An Algorithm to Optimal Two-Stage Homogenous Strip Patterns of Rectangular Pieces

Abstract

This paper presents an algorithm for two-stage homogenous strip patterns for rectangular pieces. The algorithm is appropriate for the shearing and punching process. It proposes the two-stage homogenous strip patterns that can be cut into homogenous strips in two stages, with another two stages being required to cut the strips into pieces. Firstly vertical cuts divide the stock sheet into segments, and then horizontal cuts divide the segments into homogenous strips. A homogenous strip contains pieces of the same type. The algorithm uses a dynamic programming recursion to determine the strip layout on each segment, solves knapsack problems to obtain the segment layout on the sheet. The algorithm is tested through benchmark problems, and compares with two famous algorithms. The pattern value and the computation speed of this paper’s algorithm are better than that of the classic two-stage algorithm. What’s more, this paper’s algorithm can give solutions very close to optimality.