中文摘要：

讨论矩形毛坯无约束两维剪切排样问题,采用两段排样方式以简化切割工艺。优化目标是使排样方式的价值最大,而排样方式的价值等于其中所含毛坯的总价值与切割成本之差,假定切割成本与切割刀数成正比。文中提出了一种动态规划算法,在生成两段排样方式的过程中既考虑毛坯价值又考虑切割刀数。采用随机生成的例题对该算法进行了测试,将算法与传统两段排样算法和考虑刀数的T型排样算法进行了比较。实验结果表明该算法的优化结果好于以上两种著名算法,而且计算时间合理。最后一个生产实例的解表明：该算法在保证板材较高利用率的同时能有效地减少切割刀数。

英文摘要：

The rectangular blank unconstrained two-dimensional cutting problem were discussed using two segment patterns to simplify the cutting process. The optimization goal is to maximize the pattern value which it is the difference between the total value of the blanks included and the cutting cost,assuming that the cutting cost is proportional to the number of cuts. This paper presents a dynamic programming algorithm,in which both the blank value and cutting numbers are considered through the process of generation two segment cutting patterns. The randomly generated examples are used to test the algorithm. Compared with the traditional two segment patterns algorithm and considering cutting numbers in T-shape patterns algorithm,the experimental results show that the optimization results of the algorithm is better than the above 2 well-known algorithms with a reasonable computation time. Finally,an example of production solution shows that the algorithm not only can ensure a high utilization rate of sheet but also can effectively reduce the number of cuts.