Heuristics for the generation problems and sequencing of patterns of two-dimensional cutting

This paper is concerned with the classical two-dimensional cutting stock problem, whose solution consists of a set of cutting patterns that optimize an objective function, for example, the waste of material. Nevertheless, the cutting patterns have to be sequenced so that another criterion is also optimized, for example, the maximum number of open stacks of the items (a stack is opened when a type of item is cut for the first time and closed when all items of this type were cut). A good solution for the problem of generating cutting patterns often does not result in a good solution for the problem of sequencing cutting patterns, and vice-versa. In general, these two problems are treated, either in practice or in the literature, in an independent and successive way. Pileggi et al. proposed heuristic approaches to solve these two problems in an integrated way, considering the trade-off between the objectives involved, and they analyzed the one-dimensional cutting case (e.g., cut of bars). In the present study these approaches are extended and applied to analyze the two-dimensional guillotine cutting case (e.g., cut of plates). Computational results are presented for randomly generated examples and for an actual instance of a furniture company.