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

In: Operations Research Proceedings 2015

Author

Listed:
  • Isabel Friedow

    (Technical University of Dresden)

  • Guntram Scheithauer

    (Technical University of Dresden)

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.

Suggested Citation

  • Isabel Friedow & Guntram Scheithauer, 2017. "Using Contiguous 2D-Feasible 1D Cutting Patterns for the 2D Strip Packing Problem," Operations Research Proceedings, in: Karl Franz Dörner & Ivana Ljubic & Georg Pflug & Gernot Tragler (ed.), Operations Research Proceedings 2015, pages 71-77, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-42902-1_10
    DOI: 10.1007/978-3-319-42902-1_10
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    Cited by:

    1. Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.

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