摘要
已有研究未能充分地表现数学原理和单纯形表计算步骤之间的关系,从单纯形表与数学模型的一一对应关系视角能够巧妙展示单纯形算法的数学原理。根据进基变量在约束条件中的系数,提出了进基变量最大取值的确定方法及出基变量的确定方法,进而建立了模型迭代算法。算例分析表明,与单纯形表迭代相比,模型迭代能够更加清晰地展示单纯形算法的数学原理。
Existing studies can not well show the relationship between mathematical principles and calculation steps of the simplex table.The mathematical principle of the simplex algorithm can be effectively demonstrated from the perspective of the one-to-one correspondence relationship between the simplex table and the mathematical model.According to the coefficients of the entering variable in the constraint conditions,the determination method of the maximum value of the entering variable and the determination method of the leaving variable were proposed,and then the model iterative algorithm was established.Case analysis showed that,compared with simplex table iteration,model iteration can more clearly show the mathematical principle of the simplex algorithm.
作者
张宝成
康帅
ZHANG Baocheng;KANG Shuai(College of Air Traffic Management,CAUC,Tianjin 300300,China;On-Site Operation Command Center,Dalian Zhoushuizi International Airport,Dalian 116000,Liaoning,China)
出处
《中国民航大学学报》
2025年第5期90-96,共7页
Journal of Civil Aviation University of China
基金
国家自然科学基金项目(71571182)
中国民航大学教改项目《基于翻转课堂的航空运行运筹学课程体系建设》。
关键词
单纯形算法
单纯形表
进基变量
最大取值
simplex algorithm
simplex table
entering variable
maximum value
