IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v57y2010i8p728-748.html
   My bibliography  Save this article

Approximation results for min‐max path cover problems in vehicle routing

Author

Listed:
  • Zhou Xu
  • Liang Xu
  • Chung‐Lun Li

Abstract

This article studies a min‐max path cover problem, which is to determine a set of paths for k capacitated vehicles to service all the customers in a given weighted graph so that the largest path cost is minimized. The problem has wide applications in vehicle routing, especially when the minimization of the latest service completion time is a critical performance measure. We have analyzed four typical variants of this problem, where the vehicles have either unlimited or limited capacities, and they start from either a given depot or any depot of a given depot set. We have developed approximation algorithms for these four variants, which achieve approximation ratios of max{3 ‐ 2/k,2}, 5, max{5 ‐ 2/k,4}, and 7, respectively. We have also analyzed the approximation hardness of these variants by showing that, unless P = NP, it is impossible for them to achieve approximation ratios less than 4/3, 3/2, 3/2, and 2, respectively. We have further extended the techniques and results developed for this problem to other min‐max vehicle routing problems.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010

Suggested Citation

  • Zhou Xu & Liang Xu & Chung‐Lun Li, 2010. "Approximation results for min‐max path cover problems in vehicle routing," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(8), pages 728-748, December.
    • Handle: RePEc:wly:navres:v:57:y:2010:i:8:p:728-748
    DOI: 10.1002/nav.20434
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20434
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20434?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. Kemal Altinkemer & Bezalel Gavish, 1990. "Technical Note—Heuristics for Delivery Problems with Constant Error Guarantees," Transportation Science, INFORMS, vol. 24(4), pages 294-297, November.
    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. Shoshana Anily & Julien Bramel, 1999. "Approximation algorithms for the capacitated traveling salesman problem with pickups and deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 654-670, September.
    4. Ann Melissa Campbell & Dieter Vandenbussche & William Hermann, 2008. "Routing for Relief Efforts," Transportation Science, INFORMS, vol. 42(2), pages 127-145, May.
    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)

    Citations

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


    Cited by:

    1. Wei Yu & Zhaohui Liu, 2019. "Better approximability results for min–max tree/cycle/path cover problems," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 563-578, February.

    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. 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.
    2. Inge Li Gørtz & Marco Molinaro & Viswanath Nagarajan & R. Ravi, 2016. "Capacitated Vehicle Routing with Nonuniform Speeds," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 318-331, February.
    3. Patrick Jaillet & Michael R. Wagner, 2008. "Generalized Online Routing: New Competitive Ratios, Resource Augmentation, and Asymptotic Analyses," Operations Research, INFORMS, vol. 56(3), pages 745-757, June.
    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. 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.
    6. Lysgaard, Jens & Wøhlk, Sanne, 2014. "A branch-and-cut-and-price algorithm for the cumulative capacitated vehicle routing problem," European Journal of Operational Research, Elsevier, vol. 236(3), pages 800-810.
    7. Anupam Gupta & Viswanath Nagarajan & R. Ravi, 2012. "Technical Note---Approximation Algorithms for VRP with Stochastic Demands," Operations Research, INFORMS, vol. 60(1), pages 123-127, February.
    8. Shoshana Anily & Julien Bramel, 1999. "Approximation algorithms for the capacitated traveling salesman problem with pickups and deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 654-670, September.
    9. 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.
    10. Tobias Harks & Felix G König & Jannik Matuschke, 2013. "Approximation Algorithms for Capacitated Location Routing," Transportation Science, INFORMS, vol. 47(1), pages 3-22, February.
    11. Zhang, Meng & Wang, Nengmin & He, Zhengwen & Jiang, Bin, 2021. "Vehicle routing optimization for hazmat shipments considering catastrophe avoidance and failed edges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 150(C).
    12. Jan Christiaens & Greet Vanden Berghe, 2020. "Slack Induction by String Removals for Vehicle Routing Problems," Transportation Science, INFORMS, vol. 54(2), pages 417-433, March.
    13. Tino Henke & M. Grazia Speranza & Gerhard Wäscher, 2019. "A branch-and-cut algorithm for the multi-compartment vehicle routing problem with flexible compartment sizes," Annals of Operations Research, Springer, vol. 275(2), pages 321-338, April.
    14. Bonet Filella, Guillem & Trivella, Alessio & Corman, Francesco, 2023. "Modeling soft unloading constraints in the multi-drop container loading problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 336-352.
    15. 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.
    16. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    17. A. Anaya-Arenas & J. Renaud & A. Ruiz, 2014. "Relief distribution networks: a systematic review," Annals of Operations Research, Springer, vol. 223(1), pages 53-79, December.
    18. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    19. A. Mor & M. G. Speranza, 2020. "Vehicle routing problems over time: a survey," 4OR, Springer, vol. 18(2), pages 129-149, June.
    20. Changshi Liu & Gang Kou & Yi Peng & Fawaz E. Alsaadi, 2019. "Location-Routing Problem for Relief Distribution in the Early Post-Earthquake Stage from the Perspective of Fairness," Sustainability, MDPI, vol. 11(12), pages 1-16, June.

    More about this item

    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:wly:navres:v:57:y:2010:i:8:p:728-748. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.