Generating optimal multiple-segment cutting patterns for rectangular blanks

Abstract

This paper considers the unconstrained two-dimensional guillotine-cutting problem of rectangular blanks. It suggests the application of multiple-segment cutting patterns. A multiple-segment pattern consists of one or more segments that have the same width as that of the stock sheet. The lengths of the segments may be different. Strips in each segment are of the same length and direction. An algorithm based on dynamic programming is presented for generating the optimal multiple-segment patterns. Computations are performed both on benchmark problems and on random problems. The algorithm can solve most small-scale problems to optimality. For problems of larger scale, it can give solutions very close to optimal, and the time efficiency is much more higher than that of the exact algorithm for non-staged cutting. Furthermore, the algorithm can consider the restriction of the cutting process and generate cutting patterns that are easy to cut.