【作者】 韩路英；

【导师】 李智慧；

【作者基本信息】 燕山大学 ， 计算数学， 2010， 硕士

【摘要】 多层规划是研究递阶系统优化问题的基本模型,众多研究者对此进行了深入的研究,并且已广泛地应用在许多领域中,如社会经济、工程技术、管理部门及军事等领域。二层规划是多层规划的重要组成部分,是近年来受到众多领域广泛关注的前沿课题,现实的决策系统大都可以看成二层决策系统。论文的研究对象为二层线性规划问题中的价格控制问题和食用豆腐生产经营过程中的区间决策问题,其主要工作如下:首先,在对国内外研究现状进行了深入分析的基础上,对二层决策系统中的上层无约束的二层线性规划做了详细介绍,给出了相应的基本模型、定义及在不同的假设条件下它们的相关性质。其次,引入模糊结构元理论,对有关模糊结构元的基本概念做了简明扼要的介绍,给出了基于模糊结构元理论的模糊数的排序方法及运算法则,利用结构元方法将有模糊变量的价格控制问题转化为传统的价格控制问题,并给出了求解算法;而后给出了优面的定义和性质以及最优解和优面的关系,对二层价格控制问题的优面算法步骤进行了设计,并通过算例说明了该算法的有效性。最后,由于在豆腐生产过程中存在着许多不确定性,自然环境的改变、生产条件的变化以及市场资源的变化,给豆腐作坊的净收益带来了不确定的因素,于是豆腐作坊的最优净收益就呈现出区间的特性。第五章针对豆腐作坊生产经营豆腐的问题,建立了改变生产规模的区间决策模型和不改变生产规模的区间决策模型,给出了区间决策问题的基本定理及求解方法,并对实际问题进行了求解,对豆腐作坊给出了结果分析和建议。更多还原

【Abstract】 Multilevel programming is fundamental model used to study hierarchical system problem, many researchers proceed thorough research to the hierarchical system, and it has been extensively applied in society economy, engineering technique, manage department and military etc. Bilevel programming is the main part of the multilevel programming, attracting the extensive attention in multitudinous in recent years. In fact, most of the realistic decision making systems can be treated as bilevel decision making systems. The research object of this paper is the price control problem of bilevel linear programming and interval decision making problem for making and management of tofu, main works are as follows:Firstly, in this thesis, according to the thorough research to domestic and international present condition, the bilevel linear programming without constraint in the upper level is elaborated in the beginning, the basic model, definition and theorem are given and the interrelated properties are discussed respectively under different hypothesis.Secondly, the theory of fuzzy structured element is induced. The basic concept and the basic theorem are briefly introduced. Sequencing and operations of fuzzy numbers based on the theory of fuzzy structured element are given in the paper. By using the method of fuzzy structured element, we transform price control problem with fuzzy variables into traditional price control problem, and give the algorithm. In addition, we give the definitions and some properties of optimal plane, and give the relationship between optimal solution and optimal plane. Then, the optimal plane algorithm steps of the price control problem is designed, and an example is adopted to verify the effectiveness of the proposed algorithm.Finally, in making of tofu, with the changing of the nature envoronment, the producting condition and market source, the wet profit of tofu in the tofu factory is not distinct, so the wet profit of tofu in the tofu factory takes on interval character. In the fifth chapter, for the problem about making and management of tofu in the tofu factory, we establish interval decision making model of changed producting scale and unchanged one, and give some theorems and a method for solving the interval decision making problem. Then, we solve the above real problem and give the result analysis and advice to the tofu factory.更多还原