Determining the Optimum Stratum Boundaries Using Mathematical Programming

The method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation, is known as optimum stratification. In order to make the strata internally homogeneous, the strata are constructed in such a way that the strata variances should be as small as possible for the characteristic under study. In this paper the problem of determining optimum strata boundaries (OSB) is discussed when strata are formed based on a single auxiliary variable with a varying measurement cost per units across strata. The auxiliary variable considered in the problem is a size variable that holds a common model for a whole population. The OSB are achieved effectively by assuming a suitable distribution of the auxiliary variable and creating strata by cutting the range of the distribution at optimum points. The problem of finding the OSB, which minimizes the variance of the estimated population mean under a weighted stratified balanced sampling, is formulated as a mathematical programming problem (MPP). Treating the formulated MPP as a multistage decision problem, a solution procedure using dynamic programming technique is developed. A numerical example using a hospital population data is presented to illustrate the computational details of the solution procedure. A software program coded in JAVA is written to carry out the computation. The distribution of the auxiliary variable in this example is considered to be continuous with an exponential density function.     

Using Statistical Models for Mathematical Programming Sensitivity Analysis

When exploring the potential payoffs from energy R & D, it is necessary to perform benefit-cost calculations over a wide range of future scenarios. Repeated runs of large-scale mathematical programming models are often required. This paper describes how simple statistical models might be used to eliminate at least some of the costly computer runs. The approach is illustrated in the context of a recent study on the effect of breeder timing on electricity generating costs.     

MAGIC: The Design and Use of an Interactive Modelling Language for Mathematical Programming

The desirability of computer aids for the building as well asthe solving of Mathematical Programming models is argued. Ashort survey is given of some of the distinct approaches possiblein designing matrix generators/languages for such a role. Itis then suggested that the approach most suited to general modelsis to design a language close to widely used mathematical notation.The facilities needed in such a language are discussed and theimplementation using the MAGIC (MAtrix Generator InstructionConvertor) language described.     

链梯法中进展因子估计的数学规划法

对传统链梯法中进展因子估计方法的不足进行了简要分析,提出将两种形式的偏差函数作为目标函数,建立二次规划和目标规划模型对进展因子进行估计.同时,对不同事故年赋予不同的权重因子,以区别不同数据信息在进展因子估计中的作用,弱化异常数据对进展因子估计的影响.通过数值实验对所述方法的可行性进行验证.     

用LINGO6.0求解大型数学规划

LINGO6.0的特出功能是求解大型数学规划 ,它提供的内部建模语言能够自然地描述各种规划问题 ,使大规模数学规划的求解不再困难 .本文以 2 0 0 0年全国大学生数学建模竞赛 B题——钢管订购和运输计划的模型求解为例 ,介绍最新版本 LINGO建模语言和它的用法 .     

数学规划的求解与广义Hopfield神经网络

神经网络技术最为成功的应用领域之一是用于求解优化问题,本文就近年来的求解优化问题的神经网络方法进行了综述