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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
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Bock, Stefan, 2024. "Vehicle routing for connected service areas - a versatile approach covering single, hierarchical, and bi-criteria objectives," European Journal of Operational Research, Elsevier, vol. 313(3), pages 905-925.
    4. Yuanxiao Wu & Xiwen Lu, 0. "Capacitated vehicle routing problem on line with unsplittable demands," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-11.
    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. 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.
    7. 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.
    8. 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.
    9. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Roland Braune, 2022. "Packing-based branch-and-bound for discrete malleable task scheduling," Journal of Scheduling, Springer, vol. 25(6), pages 675-704, December.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

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    Keywords

    transportation: vehicle routing;

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