An exact algorithm for two-staged cutting patterns of rectangular pieces

Packing of rectangular is an NP-complete problem, and is widespread application in the industry. An algorithm is proposed for generating the optimal two-staged cutting patterns for rectangular blanks based on the homogenous block. In 43 problems, compared with the general two-staged algorithm, the pattern value of this paper's algorithm is larger in 21 problems, equal in 22 problems. In 20 problems, compared with the three block algorithm, the pattern value of this paper's algorithm is larger in 13 problems, equal in 7 problems. In all instances, the computation time of this paper's algorithm is 0–2 seconds.