Optimization integrated approaches to the problems of generation and sequencing patterns of cutting: unidimensional case

The cutting pattern generating problem (or cutting stock problem) consists in determining the set of patterns in which ordered units (items) are cut from larger units (objects) so that, for example, the cost or waste of material is minimized. The cutting pattern sequencing problem consists in determining the sequence in which the patterns are cut so that, for example, the maximum number of open stacks (stacks of items with demand only partially produced and that will be cut in the next cutting patterns of the sequence) is minimized. In general a good solution for the pattern generating problem does not correspond to a good solution for the pattern sequencing problem and vice-versa. These problems are frequently solved, both in practice and in the literature, in an independent and successive way. This work presents three heuristic approaches to deal with the integrated pattern generating and sequencing problem, considering the trade-off between the objectives involved. Although the approaches can be applied to cutting and packing problems of any dimension, in this work they are analyzed and compared only for the one-dimensional cutting case.