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A Branch-and-Bound Algorithm for the Capacitated Vehicle Routing Problem on Directed Graphs

Author

Listed:
  • Matteo Fischetti

    (DEI, University of Padova, Padova, Italy)

  • Paolo Toth

    (DEIS, University of Bologna, Bologna, Italy)

  • Daniele Vigo

    (DEIS, University of Bologna, Bologna, Italy)

Abstract

We consider the asymmetric capacitated vehicle routing problem ( CVRP ), a particular case of the standard asymmetric vehicle routing problem in which only the vehicle capacity constraints are imposed. CVRP is known to be NP-hard and finds practical applications in distribution and scheduling. We describe two new bounding procedures for CVRP , based on the so-called additive approach . Each procedure computes a sequence of nondecreasing lower bounds, obtained by solving different relaxations of CVRP . Effective implementations of the procedures are also outlined which considerably reduce the computational effort. The two procedures are combined into an overall bounding algorithm. A branch-and-bound exact algorithm is then proposed, whose performance is enhanced by means of reduction procedures, dominance criteria, and feasibility checks. Extensive computational results on both real-world and random test problems are presented, showing that the proposed approach favorably compares with previous algorithms from the literature.

Suggested Citation

  • Matteo Fischetti & Paolo Toth & Daniele Vigo, 1994. "A Branch-and-Bound Algorithm for the Capacitated Vehicle Routing Problem on Directed Graphs," Operations Research, INFORMS, vol. 42(5), pages 846-859, October.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:5:p:846-859
    DOI: 10.1287/opre.42.5.846
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    Citations

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    Cited by:

    1. Michiel A. J. uit het Broek & Albert H. Schrotenboer & Bolor Jargalsaikhan & Kees Jan Roodbergen & Leandro C. Coelho, 2021. "Asymmetric Multidepot Vehicle Routing Problems: Valid Inequalities and a Branch-and-Cut Algorithm," Operations Research, INFORMS, vol. 69(2), pages 380-409, March.
    2. Roberto Baldacci & Paolo Toth & Daniele Vigo, 2010. "Exact algorithms for routing problems under vehicle capacity constraints," Annals of Operations Research, Springer, vol. 175(1), pages 213-245, March.
    3. Letchford, Adam N. & Lysgaard, Jens & Eglese, Richard W., 2006. "A Branch-and-Cut Algorithm for the Capacitated Open Vehicle Routing Problem," CORAL Working Papers L-2006-06, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    4. Belhoul, Lyes, 2014. "Résolution de problèmes d'optimisation combinatoire mono et multi-objectifs par énumération ordonnée," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14672 edited by Vanderpooten, Daniel.
    5. Amirsaman Kheirkhah & HamidReza Navidi & Masume Messi Bidgoli, 2016. "A bi-level network interdiction model for solving the hazmat routing problem," International Journal of Production Research, Taylor & Francis Journals, vol. 54(2), pages 459-471, January.
    6. R. Baldacci & E. Hadjiconstantinou & A. Mingozzi, 2004. "An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation," Operations Research, INFORMS, vol. 52(5), pages 723-738, October.
    7. 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.
    8. Vigo, Daniele, 1996. "A heuristic algorithm for the asymmetric capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 89(1), pages 108-126, February.
    9. Yossiri Adulyasak & Patrick Jaillet, 2016. "Models and Algorithms for Stochastic and Robust Vehicle Routing with Deadlines," Transportation Science, INFORMS, vol. 50(2), pages 608-626, May.
    10. Benjamin C. Shelbourne & Maria Battarra & Chris N. Potts, 2017. "The Vehicle Routing Problem with Release and Due Dates," INFORMS Journal on Computing, INFORMS, vol. 29(4), pages 705-723, November.
    11. J Faulin & A García del Valle, 2008. "Solving the capacitated vehicle routing problem using the ALGELECT electrostatic algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(12), pages 1685-1695, December.
    12. Lawrence Bodin & Aristide Mingozzi & Roberto Baldacci & Michael Ball, 2000. "The Rollon–Rolloff Vehicle Routing Problem," Transportation Science, INFORMS, vol. 34(3), pages 271-288, August.
    13. Altinkemer, Kemal & Kazaz, Burak & Koksalan, Murat & Moskowitz, Herbert, 2000. "Optimization of printed circuit board manufacturing: Integrated modeling and algorithms," European Journal of Operational Research, Elsevier, vol. 124(2), pages 409-421, July.
    14. Toth, Paolo & Vigo, Daniele, 1999. "A heuristic algorithm for the symmetric and asymmetric vehicle routing problems with backhauls," European Journal of Operational Research, Elsevier, vol. 113(3), pages 528-543, March.
    15. Taş, D. & Gendreau, M. & Dellaert, N. & van Woensel, T. & de Kok, A.G., 2014. "Vehicle routing with soft time windows and stochastic travel times: A column generation and branch-and-price solution approach," European Journal of Operational Research, Elsevier, vol. 236(3), pages 789-799.
    16. AVELLA, Pasquale & BOCCIA, Maurizio & WOLSEY, Laurence A., 2014. "Single-period cutting planes for inventory routing problems," LIDAM Discussion Papers CORE 2014055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    17. A N Letchford & J Lysgaard & R W Eglese, 2007. "A branch-and-cut algorithm for the capacitated open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(12), pages 1642-1651, December.
    18. Marcel Turkensteen & Dmitry Malyshev & Boris Goldengorin & Panos M. Pardalos, 2017. "The reduction of computation times of upper and lower tolerances for selected combinatorial optimization problems," Journal of Global Optimization, Springer, vol. 68(3), pages 601-622, July.
    19. 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.
    20. Leggieri, Valeria & Haouari, Mohamed, 2017. "Lifted polynomial size formulations for the homogeneous and heterogeneous vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 263(3), pages 755-767.

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