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Arc Routing with Time-Dependent Travel Times and Paths

Author

Listed:
  • Thibaut Vidal

    (Departamento de Informática, Pontifícia Universidade Católica do Rio de Janeiro, 22541-900 Gávea, Rio de Janeiro, Brazil)

  • Rafael Martinelli

    (Departamento de Engenharia Industrial, Pontifícia Universidade Católica do Rio de Janeiro, 22451-900 Gávea, Rio de Janeiro, Brazil)

  • Tuan Anh Pham

    (ORLab, VNU University of Engineering and Technology, Hanoi 100000, Vietnam; Military Logistics Research Center, Military Logistics Academy, Hanoi 100000, Vietnam)

  • Minh Hoàng Hà

    (ORLab, Faculty of Computer Science, Phenikaa University, Hanoi 100000, Vietnam)

Abstract

Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the speed functions on the complete graph. We argue that this model is often inadequate, in particular for arc routing problems involving services on edges of a road network. To fill this gap, we formally define the time-dependent capacitated arc routing problem (TDCARP), with travel and service speed functions given directly at the network level. Under these assumptions, the quickest path between locations can change over time, leading to a complex problem that challenges the capabilities of current solution methods. We introduce effective algorithms for preprocessing quickest paths in a closed form, efficient data structures for travel time queries during routing optimization, and heuristic and exact solution approaches for the TDCARP. Our heuristic uses the hybrid genetic search principle with tailored solution-decoding algorithms and lower bounds for filtering moves. Our branch-and-price algorithm exploits dedicated pricing routines, heuristic dominance rules, and completion bounds to find optimal solutions for problems counting up to 75 services. From these algorithms, we measure the benefits of time-dependent routing optimization for different levels of travel-speed data accuracy.

Suggested Citation

  • Thibaut Vidal & Rafael Martinelli & Tuan Anh Pham & Minh Hoàng Hà, 2021. "Arc Routing with Time-Dependent Travel Times and Paths," Transportation Science, INFORMS, vol. 55(3), pages 706-724, May.
    • Handle: RePEc:inm:ortrsc:v:55:y:2021:i:3:p:706-724
    DOI: 10.1287/trsc.2020.1035
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    References listed on IDEAS

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    1. Nicolas Rincon-Garcia & Ben J. Waterson & Tom J. Cherrett, 2018. "Requirements from vehicle routing software: perspectives from literature, developers and the freight industry," Transport Reviews, Taylor & Francis Journals, vol. 38(1), pages 117-138, January.
    2. Jinghao Sun & Yakun Meng & Guozhen Tan, 2015. "An integer programming approach for the Chinese postman problem with time-dependent travel time," Journal of Combinatorial Optimization, Springer, vol. 29(3), pages 565-588, April.
    3. W Maden & R Eglese & D Black, 2010. "Vehicle routing and scheduling with time-varying data: A case study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(3), pages 515-522, March.
    4. Beullens, Patrick & Muyldermans, Luc & Cattrysse, Dirk & Van Oudheusden, Dirk, 2003. "A guided local search heuristic for the capacitated arc routing problem," European Journal of Operational Research, Elsevier, vol. 147(3), pages 629-643, June.
    5. Martinelli, Rafael & Pecin, Diego & Poggi, Marcus, 2014. "Efficient elementary and restricted non-elementary route pricing," European Journal of Operational Research, Elsevier, vol. 239(1), pages 102-111.
    6. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2014. "A unified solution framework for multi-attribute vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 234(3), pages 658-673.
    7. Roberto Baldacci & Aristide Mingozzi & Roberto Roberti, 2011. "New Route Relaxation and Pricing Strategies for the Vehicle Routing Problem," Operations Research, INFORMS, vol. 59(5), pages 1269-1283, October.
    8. Thomas R. Visser & Remy Spliet, 2020. "Efficient Move Evaluations for Time-Dependent Vehicle Routing Problems," Transportation Science, INFORMS, vol. 54(4), pages 1091-1112, July.
    9. Irnich, Stefan, 2008. "Solution of real-world postman problems," European Journal of Operational Research, Elsevier, vol. 190(1), pages 52-67, October.
    10. Vidal, Thibaut & Crainic, Teodor Gabriel & Gendreau, Michel & Prins, Christian, 2013. "Heuristics for multi-attribute vehicle routing problems: A survey and synthesis," European Journal of Operational Research, Elsevier, vol. 231(1), pages 1-21.
    11. Vidal, Thibaut & Laporte, Gilbert & Matl, Piotr, 2020. "A concise guide to existing and emerging vehicle routing problem variants," European Journal of Operational Research, Elsevier, vol. 286(2), pages 401-416.
    12. Gianpaolo Ghiani & Emanuela Guerriero, 2014. "A Note on the Ichoua, Gendreau, and Potvin (2003) Travel Time Model," Transportation Science, INFORMS, vol. 48(3), pages 458-462, August.
    13. Ian Herszterg & Marcus Poggi & Thibaut Vidal, 2019. "Two-Dimensional Phase Unwrapping via Balanced Spanning Forests," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 527-543, July.
    14. Huang, Yixiao & Zhao, Lei & Van Woensel, Tom & Gross, Jean-Philippe, 2017. "Time-dependent vehicle routing problem with path flexibility," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 169-195.
    15. Thibaut Vidal, 2017. "Node, Edge, Arc Routing and Turn Penalties: Multiple Problems—One Neighborhood Extension," Operations Research, INFORMS, vol. 65(4), pages 992-1010, August.
    16. Gmira, Maha & Gendreau, Michel & Lodi, Andrea & Potvin, Jean-Yves, 2021. "Tabu search for the time-dependent vehicle routing problem with time windows on a road network," European Journal of Operational Research, Elsevier, vol. 288(1), pages 129-140.
    17. Diego Pecin & Eduardo Uchoa, 2019. "Comparative Analysis of Capacitated Arc Routing Formulations for Designing a New Branch-Cut-and-Price Algorithm," Transportation Science, INFORMS, vol. 53(6), pages 1673-1694, November.
    18. Diego Cattaruzza & Nabil Absi & Dominique Feillet & Jesús González-Feliu, 2017. "Vehicle routing problems for city logistics," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 51-79, March.
    19. Thibaut Vidal & Nelson Maculan & Luiz Satoru Ochi & Puca Huachi Vaz Penna, 2016. "Large Neighborhoods with Implicit Customer Selection for Vehicle Routing Problems with Profits," Transportation Science, INFORMS, vol. 50(2), pages 720-734, May.
    20. Ichoua, Soumia & Gendreau, Michel & Potvin, Jean-Yves, 2003. "Vehicle dispatching with time-dependent travel times," European Journal of Operational Research, Elsevier, vol. 144(2), pages 379-396, January.
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