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

  • Michael KhachayEmail author
  • Yuri Ogorodnikov
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)

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.

Keywords

Capacitated Vehicle Routing Problem Time windows Efficient 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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