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International Workshop on Approximation and Online Algorithms

WAOA 2010: Approximation and Online Algorithms pp 94–105Cite as

The Train Delivery Problem - Vehicle Routing Meets Bin Packing

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6534))

Abstract

We consider the train delivery problem which is a generalization of the bin packing problem and is equivalent to a one dimensional version of the vehicle routing problem with unsplittable demands. The problem is also equivalent to the problem of minimizing the makespan on a single batch machine with non-identical job sizes.

The train delivery problem is strongly NP-hard and does not admit an approximation ratio better than 3/2. We design the first approximation schemes for the general problem. We give an asymptotic polynomial time approximation scheme, under a notion of asymptotic that makes sense even though scaling can cause the cost of the optimal solution of any instance to be arbitrarily large. Alternatively, we give a polynomial time approximation scheme for the case where W, an input parameter that corresponds to the bin size or the vehicle capacity, is polynomial in the number of items or demands.

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Author information

Authors and Affiliations

  1. Brown University, Providence, RI, 02918, USA

    Aparna Das, Claire Mathieu & Shay Mozes

Authors
  1. Aparna Das
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  2. Claire Mathieu
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  3. Shay Mozes
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  2. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, Ontario, Canada

    Roberto Solis-Oba

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© 2011 Springer-Verlag Berlin Heidelberg

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Das, A., Mathieu, C., Mozes, S. (2011). The Train Delivery Problem - Vehicle Routing Meets Bin Packing. In: Jansen, K., Solis-Oba, R. (eds) Approximation and Online Algorithms. WAOA 2010. Lecture Notes in Computer Science, vol 6534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18318-8_9

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  • DOI: https://doi.org/10.1007/978-3-642-18318-8_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-18317-1

  • Online ISBN: 978-3-642-18318-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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