Skip to main content
SpringerLink
Log in

Using Contiguous 2D-Feasible 1D Cutting Patterns for the 2D Strip Packing Problem

  • Conference paper
  • First Online:
Operations Research Proceedings 2015

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

  • 1396 Accesses

Abstract

We consider the 2D rectangular strip packing problem without rotation. A relaxation of that problem is the 1D horizontal bar relaxation, the LP relaxation of the 1D binary cutting stock problem. To represent a solution of the strip packing problem, a solution of the horizontal bar relaxation has to satisfy, among others, the vertical contiguous condition. To strengthen the bar relaxation with respect to that vertical contiguity, we investigate a cutting plane approach. Furthermore, a solution of the bar relaxation must ensure constant location of items. Because 1D cutting patterns do not provide any information about the location of the items contained, we investigate methods to provide 2D feasibility of patterns in the column generation and cutting plane process, respectively. Some computational results are also reported.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Alvarez-Valdez, R., Parreño, F., Tamarit, J.M.: A branch and bound algorithm for the strip paking problem. OR Spectr. 31, 431–459 (2009)

    Article  Google Scholar 

  2. Friedow, I., Scheithauer, G.: New inequalities for 1D relaxations of the 2D rectangular strip packing problem. In: Operations Research Proceedings 2014. Springer (2016)

    Google Scholar 

  3. Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems - a survey. Eur. J. Op. Res. 141, 241–252 (2002)

    Article  Google Scholar 

  4. Martello, S., Monaci, M., Vigo, D.: An exact approach to the strip-packing problem. INFORMS J. Comput. 15(3), 310–319 (2003)

    Article  Google Scholar 

  5. Padberg, M.: Packing small boxes into a big box. Math. Methods Op. Res. 52, 1–21 (2000)

    Article  Google Scholar 

  6. Scheithauer, G.: LP-based bounds for the container and multi-container loading problem. Int. Trans. Op. Res. 6, 199–213 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Numerical Mathematics, Technical University of Dresden, 01069, Dresden, Germany

    Isabel Friedow & Guntram Scheithauer

Authors
  1. Isabel Friedow
    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 Isabel Friedow .

Editor information

Editors and Affiliations

  1. Department of Business Administration, University of Vienna, Vienna, Austria

    Karl Franz Dörner

  2. Decision Sciences and Statistics (IDS) Department, ESSEC Business School of Paris, Cergy Pontoise Cedex, France

    Ivana Ljubic

  3. Department of Statistics and Operations Research, University of Vienna, Vienna, Austria

    Georg Pflug

  4. Operations Research and Control Systems, TU Wien, Vienna, Austria

    Gernot Tragler

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this paper

Cite this paper

Friedow, I., Scheithauer, G. (2017). Using Contiguous 2D-Feasible 1D Cutting Patterns for the 2D Strip Packing Problem. In: Dörner, K., Ljubic, I., Pflug, G., Tragler, G. (eds) Operations Research Proceedings 2015. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-42902-1_10

Download citation

Publish with us

Policies and ethics

Search

Navigation