理学院
毕业设计（论文）
题目：线性规划算法的应用及其MATLAB实现
专 业 班 级 学 号
数学与应用数学 10122111 1012211139
姓 名 蒋芬 指 导 教 师
许建强
2013年5月2日
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线性规划算法的应用及其MATLAB实现
摘要：线性规划作为一种优化工具，50年代后线性规划的应用范围不断扩大。已
被广泛的运用于军事，经济等部门，是辅助人们进行科学管理的一种数学方法。它广泛应用现有的科学技术和数学方法，解决实际中的问题，帮助决策人员选择最优方案和决策。本篇文章主要论述了线性规划的算法及其在实际生活中的几种典型的应用及算法在Matlab中的实现。如在运输中的应用，通过线性规划计算出的方案合理安排人力物力等资源，使经济效果达到最好。利用lingo软件得出模型运行结果，分析模型的影子价格。
关键词：线性规划的算法、最优方案、Matlab、应用、lingo、影子价格
Application of MATLAB linear programming
algorithm
Abstract：Linear programming as an optimization tool, After the 1950s, the scope of application of linear programming continues to expand. Has been widely used in military, economic and other sectors, Is a mathematical method to help people to achieve a scientific management It is widely used in the existing science and technology and mathematical methods to solve practical problems and help decision makers choose the best solution and decision making. This article discusses the linear programming algorithm and some typical applications and algorithms in real life implementations in Matlab. Such as transportation, computed by linear programming of the program reasonable arrangement manpower material resources, make the economic effect is the best.The results of model runs using the lingo software, the analysismodel of shadow price.
Keywords: Linear programming algorithm, the optimal scheme, Matlab,Application，Lingo The shadow price
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目录
1 引言.............................................................. 4
1.1 课题的目的和意义 ............................................ 4 1.2 国内外研究现状与发展趋势 .................................... 4 1.3 文献综述 .................................................... 5 1.4 论文研究主要内容 ............................................ 5 2 背景知识介绍...................................................... 6
2.1线性规划..................................................... 6 2.2运输问题..................................................... 7 2.3选址问题..................................................... 7 2.4线性规划几种常见的模型....................................... 9 2.5小结........................................................ 10 3线性规划求解实际问题 ............................................ 11
3.1运输问题.................................................... 11
3.1.1问题概述 .............................................. 11 3.1.2实际问题模型建立及求解 ................................ 12 3.1.3结果分析 .............................................. 15 3.1.4运输问题“影子价格” .................................. 15 3.2选址问题.................................................... 16
3.2.1问题概述 .............................................. 16 3.2.2实际问题模型建立及求解 ................................ 17 3.2.3结果分析 .............................................. 19
4总结 ............................................................. 20 5致谢 ............................................................. 20 6参考文献 ......................................................... 21 7附录 ............................................................. 22
7.1程序........................................................ 22
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