A recursive algorithm for generating homogeneous T-shape cutting patterns

Abstract

Both the material utilization and the complexity of the cutting process should be considered when generating cutting patterns. This paper presents a recursive algorithm for constrained two-dimensional guillotine-cutting problems of rectangles. It uses homogeneous T-shape patterns to simplify the cutting process. Only homogeneous strips are allowed, each of which contains rectangular items of the same type. The plate is divided into two segments, each of which consists of strips with the same length and direction. The strip directions of the two segments are perpendicular to each other. Two recursion functions are established. The first generates optimal layouts of parallel strips on segments with specified sizes, and the second determines the optimal T-shape pattern on the plate. The optimal solution to the unconstrained version of the cutting problem is used to reduce the computation time. The computational results indicate that the algorithm is efficient both in computation time and in material utilization.