Integrated approaches for generating and sequencing cutting patterns in two-dimensional cutting stock problems

This paper deals with the classical two-dimensional cutting stock problem, which consists of generating cutting patterns to produce bi rectangular items of sizes (li,wi), i=1,..,m, from rectangular objects of sizes (L,W), so that an objective is optimized, for example, the cost or trim loss. However, to cut the patterns they should be sequenced in such a way as to optimize another objective, for example, minimize the maximum number of open stacks of items. Despite their dependence, the cutting pattern generation and sequencing problems have often been solved independently in practice, although a good solution for the former problem may not be a good solution for the latter, and vice-versa. In this study we present three heuristics to solve the integrated generation and sequencing problem, considering the trade-off between the objectives involved. To analyze the performance of the approaches, computational results are presented for randomly generated instances of two-dimensional 2-staged and non-staged guillotine cutting problems, as well as an instance from a furniture company.