毕业论文
摘要
参数线性规划是约束条件和目标函数中的价值系数、工艺系数、资源限量中含有一个或多个参数的优化模型，是线性规划理论的重要组成部分，线性规划是运筹学的一个重要分支，从解决技术问题的最优化设计，到工业、农业、商业、交通运输、军事、经济等，在许多领域中都有着重要的应用。在生产过程中，由于工艺条件、资源限量、市场需求、市场价格等因素都在不断的变化，因此，最优解也就带有一定程度的不确定性。为了及时根据市场动态及数据资料的变化调整决策方案，运用参数线性规划这一工具，建立参数线性规划模型，可以更好地指导实际工作，适应市场的变化达到增加收益、降低成本的目的。
1947年，Dantzig针对线性规划提出了单纯形法，为线性规划发展奠定了基础；1954年，C.莱姆基提出了对偶单纯形法；1954年，S.加斯和T.萨迪等人在对偶单纯形法的基础上解决了线性规划的灵敏度分析和参数规划问题。
近年来，参数线性规划模型在单纯形法和对偶单纯形法的基础上，又产生了搜索法、分块矩阵法、建立神经网络模型法等方法，随着计算机软件的发展，通过建立仿真模型用计算机解决参数线性规划问题也成为一种重要的途径。
本文针对价格系数和右端资源数据中同时含有两个参数的复杂情形，对实际问题建立了参数线性规划模型，并分析了最优解不变的情况下，参数的变化区间，找到了最优目标函数的变化规律，并用Matlab绘出了三维仿真图，为求解大型参数线性规划问题提供了基础。
关键词：参数线性规划；最优解；区间；对偶；决策变量
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Abstract
Parametric linear programming is one kind of optimal modle with some constraint conditions,which there exist one or more parametrics in the objective function,technology factors,or limited resourses.It is widly applicated to many fields from technical problems to optimization design,such as industrial,agricalfural,transportation,military,economic and so on.
In the producing process,the solution of the parametric linear programming often will be some uncertainties,due to the change of technology conditions,resources,market demands,material prices and other factons.So in order to adjust decision schem and meet with the market needs,data must be changed timely and immdiatly.Parametric linear programming has play a important role in dealing with such problems.It has been a very useful tool for us to obtain decision plan and to increase value and reduce costs.
In 1947, Dantzig proposed a important method,simplex method, laying the foundation for solving linear programming; in 1954, C.Lemke proposed dual simplex method; in 1954, S. Gaston and T. Saadi and others solved the parametric programming based on studing dual simplex method to the problem of the linear programming. In recent years, many new methods the parameters of linear programming model with the basis of simplex method and the dual simplex method, produced the search method, sub-block matrix method, the establishment of neural network models and other methods. With the development of computer software, linear programming problem with parameters can be solved by computer through the establishment of simulation computer model.
In this paper, a mathematical model is created in accordance with the practical problem which has two parameters,one is in the price coefficients,anothisin the right resource data.The interval is obtained in the condition of analysis the optimal solution unchanged to provide the fundation to solve complicated parametric linear programming.By solving optimal solution,we have obtained the fuction with two parametrics.At last,the simulations have been given by MATLAB.
Keywords: Parametric linear programming; the optimal solution; interval; dual; decision variation
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目录
第一章 绪论 ............................................................. 1 1.1参数线性规划的研究背景 ................................................ 1 1.1.1什么是线性规划 ....................................................... 1 1.1.2参数线性规划的内容 ................................................... 1 1.2参数线性规划的研究现状 ................................................ 2 1.3参数线性规划研究的意义 ................................................ 3 第二章 参数线性规划的理论 ............................................... 4 2.1参数线性规划研究的常用方法 ............................................ 4 2.1.1目标函数的系数含有参数的线性规划问题 ................................. 4 2.1.2约束条件右端的常数项含有参数的线性规划问题 ........................... 5 2.2线性规划灵敏度分析 .................................................... 7 2.2.1什么是线性规划的灵敏度 ............................................... 7 2.2.2价值系数的灵敏度分析 ................................................. 7 2.2.3资源限量的灵敏度分析 ................................................ 10 第三章 参数线性规划的数学建模 .......................................... 14 3.1实际问题的提出 ....................................................... 14 3.2实际问题的分析与解决 ................................................. 14 3.2.1获利最大的生产计划模型 .............................................. 14 3.2.2 A产品的利润变化区间的确定方法 ...................................... 16 3.2.3关于开发新产品的决策研究 ............................................ 16 3.2.4购入原材料进行扩大再生产的必要性的理论分析 .......................... 17 3.2.5影子价格的含义及分析 ................................................ 18 第四章 两参数线性规划问题的解法 ........................................ 20 4.1两参数线性规划的定义 ................................................. 20 4.2两参数线性规划问题的求解方法 ......................................... 20 4.3两参数线性规划问题的分析与求解 ....................................... 22 第五章 结论 ............................................................ 27 参考文献 ................................................................ 28
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谢辞 .................................................................... 29 附录一 ................................................................... 1 附录二 ................................................................... 6
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