An Optimum Solution for One-Dimensional Slitting Problems: A Dynamic Programming Approach
针对纺织、造纸或金属板材行业中一维分切问题，提出动态规划方法，在考虑宽度和缺陷数量对价值影响的前提下，最大化销售总价值。
One-dimensional slitting problems are often encountered in textile, paper or sheet-metal industries where a roll of this product needs to be divided into various narrower-width rolls. The rolls are slit into pieces such that the total value of the sale is maximized depending on the width and the number of defects in the sheet. As the width of a piece increases, the value of the piece increases also, but on the other hand, the number of defects in the piece increases as well, causing reduction in its value. Based on these constraints, a dynamic programming formulation is framed so as to maximize the total value of the sale. Computational complexity with a numerical example is discussed to demonstrate how the procedure works.