IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v52y2004i5p723-738.html
   My bibliography  Save this article

An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation

Author

Listed:
  • R. Baldacci

    (DISMI, University of Modena and Reggio Emilia, Viale A. Allegri, 15, 42100 Reggio Emilia, Italy)

  • E. Hadjiconstantinou

    (Imperial College, Management School, Exhibition Road, London SW7 2PG, United Kingdom)

  • A. Mingozzi

    (Department of Mathematics, University of Bologna, Via Sacchi 3, 47023 Cesena, Italy)

Abstract

The capacitated vehicle routing problem (CVRP) is the problem in which a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. In this paper, we describe a new integer programming formulation for the CVRP based on a two-commodity network flow approach. We present a lower bound derived from the linear programming (LP) relaxation of the new formulation which is improved by adding valid inequalities in a cutting-plane fashion. Moreover, we present a comparison between the new lower bound and lower bounds derived from the LP relaxations of different CVRP formulations proposed in the literature. A new branch-and-cut algorithm for the optimal solution of the CVRP is described. Computational results are reported for a set of test problems derived from the literature and for new randomly generated problems.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:5:p:723-738
    DOI: 10.1287/opre.1040.0111
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1040.0111
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1040.0111?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Marshall L. Fisher, 1994. "Optimal Solution of Vehicle Routing Problems Using Minimum K-Trees," Operations Research, INFORMS, vol. 42(4), pages 626-642, August.
    2. Gouveia, Luis, 1995. "A result on projection for the vehicle routing ptoblem," European Journal of Operational Research, Elsevier, vol. 85(3), pages 610-624, September.
    3. M. L. Balinski & R. E. Quandt, 1964. "On an Integer Program for a Delivery Problem," Operations Research, INFORMS, vol. 12(2), pages 300-304, April.
    4. Michel Gendreau & Alain Hertz & Gilbert Laporte, 1994. "A Tabu Search Heuristic for the Vehicle Routing Problem," Management Science, INFORMS, vol. 40(10), pages 1276-1290, October.
    5. Donald L. Miller, 1995. "A Matching Based Exact Algorithm for Capacitated Vehicle Routing Problems," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 1-9, February.
    6. Araque, J. & Hall, L. & Magnanti, T., 1990. "Capacitated trees, capacitated routing, and associated polyhedra," LIDAM Discussion Papers CORE 1990061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. 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.
    8. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    9. Gilbert Laporte & Yves Nobert & Martin Desrochers, 1985. "Optimal Routing under Capacity and Distance Restrictions," Operations Research, INFORMS, vol. 33(5), pages 1050-1073, October.
    10. Augerat, P. & Belenguer, J. M. & Benavent, E. & Corberan, A. & Naddef, D., 1998. "Separating capacity constraints in the CVRP using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 546-557, April.
    11. Alberto Caprara & Paolo Toth & Matteo Fischetti, 2000. "Algorithms for the Set Covering Problem," Annals of Operations Research, Springer, vol. 98(1), pages 353-371, December.
    12. Laporte, Gilbert, 1992. "The vehicle routing problem: An overview of exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 59(3), pages 345-358, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    4. 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.
    5. Gianpaolo Ghiani & Gilbert Laporte & Frédéric Semet, 2006. "The Black and White Traveling Salesman Problem," Operations Research, INFORMS, vol. 54(2), pages 366-378, April.
    6. 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.
    7. Malaguti, Enrico & Martello, Silvano & Santini, Alberto, 2018. "The traveling salesman problem with pickups, deliveries, and draft limits," Omega, Elsevier, vol. 74(C), pages 50-58.
    8. César Rego, 1998. "A Subpath Ejection Method for the Vehicle Routing Problem," Management Science, INFORMS, vol. 44(10), pages 1447-1459, October.
    9. Martinhon, Carlos & Lucena, Abilio & Maculan, Nelson, 2004. "Stronger K-tree relaxations for the vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 158(1), pages 56-71, October.
    10. Paredes-Belmar, Germán & Montero, Elizabeth & Lüer-Villagra, Armin & Marianov, Vladimir & Araya-Sassi, Claudio, 2022. "Vehicle routing for milk collection with gradual blending: A case arising in Chile," European Journal of Operational Research, Elsevier, vol. 303(3), pages 1403-1416.
    11. 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.
    12. Van Woensel, T. & Kerbache, L. & Peremans, H. & Vandaele, N., 2008. "Vehicle routing with dynamic travel times: A queueing approach," European Journal of Operational Research, Elsevier, vol. 186(3), pages 990-1007, May.
    13. N. R. Achuthan & L. Caccetta & S. P. Hill, 2003. "An Improved Branch-and-Cut Algorithm for the Capacitated Vehicle Routing Problem," Transportation Science, INFORMS, vol. 37(2), pages 153-169, May.
    14. Letchford, Adam N. & Salazar-González, Juan-José, 2019. "The Capacitated Vehicle Routing Problem: Stronger bounds in pseudo-polynomial time," European Journal of Operational Research, Elsevier, vol. 272(1), pages 24-31.
    15. 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.
    16. Aardal, K.I. & van Hoesel, S., 1995. "Polyhedral Techniques in Combinatorial Optimization," Other publications TiSEM ed028a07-eb6a-4c8d-8f21-d, Tilburg University, School of Economics and Management.
    17. 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.
    18. N A Wassan, 2006. "A reactive tabu search for the vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(1), pages 111-116, January.
    19. Markus Wagner & Marius Lindauer & Mustafa Mısır & Samadhi Nallaperuma & Frank Hutter, 2018. "A case study of algorithm selection for the traveling thief problem," Journal of Heuristics, Springer, vol. 24(3), pages 295-320, June.
    20. Chrysanthos E. Gounaris & Wolfram Wiesemann & Christodoulos A. Floudas, 2013. "The Robust Capacitated Vehicle Routing Problem Under Demand Uncertainty," Operations Research, INFORMS, vol. 61(3), pages 677-693, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:52:y:2004:i:5:p:723-738. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.