板材优化下料的数学模型的研究

A Study on the Mathematical Models for Two Dimensional Guillotine Cullting-stock

对国内外已有的几种板材下料数学模型进行了分析，指出了某些模型可能导致一些较好的初始切割方式的漏选，有些模型单纯追求剩余面积最小的下料方式而使下料结果不适当。在此基础上建立了修正过的下料数学模型。该模型采用降维启发式法将二维问题转化为一维问题，其中初始切割方式的选取综合考虑了最小剩余面积、待求零件的相对面积大小、数量要求等多方面的因素。

Based on the analysis and study on some existed models for two-dimensional Guillotine Cutting-Stock problem, it is pointed out that some kinds of the models may miss some good cutting patterns,and some may result in inadequate solutions because of only considering the patterns with the smallest waste. A kind of revised two-dimensional cutting-stock models are developed,which transform the two-dimensional problem into the one-dimensional one using the dimension-decreasing heuristic method and whose initial patterns are considered comprehensively. In this kind of models, not only the least waste,but also the other constraints,such as the demands and the relative area of the order plates are considered.