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A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows

Author

Listed:
  • Jonathan F. Bard

    (Graduate Program in Operations Research, Department of Mechanical Engineering, The University of Texas, Austin, Texas 78712-1063)

  • George Kontoravdis

    (Graduate Program in Operations Research, Department of Mechanical Engineering, The University of Texas, Austin, Texas 78712-1063)

  • Gang Yu

    (Management Science and Information Systems, College of Business Administration, The University of Texas, Austin, Texas 78712)

Abstract

This paper addresses the problem of finding the minimum number of vehicles required to visit a set of nodes subject to time window and capacity constraints. The fleet is homogeneous and is located at a common depot. Each node requires the same type of service. An exact method is introduced based on branch and cut. In the computations, ever increasing lower bounds on the optimal solution are obtained by solving a series of relaxed problems that incorporate newly found valid inequalities. Feasible solutions or upper bounds are obtained with the help of greedy randomized adaptive search procedure (GRASP). A wide variety of cuts is introduced to tighten the linear programming (LP) relaxation of the original mixed-integer program. To find violated cuts, it is necessary to solve a separation problem. A substantial portion of the paper is aimed at describing the heuristics developed for this purpose. A new approach for obtaining feasible solutions from the LP relaxation is also discussed. Numerical results for standard 50- and 100-node benchmark problems are reported.

Suggested Citation

  • Jonathan F. Bard & George Kontoravdis & Gang Yu, 2002. "A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 36(2), pages 250-269, May.
    • Handle: RePEc:inm:ortrsc:v:36:y:2002:i:2:p:250-269
    DOI: 10.1287/trsc.36.2.250.565
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    References listed on IDEAS

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    Cited by:

    1. Guy Desaulniers & François Lessard & Ahmed Hadjar, 2008. "Tabu Search, Partial Elementarity, and Generalized k -Path Inequalities for the Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 42(3), pages 387-404, August.
    2. Martin Durbin & Karla Hoffman, 2008. "OR PRACTICE---The Dance of the Thirty-Ton Trucks: Dispatching and Scheduling in a Dynamic Environment," Operations Research, INFORMS, vol. 56(1), pages 3-19, February.
    3. Yibo Dang & Manjeet Singh & Theodore T. Allen, 2021. "Network Mode Optimization for the DHL Supply Chain," Interfaces, INFORMS, vol. 51(3), pages 179-199, May.
    4. Jonathan F. Bard & Siwate Rojanasoonthon, 2006. "A branch‐and‐price algorithm for parallel machine scheduling with time windows and job priorities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 24-44, February.
    5. Ran Liu & Zhibin Jiang, 2019. "A constraint relaxation-based algorithm for the load-dependent vehicle routing problem with time windows," Flexible Services and Manufacturing Journal, Springer, vol. 31(2), pages 331-353, June.
    6. Tan, K.C. & Chew, Y.H. & Lee, L.H., 2006. "A hybrid multi-objective evolutionary algorithm for solving truck and trailer vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 172(3), pages 855-885, August.
    7. Jourdan, L. & Basseur, M. & Talbi, E.-G., 2009. "Hybridizing exact methods and metaheuristics: A taxonomy," European Journal of Operational Research, Elsevier, vol. 199(3), pages 620-629, December.
    8. Pedro Munari & Reinaldo Morabito, 2018. "A branch-price-and-cut algorithm for the vehicle routing problem with time windows and multiple deliverymen," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 437-464, October.
    9. D. G. N. D. Jayarathna, 2024. "Survey on Thirty Years of Vehicle Routing Problems: Mathematical Models, Solution Methods, and Real-Life Applications," International Journal of Research and Scientific Innovation, International Journal of Research and Scientific Innovation (IJRSI), vol. 11(7), pages 435-449, July.
    10. Jeng-Shyang Pan & Qing-yong Yang & Shu-Chuan Chu & Kuo-Chi Chang, 2021. "Compact Sine Cosine Algorithm applied in vehicle routing problem with time window," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 78(4), pages 609-628, December.
    11. Liu, Mengyang & Luo, Zhixing & Lim, Andrew, 2015. "A branch-and-cut algorithm for a realistic dial-a-ride problem," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 267-288.
    12. Junfang Yu & Randy Hoff, 2013. "Optimal Routing and Assignment of Consultants for Energy Education, Inc," Interfaces, INFORMS, vol. 43(2), pages 142-151, April.
    13. Yuan Qu & Jonathan F. Bard, 2015. "A Branch-and-Price-and-Cut Algorithm for Heterogeneous Pickup and Delivery Problems with Configurable Vehicle Capacity," Transportation Science, INFORMS, vol. 49(2), pages 254-270, May.
    14. Lysgaard, Jens, 2006. "Reachability cuts for the vehicle routing problem with time windows," European Journal of Operational Research, Elsevier, vol. 175(1), pages 210-223, November.
    15. Manuel Iori & Juan-José Salazar-González & Daniele Vigo, 2007. "An Exact Approach for the Vehicle Routing Problem with Two-Dimensional Loading Constraints," Transportation Science, INFORMS, vol. 41(2), pages 253-264, May.
    16. G Zhu & J F Bard & G Yu, 2005. "Disruption management for resource-constrained project scheduling," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 365-381, April.
    17. Ann Melissa Campbell & Dieter Vandenbussche & William Hermann, 2008. "Routing for Relief Efforts," Transportation Science, INFORMS, vol. 42(2), pages 127-145, May.
    18. Lysgaard, Jens, 2004. "Reachability cuts for the vehicle routing problem with time windows," CORAL Working Papers L-2004-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    19. Guidong Zhu & Jonathan F. Bard & Gang Yu, 2006. "A Branch-and-Cut Procedure for the Multimode Resource-Constrained Project-Scheduling Problem," INFORMS Journal on Computing, INFORMS, vol. 18(3), pages 377-390, August.
    20. Theodore Athanasopoulos & Ioannis Minis, 2013. "Efficient techniques for the multi-period vehicle routing problem with time windows within a branch and price framework," Annals of Operations Research, Springer, vol. 206(1), pages 1-22, July.
    21. Pureza, Vitória & Morabito, Reinaldo & Reimann, Marc, 2012. "Vehicle routing with multiple deliverymen: Modeling and heuristic approaches for the VRPTW," European Journal of Operational Research, Elsevier, vol. 218(3), pages 636-647.
    22. Calvete, Herminia I. & Gale, Carmen & Oliveros, Maria-Jose & Sanchez-Valverde, Belen, 2007. "A goal programming approach to vehicle routing problems with soft time windows," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1720-1733, March.
    23. Zhi-Long Chen & Hang Xu, 2006. "Dynamic Column Generation for Dynamic Vehicle Routing with Time Windows," Transportation Science, INFORMS, vol. 40(1), pages 74-88, February.

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