IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v80y2021i3d10.1007_s10898-020-00990-0.html
   My bibliography  Save this article

Efficient approximation of the metric CVRP in spaces of fixed doubling dimension

Author

Listed:
  • Michael Khachay

    (Krasovsky Institute of Mathematics and Mechanics
    Ural Federal University)

  • Yuri Ogorodnikov

    (Krasovsky Institute of Mathematics and Mechanics
    Ural Federal University)

  • Daniel Khachay

    (KEDGE Business School)

Abstract

The capacitated vehicle routing problem (CVRP) is the well-known combinatorial optimization problem having numerous practically important applications. CVRP is strongly NP-hard (even on the Euclidean plane), hard to approximate in general case and APX-complete for an arbitrary metric. Meanwhile, for the geometric settings of the problem, there are known a number of quasi-polynomial and even polynomial time approximation schemes. Among these results, the well-known QPTAS proposed by Das and Mathieu appears to be the most general. In this paper, we propose the first extension of this scheme to a more wide class of metric spaces. Actually, we show that the metric CVRP has a QPTAS any time when the problem is set up in the metric space of any fixed doubling dimension $$d>1$$ d > 1 and the capacity does not exceed $$\mathrm {polylog}{(n)}$$ polylog ( n ) .

Suggested Citation

  • Michael Khachay & Yuri Ogorodnikov & Daniel Khachay, 2021. "Efficient approximation of the metric CVRP in spaces of fixed doubling dimension," Journal of Global Optimization, Springer, vol. 80(3), pages 679-710, July.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:3:d:10.1007_s10898-020-00990-0
    DOI: 10.1007/s10898-020-00990-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10898-020-00990-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10898-020-00990-0?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. G. B. Dantzig & J. H. Ramser, 1959. "The Truck Dispatching Problem," Management Science, INFORMS, vol. 6(1), pages 80-91, October.
    2. M. Haimovich & A. H. G. Rinnooy Kan, 1985. "Bounds and Heuristics for Capacitated Routing Problems," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 527-542, November.
    3. Jing Chen & Pengfei Gui & Tao Ding & Sanggyun Na & Yingtang Zhou, 2019. "Optimization of Transportation Routing Problem for Fresh Food by Improved Ant Colony Algorithm Based on Tabu Search," Sustainability, MDPI, vol. 11(23), pages 1-22, November.
    4. Pessoa, Artur & Sadykov, Ruslan & Uchoa, Eduardo, 2018. "Enhanced Branch-Cut-and-Price algorithm for heterogeneous fleet vehicle routing problems," European Journal of Operational Research, Elsevier, vol. 270(2), pages 530-543.
    5. Gilbert Laporte, 2009. "Fifty Years of Vehicle Routing," Transportation Science, INFORMS, vol. 43(4), pages 408-416, November.
    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. Nicolas Rincon-Garcia & Ben J. Waterson & Tom J. Cherrett, 2018. "Requirements from vehicle routing software: perspectives from literature, developers and the freight industry," Transport Reviews, Taylor & Francis Journals, vol. 38(1), pages 117-138, January.
    2. A. Mor & M. G. Speranza, 2020. "Vehicle routing problems over time: a survey," 4OR, Springer, vol. 18(2), pages 129-149, June.
    3. Coelho, V.N. & Grasas, A. & Ramalhinho, H. & Coelho, I.M. & Souza, M.J.F. & Cruz, R.C., 2016. "An ILS-based algorithm to solve a large-scale real heterogeneous fleet VRP with multi-trips and docking constraints," European Journal of Operational Research, Elsevier, vol. 250(2), pages 367-376.
    4. Zhiping Zuo & Yanhui Li & Jing Fu & Jianlin Wu, 2019. "Human Resource Scheduling Model and Algorithm with Time Windows and Multi-Skill Constraints," Mathematics, MDPI, vol. 7(7), pages 1-18, July.
    5. M. Angélica Salazar-Aguilar & Vincent Boyer & Romeo Sanchez Nigenda & Iris A. Martínez-Salazar, 2019. "The sales force sizing problem with multi-period workload assignments, and service time windows," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(1), pages 199-218, March.
    6. Luciano Costa & Claudio Contardo & Guy Desaulniers, 2019. "Exact Branch-Price-and-Cut Algorithms for Vehicle Routing," Transportation Science, INFORMS, vol. 53(4), pages 946-985, July.
    7. Shubhechyya Ghosal & Wolfram Wiesemann, 2020. "The Distributionally Robust Chance-Constrained Vehicle Routing Problem," Operations Research, INFORMS, vol. 68(3), pages 716-732, May.
    8. Neves-Moreira, F. & Amorim, P. & Guimarães, L. & Almada-Lobo, B., 2016. "A long-haul freight transportation problem: Synchronizing resources to deliver requests passing through multiple transshipment locations," European Journal of Operational Research, Elsevier, vol. 248(2), pages 487-506.
    9. Zhongxiu Peng & Cong Wang & Wenqing Xu & Jinsong Zhang, 2022. "Research on Location-Routing Problem of Maritime Emergency Materials Distribution Based on Bi-Level Programming," Mathematics, MDPI, vol. 10(8), pages 1-23, April.
    10. Gilbert Laporte, 2016. "Scheduling issues in vehicle routing," Annals of Operations Research, Springer, vol. 236(2), pages 463-474, January.
    11. 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.
    12. Schyns, M., 2015. "An ant colony system for responsive dynamic vehicle routing," European Journal of Operational Research, Elsevier, vol. 245(3), pages 704-718.
    13. Salavati-Khoshghalb, Majid & Gendreau, Michel & Jabali, Ola & Rei, Walter, 2019. "An exact algorithm to solve the vehicle routing problem with stochastic demands under an optimal restocking policy," European Journal of Operational Research, Elsevier, vol. 273(1), pages 175-189.
    14. Yu, Junfang & Dong, Yuanyuan, 2013. "Maximizing profit for vehicle routing under time and weight constraints," International Journal of Production Economics, Elsevier, vol. 145(2), pages 573-583.
    15. Anirudh Subramanyam & Panagiotis P. Repoussis & Chrysanthos E. Gounaris, 2020. "Robust Optimization of a Broad Class of Heterogeneous Vehicle Routing Problems Under Demand Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 32(3), pages 661-681, July.
    16. Campelo, Pedro & Neves-Moreira, Fábio & Amorim, Pedro & Almada-Lobo, Bernardo, 2019. "Consistent vehicle routing problem with service level agreements: A case study in the pharmaceutical distribution sector," European Journal of Operational Research, Elsevier, vol. 273(1), pages 131-145.
    17. 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.
    18. Baozhen Yao & Qianqian Yan & Mengjie Zhang & Yunong Yang, 2017. "Improved artificial bee colony algorithm for vehicle routing problem with time windows," PLOS ONE, Public Library of Science, vol. 12(9), pages 1-18, September.
    19. A. Mor & M. G. Speranza, 2022. "Vehicle routing problems over time: a survey," Annals of Operations Research, Springer, vol. 314(1), pages 255-275, July.
    20. Karina Thiebaut & Artur Pessoa, 2023. "Approximating the chance-constrained capacitated vehicle routing problem with robust optimization," 4OR, Springer, vol. 21(3), pages 513-531, September.

    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:spr:jglopt:v:80:y:2021:i:3:d:10.1007_s10898-020-00990-0. 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.springer.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.