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The two-dimensional cutting stock problem revisited

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Abstract.

In the strip packing problem (a standard version of the two-dimensional cutting stock problem), the goal is to pack a given set of rectangles into a vertical strip of unit width so as to minimize the total height of the strip needed. The k-stage Guillotine packings form a particularly simple and attractive family of feasible solutions for strip packing. We present a complete analysis of the quality of k-stage Guillotine strip packings versus globally optimal packings: k=2 stages cannot guarantee any bounded asymptotic performance ratio. k=3 stages lead to asymptotic performance ratios arbitrarily close to 1.69103; this bound is tight. Finally, k=4 stages yield asymptotic performance ratios arbitrarily close to 1.

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Authors and Affiliations

  1. Department of Computing Science, Lousiana State University, Baton Rouge, LA 70803, USA

    Steven S. Seiden

  2. Department of Mathematics and Computer Science, TU Eindhoven, 513, 5600 MB, Eindhoven, The Netherlands

    Gerhard J. Woeginger

Authors
  1. Steven S. Seiden
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  2. Gerhard J. Woeginger
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Additional information

Steve Seiden died in a tragic accident on June 11, 2002. This paper resulted from a number of email discussions between the authors in spring 2002.

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Seiden, S., Woeginger, G. The two-dimensional cutting stock problem revisited. Math. Program. 102, 519–530 (2005). https://doi.org/10.1007/s10107-004-0548-1

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  • DOI: https://doi.org/10.1007/s10107-004-0548-1

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