Recursive algorithm for the two-dimensional cutting problem of punched strips

摘要

Purpose - To provide an algorithm for the two-dimensional guillotine-cutting problem of punched strips. Design/methodology/approach - It is assumed that the stock sheet is cut into blanks in two stages. First a guillotine shear cuts the sheet into strips, and then a stamping press punches out the blanks from the strips. To generate good strip layout, the sheet is divided into two segments with an orthogonal cut. Each segment consists of strips in the same direction. The strip directions of the two segments are perpendicular to each other. A recursion function is established to determine the optimal strip layouts on segments of different lengths. All possible segment lengths are considered either explicitly or implicitly. Two segments of different strip directions are selected optimally to compose the final cutting pattern. Findings - A strip can be taken as consisting of rectangular pieces, where the length of the first piece may be longer than that of the others. Normal lengths and widths can be defined according to the properties of punched strips. Considering only normal segment lengths and using lower bound in the recursion function can reduce the computation time drastically. Practical implications - Based on the algorithm, practitioners may develop applications to solve real world two-dimensional cutting problem of punched strips. Originality/value - The two-segment cutting patterns for punched strips are proposed. They are simple to cut and may be welcomed in practice.