowed to travel a distance longer than a predetermined limit and each customer must be visited exactly once. The objective is to minimize the total waiting time of all customers after the vehicles leave the depot. To optimally solve the MTRPD, we propose a new exact branch-and-price-and-cut algorithm, where the column generation pricing subproblem is a resource-constrained elementary shortest-path problem with cumulative costs. An ad hoc label-setting algorithm armed with bidirectional search strategy is developed to solve the pricing subproblem. Computational results show the effectiveness of the proposed method. The optimal solutions to 179 out of 180 test instances are reported in this paper. Our computational results serve as benchmarks for future researchers on the problem.

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  • 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.
  • Handle: RePEc:eee:ejores:v:234:y:2014:i:1:p:49-60
    DOI: 10.1016/j.ejor.2013.09.014
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    9. 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.
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    16. Bock, Stefan, 2015. "Solving the traveling repairman problem on a line with general processing times and deadlines," European Journal of Operational Research, Elsevier, vol. 244(3), pages 690-703.
    17. Irawan, Chandra Ade & Ouelhadj, Djamila & Jones, Dylan & Stålhane, Magnus & Sperstad, Iver Bakken, 2017. "Optimisation of maintenance routing and scheduling for offshore wind farms," European Journal of Operational Research, Elsevier, vol. 256(1), pages 76-89.
    18. Li, Jiliu & Qin, Hu & Baldacci, Roberto & Zhu, Wenbin, 2020. "Branch-and-price-and-cut for the synchronized vehicle routing problem with split delivery, proportional service time and multiple time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 140(C).
    19. 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.
    20. Sze, Jeeu Fong & Salhi, Said & Wassan, Niaz, 2017. "The cumulative capacitated vehicle routing problem with min-sum and min-max objectives: An effective hybridisation of adaptive variable neighbourhood search and large neighbourhood search," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 162-184.

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