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New Classes of Lower Bounds for Bin Packing Problems

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Integer Programming and Combinatorial Optimization (IPCO 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1412))

Abstract

The bin packing problem is one of the classical NP-hard op- timization problems. Even though there are many excellent theoretical results, including polynomial approximation schemes, there is still a lack of methods that are able to solve practical instances optimally. In this paper, we present a fast and simple generic approach for obtaining new lower bounds, based on dual feasible functions. Worst case analysis as well as comutational results show that one of our classes clearly out- performs the currently best known ‘economical’ lower bound for the bin packing problem by Martello and Toth, which can be understood as a special case. This indicates the usefulness of our results in a branch and bound framework.

This work was supported by the German Federal Ministry of Education, Science, Research and Technology (BMBF, Förderkennzeichen 01 IR 411 C7).

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Author information

Authors and Affiliations

  1. Center for Parallel Computing, Universität zu Köln, D-50923, Köln, Germany

    Sándor P. Fekete & Jörg Schepers

Authors
  1. Sándor P. Fekete
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  2. Jörg Schepers
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Editor information

Editors and Affiliations

  1. Department of Computational and Applied Mathematics, Rice University, 6020 Annapolis, Houston, TX, 77005, USA

    Robert E. Bixby

  2. PROS Strategic Solutions, 3223 Smith Street, Houston, TX, 77006, USA

    E. Andrew Boyd

  3. Department of Industrial, Engineering, Texas A&M University, 1000 Country Place Dr. Apt. 69, Houston, TX, 77079, USA

    Roger Z. Ríos-Mercado

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© 1998 Springer-Verlag Berlin Heidelberg

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Fekete, S.P., Schepers, J. (1998). New Classes of Lower Bounds for Bin Packing Problems. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_20

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  • DOI: https://doi.org/10.1007/3-540-69346-7_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64590-0

  • Online ISBN: 978-3-540-69346-8

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