关于切割限制的钢材下料问题的探究

On Steel Blanking with Cutting Limitation

本文主要研究有切割条件限制的钢材切割下料问题,通过给定的原料完成订单,并保证较高的成材率.对于问题1,仅考虑尺寸较大的卷料订单,本文建立线性规划模型,利用剪枝法,求出满足卷料订单的切割模式,并根据约束条件得到成材率最高的切割方法.对于问题2,在考虑所有订单时建立分组优化模型,通过增加约束和分组,将问题简化,得到新的模式,从而求解得到满足要求的切割方法.对于问题3,考虑额外指定浮动比例的所有订单,本文在上一问题基础上考虑到在浮动范围内切割的钢材减小会减少原料使用张数,而适当增大切割钢材会增大原料成材率,因此选用最小长度确定张数,得出满足要求的切割方法.

This paper studies the steel blanking with cutting conditions,through the given raw materials to complete the order,and ensure a higher yield.For Problem 1,considering only the size coil order,we establish a linear programming model,use pruning method to find the cutting mode that meets the coil order,and obtain the cutting method with the highest yield according to the constraint conditions.For Problem 2,we establish a grouping optimization model when all orders are considered,and the problem is simplified by adding constraints and grouping so that a new mode is obtained,and the cutting method meeting the requirements is solved.For Problem 3,considering the fluctuation ratio in all orders on the basis of the previous question,we consider that the reduction of the steel cut in the fluctuation range will reduce the number of sheets used in raw materials,and the appropriate increase of the steel cut will increase the yield of raw materials,so the minimum length is selected to determine the number of sheets,and the cutting method meeting the requirements is obtained.