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Improved Polynomial Time Approximation Scheme for Capacitated Vehicle Routing Problem with Time Windows

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Optimization and Applications (OPTIMA 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 974))

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Abstract

The Capacitated Vehicle Routing Problem with Time Windows is the well-known combinatorial optimization problem having numerous valuable applications in operations research. In this paper, following the famous framework by M. Haimovich and A. Rinnooy Kan and technique by T. Asano et al., we propose a novel approximation scheme for the planar Euclidean CVRPTW. For any fixed \(\varepsilon >0\), the proposed scheme finds a \((1+\varepsilon )\)-approximate solution of CVRPTW in time

$$TIME(\mathrm {TSP},\rho ,n)+O(n^2)+O\left( e^{O\left( q\,\left( \frac{q}{\varepsilon }\right) ^3(p\rho )^2\log (p\rho )\right) }\right) ,$$

where q is the given vehicle capacity bound, p is the number of time windows for servicing the customers, and \(TIME(\mathrm {TSP},\rho ,n)\) is the time needed to find a \(\rho \)-approximate solution for an auxiliary instance of the metric TSP.

This research was supported by Russian Science Foundation, grant no. 14-11-00109.

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Notes

  1. 1.

    By construction, \(Q\subset X[S]\).

  2. 2.

    As it follows from Lemma 1.

  3. 3.

    Also known as Ferrers board.

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Author information

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 author

Correspondence to Michael Khachay .

Editor information

Editors and Affiliations

  1. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Yury Evtushenko

  2. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

  3. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  4. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

    Yury Kochetov

  5. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Vlasta Malkova

  6. FRC CSC RAS, Dorodnitsyn Computing Centre, Moscow, Russia

    Mikhail Posypkin

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Khachay, M., Ogorodnikov, Y. (2019). Improved Polynomial Time Approximation Scheme for Capacitated Vehicle Routing Problem with Time Windows. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_12

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  • DOI: https://doi.org/10.1007/978-3-030-10934-9_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10933-2

  • Online ISBN: 978-3-030-10934-9

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