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Mathematical Programming

, Volume 102, Issue 3, pp 519–530 | Cite as

The two-dimensional cutting stock problem revisited

  • Steven S. Seiden
  • Gerhard J. Woeginger
Article

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.

Keywords

Cutting stock Strip packing Guillotine cuts Packing problem Approximation scheme Worst case analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Steven S. Seiden
    • 1
  • Gerhard J. Woeginger
    • 2
  1. 1.Department of Computing ScienceLousiana State UniversityBaton RougeUSA
  2. 2.Department of Mathematics and Computer ScienceTU EindhovenEindhovenThe Netherlands

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