Skip to main content
SpringerLink
Log in

Creating Worst-Case Instances for Lower Bounds of the 2D Strip Packing Problem

  • Conference paper
  • First Online:
Operations Research Proceedings 2016

Part of the book series: Operations Research Proceedings ((ORP))

  • 1990 Accesses

Abstract

We present a new approach to create instances with high absolute worst-case performance ratio of common lower bounds for the two-dimensional rectangular Strip Packing Problem. The idea of this new approach is to optimize the width and the height of all items regarding the absolute worst case performance ratio of the lower bound. Therefore, we model the pattern related to the lower bound as a solution of an ILP problem and merge this model with the Padberg-type model of the two-dimensional Strip Packing Problem. The merged model maximizes the absolute worst-case performance ratio of the lower bound. We introduce this new model for the horizontal bar relaxation and the horizontal contiguous bar relaxation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Belov, G., Kartak, V., Rohling, H., Scheithauer, G.: One-dimensional relaxations and LP bounds for orthogonal packing. Int. Trans. Oper. Res. 16, 745–766 (2009)

    Article  Google Scholar 

  2. Padberg, M.: Packing small boxes into a big box. Math. Meth. OR 1, 1–21 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Numerical Mathematics, Dresden University of Technology, Dresden, Germany

    Torsten Buchwald & Guntram Scheithauer

Authors
  1. Torsten Buchwald
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guntram Scheithauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Torsten Buchwald .

Editor information

Editors and Affiliations

  1. Institute of Computer Science, Helmut Schmidt University, Institute of Computer Science, Hamburg, Germany

    Andreas Fink

  2. Applied Mathematics, Helmut Schmidt University, Applied Mathematics, Hamburg, Germany

    Armin Fügenschuh

  3. Institute of Logistics and Organization, Helmut Schmidt University, Institute of Logistics and Organization, Hamburg, Germany

    Martin Josef Geiger

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Cite this paper

Buchwald, T., Scheithauer, G. (2018). Creating Worst-Case Instances for Lower Bounds of the 2D Strip Packing Problem. In: Fink, A., Fügenschuh, A., Geiger, M. (eds) Operations Research Proceedings 2016. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-55702-1_15

Download citation

Publish with us

Policies and ethics

Search

Navigation