IDEAS home Printed from https://ideas.repec.org/a/pal/jorsoc/v58y2007i12d10.1057_palgrave.jors.2602345.html
   My bibliography  Save this article

A branch-and-cut algorithm for the capacitated open vehicle routing problem

Author

Listed:
  • A N Letchford

    (Lancaster University)

  • J Lysgaard

    (Aarhus School of Business)

  • R W Eglese

    (Lancaster University)

Abstract

In open vehicle routing problems, the vehicles are not required to return to the depot after completing service. In this paper, we present the first exact optimization algorithm for the open version of the well-known capacitated vehicle routing problem (CVRP). The algorithm is based on branch-and-cut. We show that, even though the open CVRP initially looks like a minor variation of the standard CVRP, the integer programming formulation and cutting planes need to be modified in subtle ways. Computational results are given for several standard test instances, which enables us for the first time to assess the quality of existing heuristic methods, and to compare the relative difficulty of open and closed versions of the same problem.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:12:d:10.1057_palgrave.jors.2602345
    DOI: 10.1057/palgrave.jors.2602345
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1057/palgrave.jors.2602345
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1057/palgrave.jors.2602345?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Manfred W. Padberg & M. R. Rao, 1982. "Odd Minimum Cut-Sets and b -Matchings," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 67-80, February.
    2. 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.
    3. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    4. D Sariklis & S Powell, 2000. "A heuristic method for the open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(5), pages 564-573, May.
    5. Gilbert Laporte & Yves Nobert & Martin Desrochers, 1985. "Optimal Routing under Capacity and Distance Restrictions," Operations Research, INFORMS, vol. 33(5), pages 1050-1073, October.
    6. Tarantilis, C. D. & Diakoulaki, D. & Kiranoudis, C. T., 2004. "Combination of geographical information system and efficient routing algorithms for real life distribution operations," European Journal of Operational Research, Elsevier, vol. 152(2), pages 437-453, January.
    7. Z Fu & R Eglese & L Y O Li, 2005. "A new tabu search heuristic for the open vehicle routing problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 267-274, March.
    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. 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.
    2. 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.
    3. 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.
    4. William Cook & Daniel G. Espinoza & Marcos Goycoolea, 2007. "Computing with Domino-Parity Inequalities for the Traveling Salesman Problem (TSP)," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 356-365, August.
    5. D Aksen & Z Özyurt & N Aras, 2007. "Open vehicle routing problem with driver nodes and time deadlines," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1223-1234, September.
    6. Gianpaolo Ghiani & Gilbert Laporte & Frédéric Semet, 2006. "The Black and White Traveling Salesman Problem," Operations Research, INFORMS, vol. 54(2), pages 366-378, April.
    7. Atefi, Reza & Salari, Majid & C. Coelho, Leandro & Renaud, Jacques, 2018. "The open vehicle routing problem with decoupling points," European Journal of Operational Research, Elsevier, vol. 265(1), pages 316-327.
    8. Zang, Xiaoning & Jiang, Li & Liang, Changyong & Fang, Xiang, 2023. "Coordinated home and locker deliveries: An exact approach for the urban delivery problem with conflicting time windows," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    9. S Salhi & A Al-Khedhairi, 2010. "Integrating heuristic information into exact methods: The case of the vertex p-centre problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1619-1631, November.
    10. Rafael Blanquero & Emilio Carrizosa & Amaya Nogales-Gómez & Frank Plastria, 2014. "Single-facility huff location problems on networks," Annals of Operations Research, Springer, vol. 222(1), pages 175-195, November.
    11. Martins, Francisco Leonardo Bezerra & do Nascimento, José Cláudio, 2022. "Power law dynamics in genealogical graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    12. Marjan Marzban & Qian-Ping Gu & Xiaohua Jia, 2016. "New analysis and computational study for the planar connected dominating set problem," Journal of Combinatorial Optimization, Springer, vol. 32(1), pages 198-225, July.
    13. Ferrer, José M. & Martín-Campo, F. Javier & Ortuño, M. Teresa & Pedraza-Martínez, Alfonso J. & Tirado, Gregorio & Vitoriano, Begoña, 2018. "Multi-criteria optimization for last mile distribution of disaster relief aid: Test cases and applications," European Journal of Operational Research, Elsevier, vol. 269(2), pages 501-515.
    14. Roberto Tadei & Guido Perboli & Francesca Perfetti, 2017. "The multi-path Traveling Salesman Problem with stochastic travel costs," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 6(1), pages 3-23, March.
    15. Lancia, Giuseppe & Vidoni, Paolo, 2020. "Finding the largest triangle in a graph in expected quadratic time," European Journal of Operational Research, Elsevier, vol. 286(2), pages 458-467.
    16. Oya Ekin Karaşan & A. Ridha Mahjoub & Onur Özkök & Hande Yaman, 2014. "Survivability in Hierarchical Telecommunications Networks Under Dual Homing," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 1-15, February.
    17. 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.
    18. Thanh Tan Doan & Nathalie Bostel & Minh Hoàng Hà & Vu Hoang Vuong Nguyen, 2023. "New mixed integer linear programming models and an iterated local search for the clustered traveling salesman problem with relaxed priority rule," Journal of Combinatorial Optimization, Springer, vol. 46(1), pages 1-27, August.
    19. F. Angel-Bello & Y. Cardona-Valdés & A. Álvarez, 2019. "Mixed integer formulations for the multiple minimum latency problem," Operational Research, Springer, vol. 19(2), pages 369-398, June.
    20. Jean-Charles Créput & Amir Hajjam & Abderrafiaa Koukam & Olivier Kuhn, 2012. "Self-organizing maps in population based metaheuristic to the dynamic vehicle routing problem," Journal of Combinatorial Optimization, Springer, vol. 24(4), pages 437-458, November.

    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:pal:jorsoc:v:58:y:2007:i:12:d:10.1057_palgrave.jors.2602345. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.palgrave-journals.com/ .

    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.