Simple block patterns for the two-dimensional cutting problem

Abstract

This paper presents an algorithm for the unconstrained two-dimensional cutting problem of rectangular pieces. It proposes the simple block (SB) pattern consisting of simple blocks. The SB pattern is defined recursively. Each cut on the stock plate produces just one simple block. A horizontal cut produces a horizontal block with width equal to that of the leftmost piece in the block. A vertical cut produces a vertical block with length equal to that of the bottommost piece in the block. The algorithm generates the optimal SB pattern recursively, and selects optimally the first piece in each block. It uses upper bound to prune some unpromising branches during the searching process. The computational results indicate that the algorithm is highly efficient in improving material utilization, and the computation time is reasonable.