The Research and Realization of Algorithms for Guillotine Rectangle Cutting Stock Problem

The two-dimensional material cutting optimization is a kind of problem which usually appears in life. In order to save materials, the appropriate cutting plan must be selected to make consumed the least materials. In accordance with the cutting scheme, the rectangle cutting stock problem can be divided into two categories, guillotine and non-guillotine. The problem having guillotine constraint is studied and analyzed in the paper. First, the model for two-dimensional cutting stock problem is analyzed with the knapsack column algorithm for the one-dimensional cutting stock problem. Then, based on the analysis of the guillotine rectangle cutting stock problem and the comparison with one-dimensional cutting stock problem, a rectangle knapsack column generation algorithm is proposed. Finally, through testing instances, it is proved that this algorithm is a useful way to improve utilization ratio of plate material.