关于“截断切割”的最优设计

Design on Optimal Material-Cutting Methods

针对 1 997年全国大学生数学建模竟赛 B题 ,对于换刀费用 e=0的情况 ,本文设计了一种异常简捷的切割厚度排序法来寻找最优切割方案 ,同时在数学上给出了严格的证明 .对于换刀费用 e≠ 0的情况 ,以 e=0时得到的最优切割方案为基础 ,先通过简单的调整原则寻找出限定不同换刀次数时各自的最优切割方案 ,再通过费用比较便可简捷地得到随 e值的大小而变化的最优切割方案 .本文构造的模型在求解时无须用计算机编程 。

To solve the problem B of CMCM 1997, under the condition of e=0 , this paper presents a very easy method that decides optimal cutting scheme according to the size of cutting thickness. Under the condition of e≠0 , this paper presents a modified method based on the method over the condition of e=0 . According to easy adjustment principle, the modified method firstly finds optimal cutting schemes having different number of changing knife. Then by comparing the cost of optimal cutting schemes having different number of changing knife, we can easily get optimal cutting scheme that is changed with the value of e(e≠0) . The model constructed by this paper can be easily worked out by hand and computer programming is not necessary.