IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v39y1991i4p616-622.html
   My bibliography  Save this article

Capacitated Vehicle Routing on Trees

Author

Listed:
  • Martine Labbé

    (Erasmus University, Rotterdam, The Netherlands)

  • Gilbert Laporte

    (University of Montreal, Montreal, Quebec, Canada)

  • Hélène Mercure

    (University of Montreal, Montreal, Quebec, Canada)

Abstract

T = ( V , E ) is a tree with nonnegative weights associated with each of its vertices. A fleet of vehicles of capacity Q is located at the depot represented by vertex v 1 . The Capacitated Vehicle Routing Problem on Trees (TCVRP) consists of determining vehicle collection routes starting and ending at the depot such that: the weight associated with any given vertex is collected by exactly one vehicle; the sum of all weights collected by a vehicle does not exceed Q ; a linear combination of the number of vehicles and of the total distance traveled by these vehicles is minimized. The TCVRP is shown to be NP-hard. This paper presents lower bounds for the TCVRP based on the solutions of associated bin packing problems. We develop a linear time heuristic (upper bound) procedure and present a bound on its worst case performance. These lower and upper bounds are then embedded in an enumerative algorithm. Numerical results follow.

Suggested Citation

  • Martine Labbé & Gilbert Laporte & Hélène Mercure, 1991. "Capacitated Vehicle Routing on Trees," Operations Research, INFORMS, vol. 39(4), pages 616-622, August.
    • Handle: RePEc:inm:oropre:v:39:y:1991:i:4:p:616-622
    DOI: 10.1287/opre.39.4.616
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.39.4.616
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.39.4.616?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chengbin Chu & Julien Antonio, 1999. "Approximation Algorithms to Solve Real-Life Multicriteria Cutting Stock Problems," Operations Research, INFORMS, vol. 47(4), pages 495-508, August.
    2. Xu, Liang & Xu, Zhou & Xu, Dongsheng, 2013. "Exact and approximation algorithms for the min–max k-traveling salesmen problem on a tree," European Journal of Operational Research, Elsevier, vol. 227(2), pages 284-292.
    3. Yuanxiao Wu & Xiwen Lu, 2022. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1953-1963, October.
    4. Bassem Jarboui & Saber Ibrahim & Abdelwaheb Rebai, 2010. "A new destructive bounding scheme for the bin packing problem," Annals of Operations Research, Springer, vol. 179(1), pages 187-202, September.
    5. Liao, Chung-Shou & Hsu, Chia-Hong, 2013. "New lower bounds for the three-dimensional orthogonal bin packing problem," European Journal of Operational Research, Elsevier, vol. 225(2), pages 244-252.
    6. Pontien Mbaraga & André Langevin & Gilbert Laporte, 1999. "Two exact algorithms for the vehicle routing problem on trees," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 75-89, February.
    7. Tetsuo Asano & Naoki Katoh & Kazuhiro Kawashima, 2001. "A New Approximation Algorithm for the Capacitated Vehicle Routing Problem on a Tree," Journal of Combinatorial Optimization, Springer, vol. 5(2), pages 213-231, June.
    8. Braune, Roland, 2019. "Lower bounds for a bin packing problem with linear usage cost," European Journal of Operational Research, Elsevier, vol. 274(1), pages 49-64.
    9. Maria João Santos & Pedro Amorim & Alexandra Marques & Ana Carvalho & Ana Póvoa, 2020. "The vehicle routing problem with backhauls towards a sustainability perspective: a review," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 358-401, July.
    10. Roland Braune, 2022. "Packing-based branch-and-bound for discrete malleable task scheduling," Journal of Scheduling, Springer, vol. 25(6), pages 675-704, December.
    11. Gregory S. Taylor & Yupo Chan & Ghulam Rasool, 2017. "A three-dimensional bin-packing model: exact multicriteria solution and computational complexity," Annals of Operations Research, Springer, vol. 251(1), pages 397-427, April.
    12. 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.
    13. Walter, Rico & Schulze, Philipp & Scholl, Armin, 2021. "SALSA: Combining branch-and-bound with dynamic programming to smoothen workloads in simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 295(3), pages 857-873.
    14. Scholl, Armin & Becker, Christian, 2006. "State-of-the-art exact and heuristic solution procedures for simple assembly line balancing," European Journal of Operational Research, Elsevier, vol. 168(3), pages 666-693, February.
    15. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    16. Crainic, Teodor Gabriel & Perboli, Guido & Pezzuto, Miriam & Tadei, Roberto, 2007. "Computing the asymptotic worst-case of bin packing lower bounds," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1295-1303, December.
    17. Yuanxiao Wu & Xiwen Lu, 0. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-11.
    18. H. Neil Geismar & Gilbert Laporte & Lei Lei & Chelliah Sriskandarajah, 2008. "The Integrated Production and Transportation Scheduling Problem for a Product with a Short Lifespan," INFORMS Journal on Computing, INFORMS, vol. 20(1), pages 21-33, February.
    19. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.

    More about this item

    Keywords

    transportation: vehicle routing;

    Statistics

    Access and download statistics

    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:39:y:1991:i:4:p:616-622. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.