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2019 | OriginalPaper | Chapter

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

Authors : Michael Khachay, Yuri Ogorodnikov

Published in: Mathematical Optimization Theory and Operations Research

Publisher: Springer International Publishing

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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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previous chapter A 2-Approximation Algorithm for the Graph 2-Clustering Problem

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

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Title: Approximation Scheme for the Capacitated Vehicle Routing Problem with Time Windows and Non-uniform Demand
Authors: Michael Khachay
Yuri Ogorodnikov
Publisher: Springer International Publishing
Book: Mathematical Optimization Theory and Operations Research
Print ISBN: 978-3-030-22628-2

Electronic ISBN: 978-3-030-22629-9

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-030-22629-9_22

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