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

  • Michael KhachayEmail author
  • Yuri Ogorodnikov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Capacitated vehicle routing problem Time windows Splittable demand Polynomial time approximation scheme 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Krasovsky Institute of Mathematics and MechanicsEkaterinburgRussia
  2. 2.Ural Federal UniversityEkaterinburgRussia
  3. 3.Omsk State Technical UniversityOmskRussia

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