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Approximation Scheme for the Capacitated Vehicle Routing Problem with Time Windows and Non-uniform Demand

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Book cover Mathematical Optimization Theory and Operations Research (MOTOR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11548))

Abstract

The Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) is the well-known combinatorial optimization problem having numerous valuable applications in operations research. Unlike the classic CVRP (without time windows constraints), approximation algorithms with theoretical guarantees for the CVRPTW are still developed much less, even for the Euclidean plane. In this paper, perhaps for the first time, we propose an approximation scheme for the planar CVRPTW with non-uniform splittable demand combining the well-known instance decomposition framework by A. Adamaszek et al. and Quasi-Polynomial Time Approximation Scheme (QPTAS) by L. Song et al. Actually, for any \(\varepsilon \in (0,1)\) the scheme proposed finds a \((1+\varepsilon )\)-approximate solution of the problem in polynomial time provided the capacity q and the number p of time windows does not exceed \(2^{\log ^\delta n}\) for some \(\delta =O(\varepsilon )\). For any fixed p and q the scheme is Efficient Polynomial Time Approximation Scheme (EPTAS) with subquadratic time complexity.

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Notes

  1. 1.

    Without loss of generality, we can can assume that \(d(y)=0\), for the depot y.

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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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Correspondence to Michael Khachay .

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Editors and Affiliations

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

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Khachay, M., Ogorodnikov, Y. (2019). Approximation Scheme for the Capacitated Vehicle Routing Problem with Time Windows and Non-uniform Demand. In: Khachay, M., Kochetov, Y., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2019. Lecture Notes in Computer Science(), vol 11548. Springer, Cham. https://doi.org/10.1007/978-3-030-22629-9_22

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  • DOI: https://doi.org/10.1007/978-3-030-22629-9_22

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