一类优化下料数学模型存在的问题及对策

Problems in a Kind of Mathematical Models forCutting Stock and the Solution

现有文献所建立的各种优化下料数学模型中，有一大类是以残料总和为目标函数的。本文首先揭示了此类数学模型在用于解决某些实际下料问题时可能出现无解或虽然有解但其材料利用率很低等问题，然后指出了这些问题的实质，给出了这些模型的修正方案，并论证了修正后的模型与现有的典型适用数学模型之间的等价性。

Of the mathematical models for optimum cutting stock, there is a kind of model in which theobjective function is the total sum of the scraps. Some problems in the Kind of model are revealed in thispaper. That is, for some stock cutting problems, the model may have no solution or no good solution. Theproblems may be solved by revising the model. It is proved that the revised model is equivalant to the typicalpractictaI model.