Mathematical Programming

, Volume 102, Issue 3, pp 519–530

# 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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© 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