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2019 | OriginalPaper | Buchkapitel

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

verfasst von : Michael Khachay, Yuri Ogorodnikov

Erschienen in: Mathematical Optimization Theory and Operations Research

Verlag: 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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Nächstes Kapitel Local Search Approach for the Medianoid Problem with Multi-purpose Shopping Trips

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

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

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

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