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. © Springer-Verlag 2004.
CITATION STYLE
Seiden, S. S., & Woeginger, G. J. (2005). The two-dimensional cutting stock problem revisited. Mathematical Programming, 102(3), 519–530. https://doi.org/10.1007/s10107-004-0548-1
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