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Efficient PTAS for the Euclidean Capacitated Vehicle Routing Problem with Non-uniform Non-splittable Demand

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Analysis of Images, Social Networks and Texts (AIST 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11832))

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Abstract

The Capacitated Vehicle Routing Problem (CVRP) is the well-known combinatorial optimization problem having numerous relevant applications in operations research. As known, CVRP is strongly NP-hard even in the Euclidean plane, APX-hard for an arbitrary metric, and can be approximated in polynomial time with any accuracy in the Euclidean spaces of any fixed dimension. In particular, for the several special cases of the planar Euclidean CVRP there are known Polynomial Time Approximation Schemes (PTAS) stemming from the seminal papers by M. Haimovich, A. Rinnooy Kan and S. Arora. Although, these results appear to be promising and make a solid contribution to the field of algorithmic analysis of routing problems, all of them are restricted to the special case of the CVRP, where all customers have splittable or even unit demand, which seems to be far from the practice.

In this paper, to the best of our knowledge, we propose the first Efficient Polynomial Time Approximation Scheme (EPTAS) for this problem in the case of non-uniform non-splittable demand.

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Notes

  1. 1.

    Although, in some cases, they can perform even better.

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Acknowledgments

This research was supported by the Russian Foundation for Basic Research, grants no. 17-08-01385 and 19-07-01243.

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Authors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay & Yuri Ogorodnikov

  2. Ural Federal University, Ekaterinburg, Russia

    Michael Khachay & Yuri Ogorodnikov

  3. Omsk State Technical University, Omsk, Russia

    Michael Khachay

Authors
  1. Michael Khachay
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  2. Yuri Ogorodnikov
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Corresponding authors

Correspondence to Michael Khachay or Yuri Ogorodnikov .

Editor information

Editors and Affiliations

  1. RWTH Aachen University, Aachen, Germany

    Wil M. P. van der Aalst

  2. University of Ljubljana, Ljubljana, Slovenia

    Vladimir Batagelj

  3. National Research University Higher School of Economics, Moscow, Russia

    Dmitry I. Ignatov

  4. Krasovskii Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  5. National Research University Higher School of Economics, Moscow, Russia

    Valentina Kuskova

  6. University of Oslo, Oslo, Norway

    Andrey Kutuzov

  7. National Research University Higher School of Economics, Moscow, Russia

    Sergei O. Kuznetsov

  8. National Research University Higher School of Economics, Moscow, Russia

    Irina A. Lomazova

  9. Lomonosov Moscow State University, Moscow, Russia

    Natalia Loukachevitch

  10. LORIA, Vandœuvre-lès-Nancy, France

    Amedeo Napoli

  11. University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  12. Ca Foscari University of Venice, Venice, Italy

    Marcello Pelillo

  13. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Andrey V. Savchenko

  14. Kazan Federal University, Kazan, Russia

    Elena Tutubalina

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Khachay, M., Ogorodnikov, Y. (2019). Efficient PTAS for the Euclidean Capacitated Vehicle Routing Problem with Non-uniform Non-splittable Demand. In: van der Aalst, W., et al. Analysis of Images, Social Networks and Texts. AIST 2019. Lecture Notes in Computer Science(), vol 11832. Springer, Cham. https://doi.org/10.1007/978-3-030-37334-4_35

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  • DOI: https://doi.org/10.1007/978-3-030-37334-4_35

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