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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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