Generation of Optimal Homogenous Strips Patterns for the Two-Dimensional Cutting Problem

An algorithm is proposed for generating patterns of rectangular items based on homogenous strips (RIBTHS). It divides the plate into four regions. Each region contains homogenous strips of the same direction and length. An enumeration method is used to determine the positions of the three partition lines. The knapsack algorithm is used to obtain the optimal layout of the strips in each region. The combination of the regions that has the maximum value is selected as the optimal solution. The procedure is combined with the linear programming approach to form the algorithm for generating the cutting plans of large scale cutting stock problems. The algorithm was tested using lots of benchmark instances reported in the literature. The results indicate that the algorithm is efficient both in improving material usage and simplifing the cutting process.