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Skiving is the process of joining smaller rolls to form larger rolls. When this process is combined with traditional roll-cutting technology, profitable solutions to once "hopeless" one-dimensional cutting stock problems can be found. A generalization of the classic cutting stock problem models the combined skiving and cutting stock problem. The commercial software package MAJIQTRIM solves this combined problem using both heuristic and linear programming (LP) methods.
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Johnson et al. (1997) studied this question.
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