不确定环境下一维下料问题  

One-dimensional cutting problem in random environment

作　　者：马俊燕[1,2] 韩志会 骆德铖 韩贺春 肖海华[1] Ma Junyan;Han Zhihui;Luo Decheng;Han Hechun;Xiao Haihua(College of Mechanical Engineering,Guangxi University,Nanning 530004,China;Guangxi Key Laboratory of Manufacturing Systems and Advanced Manufacturing Technology,Guangxi University,Nanning 530004,China)

机构地区：[1]广西大学机械工程学院,广西南宁530004 [2]广西大学广西制造系统与先进制造重点实验室,广西南宁530004

出　　处：《锻压技术》2020年第3期190-196,共7页Forging & Stamping Technology

基　　金：广西自然科学基金资助项目(2018GXNSFAA138158);广西教育厅项目(2017KY0023);2016年广西制造系统与先进制造技术重点实验室项目(16-380-12S006)。

摘　　要：针对实际工程中一维下料所处环境的不确定性,建立数学模型,提出一种基于递推矩阵的列生成算法求解。首先以原材料使用量最少为目标,建立确定环境下数学模型和随机环境下料模型;然后通过实验对比发现,随机环境能增加材料利用率,更加符合实际生产需求。通过建立随机期望值模型,生成随机值,将随机规划问题变成常规线性问题进行分析计算,并使用基于递推矩阵的列生成算法进行计算下料方案。根据实例优化计算所得结果,通过分析可知,在随机大量订单环境下使用基于递推矩阵的列生成算法,不仅能够减少下料方式,而且能够降低原材料消耗量。为有效提高工厂材料利用率、减少下料和降低成本提供了一种方式。For the uncertainty of one-dimensional cutting environment in practical engineering,the mathematical model was established,and a column generation algorithm based on recursive matrix was proposed.Firstly,the mathematical model under the certain environment and the cutting model under the random environment were established based on the least amount of raw materials used as the target.Then,it was found that the material utilization rate could be increased in a random environment to be more in line with the actual production demand through the comparison of experiments.Furthermore,the random programming problem transformed into a conventional linear problem was analyzed and calculated by establishing a random expected value model to generate random values,and the cutting scheme was calculated by the column generation algorithm based on recursive matrix.According to the results of optimization calculation,the result analysis shows that using the column generation algorithm based on recursive matrix in a random large order environment can not only reduce the ways of cutting,but also reduce the consumption of raw materials,which provides a way for effectively improving the utilization rate of materials,reducing the cutting schemes and the cost in factory.

关 键 词：一维下料 数学模型 随机环境 随机期望值模型 递推矩阵 列生成 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]