基于向量投影的建筑工程绩效评价

首先结合建筑工程项目管理实践,建立建筑工程绩效评价指标体系.然后利用相对隶属度公式对数据进行规范化处理、利用线性规划确定指标因素的权重、利用向量的投影公式求实际评价值与目标评价值的接近程度来对建筑工程管理绩效进行评价.案例说明评价方法是确实可行的,也很通俗易懂.     

证券组合的模糊规划模型

通过结构元方法定义了一种模糊数排序准则,利用模糊约束将Markowitz投资组舍模型转化为模糊线性规划模型,并利用模糊数来描述证券的期望收益率和风险损失率,建立模糊数模糊证券投资组合模型.最后,利用定义的模糊数排序准则把模糊数规划问题转化为经典的线性规划问题,然后再对该模型进行求解,并通过算例阐述了该方法的有效性.     

两阶段模糊生产计划期望值模型

在现实的生产系统中,生产计划问题常常是-个确定的线性规划问题.但是,在许多的实际情况中,由于生产系统中不确定性因素的影响,带有常系数的线性规划模型不能合理地描述现实的决策环境.为了准确有效地描述生产决策环境,本文提出一类新的带有模糊参数的两阶段生产计划期望值模型并且讨论模型的一些基本性质.然后,讨论补偿函数的逼近并且设计-个基了:逼近方法、神经网络和遗传算法的启发式算法来求解这个两阶段模糊生产计划模型.最后,给出一个数值例子来表明所设计算法的可行性和有效性.     

对于单纯形法矩阵描述的认识

从修正单纯形法的提出、对偶单纯形法的出现、对偶问题最优解的确定以及灵敏度分析的基本依据等四个方面阐述了对单纯形法矩阵描述的认识,充分显示出单纯形法矩阵描述在线性规划发展中的重要性.     

求解线性规划的一种单纯形矩阵法

线性规划的单纯形法一直是运筹学教学中的难点,是求解线性规划的一种重要方法.通过实例从代数角度探讨了单纯形法的迭代思想,提出了用单纯形矩阵求解线性规划的方法.同传统的单纯形表计算比较而言,此方法操作简单,不易出错,为线性规划的求解提供了一种行之有效的方法。     

求解多层线性规划的模糊规划法

本文用模糊集理论中的隶属函数描述多层线性规划的各层目标,在第一层给定最小满意水平下,通过求解相应层次的模糊规划来确定各层的最小满意度,从而最终得到问题的一个满意解。提出的方法只需求解一系列线性规划问题,具有较好的计算复杂性和可行性,最后的算例进一步验证了方法的有效性。     

求解最大割问题的半定规划松驰的序列线性规划方法

本文基于最大割问题的半定规划松弛,利用矩阵分解的方法给出了与半定规划松弛等价的非线性规划模型,提出一种序列线性规划方法求解该模型.并在适当的条件下,证明了算法的全局收敛性.数值实验表明:序列线性规划方法在时间上要优于半定规划的内点算法.所以序列线性规划方法能更有效地求解大规模的最大割问题的半定规划松弛.     

含直觉模糊弹性约束的多目标模糊线性规划求解

基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的多目标模糊线性规划问题.通过引入模糊数的加权特征数,定义了一种序关系并拓展了Verdegay的模糊线性规划方法,将上述多目标模糊线性规划问题转化成两个等价含参数约束条件的清晰多目标线性规划模型,并应用一种线性加权函数法给出了此类线性规划模型的对比最优可行解.最后通过一个数值实例来说明此类问题的一般求解方法.     

基于结构元方法的可能性线性规划

主要目的是利用结构元方法来解决含有模糊系数的线性规划问题,即可能性线性规划问题.首先,简单地介绍了结构元方法及结构元加权序,证明了其模糊优先的合理性,并同原有序关系进行了比较.然后,利用这种序关系,将可能性线性规划问题等价地转化为一个经典的线性规划问题,简化了原问题的求解.最后,借助一个实际例子,进一步表明了该方法的有效性.     

含一般模糊弹性约束的广义模糊变量线性规划

建立并讨论了一类含有一般模糊弹性约束的广义模糊变量线性规划问题.首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析.然后选取风险中性的决策者来定义序关系,应用Verdegay模糊线性规划方法将含一般模糊弹性约束的广义模糊变量线性规划转化经典的线性规划问题,简化了原问题的求解.最后通过数值算例进一步说明了该方法的有效性.     

A new method for solving fully fuzzy linear programming problems

Lotfi et al. [Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution, Appl. Math. Modell. 33 (2009) 3151–3156] pointed out that there is no method in literature for finding the fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints. In this paper, a new method is proposed to find the fuzzy optimal solution of same type of fuzzy linear programming problems. It is easy to apply the proposed method compare to the existing method for solving the FFLP problems with equality constraints occurring in real life situations. To illustrate the proposed method numerical examples are solved and the obtained results are discussed.     

On an optimal solution for maximizing the probability of retention in PPS sampling

A direct alternative proof of Keyfitz's optimal solution to the problem of maximizing the probability of retention in sampling on a second occasion is given, using techniques of elementary linear algebra. The proof and comments help one to better understand Keyfitz's solution, and they clearly demonstrate that the closed form solution of Keyfitz is one of a possible infinity of solutions offered by a linear programming approach. We also give one of those other solutions offered by linear programming, which is easy to obtain by hand calculations using only the operation of subtraction.     

A Simplified Novel Technique for Solving Fully Fuzzy Linear Programming Problems

This study proposes a novel technique for solving Linear Programming Problems in a fully fuzzy environment. A modified version of the well-known simplex method is used for solving fuzzy linear programming problems. The use of a ranking function together with the Gaussian elimination process helps in solving linear programming problems in a fully uncertain environment. The proposed algorithm is flexible, easy and reasonable.     

Restoration of efficiency in a goal programming problem with linear fractional criteria

The problem resulting from a goal programming problem with linear fractional criteria is not easy to solve due to the non-linear constraints inherent in its formulation. This paper introduces a simple and reliable test to establish whether a linear fractional goal programming problem has solutions that verify all goals and, if so, how to find them by solving a linear programming problem. This paper also outlines a new technique for restoring efficiency based on a minimax philosophy. An example is presented.     

UTA-poly and UTA-splines: Additive value functions with polynomial marginals

Additive utility function models are widely used in multiple criteria decision analysis. In such models, a numerical value is associated to each alternative involved in the decision problem. It is computed by aggregating the scores of the alternative on the different criteria of the decision problem. The score of an alternative is determined by a marginal value function that evolves monotonically as a function of the performance of the alternative on this criterion. Determining the shape of the marginals is not easy for a decision maker. It is easier for him/her to make statements such as “alternative a is preferred to b”. In order to help the decision maker, UTA disaggregation procedures use linear programming to approximate the marginals by piecewise linear functions based only on such statements. In this paper, we propose to infer polynomials and splines instead of piecewise linear functions for the marginals. In this aim, we use semidefinite programming instead of linear programming. We illustrate this new elicitation method and present some experimental results.