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New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows

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  • Diego Pecin

    (Département de mathématiques et de génie industriel, Polytechnique Montréal, Montréal QC H3T 1J4, Canada; and Group for Research in Decision Analysis (GERAD), HEC Montréal 3000, QC H3T 2A7, Canada)

  • Claudio Contardo

    (Group for Research in Decision Analysis (GERAD), HEC Montréal 3000, QC H3T 2A7, Canada; and Département de management et technologie, ESG UQÀM, Montréal, QC H2X 3X2, Canada)

  • Guy Desaulniers

    (Département de mathématiques et de génie industriel, Polytechnique Montréal, Montréal QC H3T 1J4, Canada; and Group for Research in Decision Analysis (GERAD), HEC Montréal 3000, QC H3T 2A7, Canada)

  • Eduardo Uchoa

    (Group for Research in Decision Analysis (GERAD), HEC Montréal 3000, QC H3T 2A7, Canada; and Département de management et technologie, ESG UQÀM, Montréal, QC H2X 3X2, Canada)

Abstract

The vehicle routing problem with time windows (VRPTW) consists of finding least-cost vehicle routes to satisfy the demands of customers that can be visited within specific time windows. We introduce two enhancements for the exact solution of the VRPTW by branch-price-and-cut (BPC). First, we develop a sharper form of the limited-memory subset-row inequalities by representing the memory as an arc subset rather than a node subset. Second, from the elementary inequalities introduced by Balas in 1977, we derive a family of inequalities that dominate them. These enhancements are embedded into an exact BPC algorithm that includes state-of-the-art features such as bidirectional labeling, decremental state-space relaxation, completion bounds, variable fixing, and route enumeration. Computational results show that these enhancements are particularly effective for the most difficult instances and that our BPC algorithm can solve all 56 Solomon instances with 100 customers and 51 of 60 Gehring and Homberger instances with 200 customers.

Suggested Citation

  • Diego Pecin & Claudio Contardo & Guy Desaulniers & Eduardo Uchoa, 2017. "New Enhancements for the Exact Solution of the Vehicle Routing Problem with Time Windows," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 489-502, August.
    • Handle: RePEc:inm:orijoc:v:29:y:2017:i:3:p:489-502
    DOI: 10.1287/ijoc.2016.0744
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    References listed on IDEAS

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    Cited by:

    1. Jiliu Li & Zhixing Luo & Roberto Baldacci & Hu Qin & Zhou Xu, 2023. "A New Exact Algorithm for Single-Commodity Vehicle Routing with Split Pickups and Deliveries," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 31-49, January.
    2. Qie He & Stefan Irnich & Yongjia Song, 2018. "Branch-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Working Papers 1804, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    3. Christian Tilk & Katharina Olkis & Stefan Irnich, 2020. "The Last-mile Vehicle Routing Problem with Delivery Options," Working Papers 2017, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Frómeta Moya, Jorge Israel & Pérez Campos, Javier de Jesús, 2021. "Modelo heurístico híbrido para el ruteo vehicular y manejo de inventario en una entidad comercializadora de combustibles. || Hybrid heuristic model for inventory routing management in a fuel comercial," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 31(1), pages 363-383, June.
    5. Cherkesly, Marilène & Gschwind, Timo, 2022. "The pickup and delivery problem with time windows, multiple stacks, and handling operations," European Journal of Operational Research, Elsevier, vol. 301(2), pages 647-666.
    6. Christian Tilk & Katharina Olkis & Stefan Irnich, 2021. "The last-mile vehicle routing problem with delivery options," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(4), pages 877-904, December.
    7. Pessoa, Artur & Sadykov, Ruslan & Uchoa, Eduardo, 2018. "Enhanced Branch-Cut-and-Price algorithm for heterogeneous fleet vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 270(2), pages 530-543.
    8. Yu Zhang & Zhenzhen Zhang & Andrew Lim & Melvyn Sim, 2021. "Robust Data-Driven Vehicle Routing with Time Windows," Operations Research, INFORMS, vol. 69(2), pages 469-485, March.
    9. Qiuping Ni & Yuanxiang Tang, 2023. "A Bibliometric Visualized Analysis and Classification of Vehicle Routing Problem Research," Sustainability, MDPI, vol. 15(9), pages 1-37, April.
    10. Li, Hongqi & Wang, Feilong & Zhan, Zhuopeng, 2024. "Drone routing problem with swarm synchronization," European Journal of Operational Research, Elsevier, vol. 314(2), pages 477-495.
    11. Froger, Aurélien & Sadykov, Ruslan, 2023. "New exact and heuristic algorithms to solve the prize-collecting job sequencing problem with one common and multiple secondary resources," European Journal of Operational Research, Elsevier, vol. 306(1), pages 65-82.
    12. Pedro Munari & Martin Savelsbergh, 2020. "A Column Generation-Based Heuristic for the Split Delivery Vehicle Routing Problem with Time Windows," SN Operations Research Forum, Springer, vol. 1(4), pages 1-24, December.
    13. Zhen, Lu & Baldacci, Roberto & Tan, Zheyi & Wang, Shuaian & Lyu, Junyan, 2022. "Scheduling heterogeneous delivery tasks on a mixed logistics platform," European Journal of Operational Research, Elsevier, vol. 298(2), pages 680-698.
    14. Artur Pessoa & Ruslan Sadykov & Eduardo Uchoa, 2021. "Solving Bin Packing Problems Using VRPSolver Models," SN Operations Research Forum, Springer, vol. 2(2), pages 1-25, June.
    15. Zu-Jun Ma & Fei Yang & Ying Dai & Zuo-Jun Max Shen, 2021. "The Migratory Beekeeping Routing Problem: Model and an Exact Algorithm," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 319-335, January.
    16. Ines Mathlouthi & Michel Gendreau & Jean-Yves Potvin, 2021. "Branch-and-Price for a Multi-attribute Technician Routing and Scheduling Problem," SN Operations Research Forum, Springer, vol. 2(1), pages 1-35, March.
    17. Liu, Yiming & Roberto, Baldacci & Zhou, Jianwen & Yu, Yang & Zhang, Yu & Sun, Wei, 2023. "Efficient feasibility checks and an adaptive large neighborhood search algorithm for the time-dependent green vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 310(1), pages 133-155.
    18. Ye Ding & Jiantong Zhang & Jiaqing Sun, 2022. "Branch-and-Price-and-Cut for the Heterogeneous Fleet and Multi-Depot Static Bike Rebalancing Problem with Split Load," Sustainability, MDPI, vol. 14(17), pages 1-24, August.
    19. Yang, Yu & Yan, Chiwei & Cao, Yufeng & Roberti, Roberto, 2023. "Planning robust drone-truck delivery routes under road traffic uncertainty," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1145-1160.
    20. Stefan Faldum & Timo Gschwind & Stefan Irnich, 2023. "Subset-Row Inequalities and Unreachability in Path-based Formulations for Routing and Scheduling Problems," Working Papers 2310, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    21. Qie He & Stefan Irnich & Yongjia Song, 2019. "Branch-and-Cut-and-Price for the Vehicle Routing Problem with Time Windows and Convex Node Costs," Transportation Science, INFORMS, vol. 53(5), pages 1409-1426, September.
    22. Carolin Bauerhenne & Jonathan Bard & Rainer Kolisch, 2024. "Robust Routing and Scheduling of Home Healthcare Workers: A Nested Branch-and-Price Approach," Papers 2407.06215, arXiv.org.
    23. Zhang, Guowei & Jia, Ning & Zhu, Ning & Adulyasak, Yossiri & Ma, Shoufeng, 2023. "Robust drone selective routing in humanitarian transportation network assessment," European Journal of Operational Research, Elsevier, vol. 305(1), pages 400-428.
    24. Schmidt, Jeanette & Tilk, Christian & Irnich, Stefan, 2024. "Using public transport in a 2-echelon last-mile delivery network," European Journal of Operational Research, Elsevier, vol. 317(3), pages 827-840.
    25. Homsi, Gabriel & Martinelli, Rafael & Vidal, Thibaut & Fagerholt, Kjetil, 2020. "Industrial and tramp ship routing problems: Closing the gap for real-scale instances," European Journal of Operational Research, Elsevier, vol. 283(3), pages 972-990.

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