可控制前置时间需求分布未知的部分缺货待补混合库存策略

同时考虑可控制前置时间与货币时间价值两项因素,假设前置时间内需求量的概率分布未知,建立了部分缺货欠待补混合库存模型,并对混合库存模型进行了数值验证.研究证明,混合库存模型的总变动成本函数为凸函数,然而由于前置时间内的随机性需求量会造成无法求取期望缺货量的精确值,因此采用最小最大准则找出具有最大期望总成本的现值函数,进而求取使得期望总成本现值为最小的最优值,以确定最优订购策略.

非共振二阶椭圆型方程解的存在唯一性

利用Galerkin逼近方法和minimax原理,证明了非线性非共振椭圆型方程弱解的存在唯一性。

An Approach to Continuous Approximation of Pareto Front Using Geometric Support Vector Regression for Multi-objective Optimization of Fermentation Process

The approaches to discrete approximation of Pareto front using multi-objective evolutionary algorithms have the problems of heavy computation burden, long running time and missing Pareto optimal points. In order to overcome these problems, an approach to continuous approximation of Pareto front using geometric support vector regression is presented. The regression model of the small size approximate discrete Pareto front is constructed by geometric support vector regression modeling and is described as the approximate continuous Pareto front. In the process of geometric support vector regression modeling, considering the distribution characteristic of Pareto optimal points, the separable augmented training sample sets are constructed by shifting original training sample points along multiple coordinated axes. Besides, an interactive decision-making(DM)procedure, in which the continuous approximation of Pareto front and decision-making is performed interactively, is designed for improving the accuracy of the preferred Pareto optimal point. The correctness of the continuous approximation of Pareto front is demonstrated with a typical multi-objective optimization problem. In addition,combined with the interactive decision-making procedure, the continuous approximation of Pareto front is applied in the multi-objective optimization for an industrial fed-batch yeast fermentation process. The experimental results show that the generated approximate continuous Pareto front has good accuracy and completeness. Compared with the multi-objective evolutionary algorithm with large size population, a more accurate preferred Pareto optimal point can be obtained from the approximate continuous Pareto front with less computation and shorter running time. The operation strategy corresponding to the final preferred Pareto optimal point generated by the interactive DM procedure can improve the production indexes of the fermentation process effectively.

决策论在钻头选型中的应用

本文把决策论中的最小最大决策方法和贝叶斯决策方法应用于钻头的选型 ,通过对钻头的选型 。

Using Two-layer Minimax Optimization and DEA to Determine Attribute Weights

This study aims to explore a novel method for determining attribute weights,which is a key issue in constructing and analyzing multiple-attribute decision-making(MADM)problems.To this end,a hybrid approach combining the data envelopment analysis(DEA)model without explicit inputs(DEA-WEI)and a two-layer minimax optimization scheme is developed.It is demonstrated that in this approach,the most favorable set of weights is first considered for each alternative or decision-making unit(DMU)and these weight sets are then aggregated to determine the best compromise weights for attributes,with the interests of all DMUs simultaneously considered in a fair manner.This approach is particularly suitable for situations where the preferences of decision-makers(DMs)are either unclear or difficult to acquire.Two case studies are conducted to illustrate the proposed approach and its use for determining weights for attributes in practice.The first case concerns the assessment of research strengths of 24 selected countries using certain measures,and the second concerns the analysis of the performance of 64 selected Chinese universities,where the preferences of DMs are either unknown or ambiguous,but the weights of the attributes should be assigned in a fair and unbiased manner.

未知需求分布下提前期可控的整合库存模型研究

考虑了单供应商单采购商的生产-库存联合优化问题,采购商面临未知分布的随机需求,供应商的提前期可以控制。采用Minimax方法建立了供应商和采购商联合期望总成本最小化模型,模型中允许采购商缺货,并且部分缺货延期交付,部分缺货发生销售损失,同时也考虑了运输成本,并且假设运输成本依赖于订货量和提前期。给出了求解联合最优生产批量、联合最优提前期、联合最优再订货点和订货量的算法,并通过数值算例作了说明。