An algorithm for the two-dimensional cutting problem of punched strips with blade length constraint

Abstract

This paper presents an algorithm for generating optimal T-shaped cutting patterns of punched strips. A strip contains only items of the same type. The stock plate is divided into items in two stages. First a guillotine machine cuts the plate into strips, then a stamping press punches out the items from the strips. The blade length of the guillotine machine may be shorter than the plate length. The algorithm divides the plate into two segments. Each segment contains strips of the same direction. The strip directions of the two segments are perpendicular to each other. The algorithm uses dynamic programming techniques to determine the optimal strip layouts on segments of different lengths not longer than the blade length, considers all possible combinations of two segments, and selects the best pair as the optimal solution. The computational results indicate that the new algorithm is much more efficient than the existing algorithm.