单纯形表与数学模型的对应关系

中国民航大学学报 ›› 2025, Vol. 43 ›› Issue (5): 90-96.

• 基础科学 • 上一篇

单纯形表与数学模型的对应关系

1. 中国民航大学空中交通管理学院，天津 300000； 2. 大连周水子国际机场现场运营指挥中心，大连 116000

收稿日期:2023-05-06 修回日期:2023-07-08 出版日期:2025-11-17 发布日期:2025-11-17
作者简介:张宝成（1979— ），男，天津人，博士，副教授，研究方向为运筹学基础理论方法研究、空中交通系统优化与管理
基金资助:
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》

Correspondence relationship between simplex table and mathematical model

1. College of Air Traffic Management, CAUC, Tianjin 300300, China; 2. On-Site Operation Command Center,

Dalian Zhoushuizi International Airport, Dalian 116000, Liaoning, China

Received:2023-05-06 Revised:2023-07-08 Online:2025-11-17 Published:2025-11-17

摘要/Abstract

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。

关键词:

单纯形算法, 单纯形表, 进基变量, 最大取值

Abstract:

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.

Key words:

simplex algorithm, simplex table, entering variable, maximum value

中图分类号:

O221.1

张宝成 a, 康帅 a, b.

单纯形表与数学模型的对应关系

[J]. 中国民航大学学报, 2025, 43(5): 90-96.

ZHANG Baocheng a, KANG Shuai a, b.

Correspondence relationship between simplex table and mathematical model

[J]. Journal of Civil Aviation University of China, 2025, 43(5): 90-96.

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单纯形表与数学模型的对应关系

Correspondence relationship between simplex table and mathematical model

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