生产可能集为凸包时的相对有效性评价模型

给出了一个评价决策单元相对有效性的新的DEA模型,它所对应的生产可能集被称为凸包形生产可能集,同时讨论了该模型解的存在性,定义了决策单元技术DEA有效和"上投影"的概念,断定一个决策单元的"上投影"相对于原来的决策单元是技术DEA有效的。最后给出一个应用新模型进行设施农业效率评价的例子。     

数量差异较大决策单元的DEA有效性评价

传统DEA方法基于决策单元集对每个决策单元进行相对效率评价,如果决策单元之间在数量上存在较大差异,评价结果可能不尽合理.为了解决这个问题,首先利用聚类分析按一定标准将决策单元进行分类,然后计算每个决策单元相对其所在类的相对效率,最后根据决策单元集和每个类的数量规模进行赋权,给出决策单元的加权综合效率.     

样本评价DEA模型的灵敏度分析

利用样本评价DEA模型的有效性理论,对决策单元的有效性进行灵敏度分析,给出了当移动因子d保持不变时,样本单元和决策单元的输入或输出变化后,决策单元的有效性保持不变的充分条件和必要条件,此外还给出了使决策单元的有效性保持不变的移动因子d的精确变化范围,最后通过实例表明了该灵敏度分析方法的可行性.     

混合的数据包络分析模型的灵敏度分析的研究

本文研究了混合的数据包络分析(DEA)模型的灵敏度分析,给出了有关所有决策单元的输入与输出都变化的情况下某决策单元保持其有效性(M)的两个充分条件。     

带有随机决策单元的广义数据包络分析方法

广义DEA方法是一种相对效率评价方法,解决了决策单元相对于任意参考系(样本单元集)的效率比较问题.在实际中,有时评价标准是确定的,决策单元的生产具有不确定性,有必要在进行生产之前基于确定性样本单元对随机性决策单元进行相对效率评价.为了解决这个问题,研究样本单元为确定值,决策单元为随机变量的广义DEA模型,分别通过期望值和机会约束将随机模型转化为确定性规划,给出决策单元GEDEA有效和GCDEA有效的概念,GEDEA有效与多目标规划Pareto有效关系,以及利用移动因子对决策单元进行有效性排序方法.     

混合的DEA模型最优解的存在性

有ｎ个决策单元。设被评价的决策单元可以不是这ｎ个之一,且它们的输入或输出可以取负值,在这样情况下,给出了混合的ＤＥＡ模型存在最优解的必要条件或充分条件     

灰变量逆DEA模型的初步研究

初步研究了变量为区间灰数的逆DEA模型。变量为区间灰数时,决策单元效率水平保持不变表达为:对决策单元的输入输出值改变前后对应的灰区间效率进行比较,前者大于等于后者与小于等于后者的可信度相等(均等于0.5)。给出了决策单元非DEA有效时,灰区间变量逆DEA模型解存在的充要条件及一般表达式,以及决策单元弱DEA有效时灰变量逆DEA模型的部分解。     

一类多指标对象评价模型

以C2R模型为基础给出了一类多指标对象评价模型——C2RM模型.我们首先定义了决策单元的优势集,论证了C2RM模型比一类多目标规划模型在优化意义上更进一步——排除了此类多目标规划模型的一些优势集为空的Pareto有效解.我们建立的C2RM模型是线性规划模型,易于判定一个决策单元是否DEA有效.在优势集性质基础上我们进一步定义了C2RM模型下DEA有效决策单元的实际有效率,并给出了所有决策单元的一种排序,最后举例予以说明.     

模糊条件下的决策单元相对有效性评价

研究了模糊条件下决策单元的相对有效性评价问题。首先分析了模糊性因素对决策单元相对有效性的影响;然后根据模糊规划取截集方法和DEA评价的经济含义,给出了模糊DEA模型的求解方法;最后定义了决策单元的模糊DEA有效性以及进行有效性排序的平均置信有效性。文末是一个模糊DEA应用的例子。     

带有随机样本单元的广义数据包络分析方法

广义数据包络分析(Generalized data envelopment analysis)方法是一种相对效率评价方法,能够获得决策单元相对于样本单元的比较信息.研究了基于随机样本单元对确定性决策单元进行评价的广义DEA模型,利用期望值和机会约束,将其转化为确定性规划.给出了决策单元GEDEA有效和GCDEA有效的概念及其判别,与多目标规划Pareto有效关系,以及利用移动因子进行有效性排序.     

有关判断决策单元的DEA有效性的新方法的探讨

为了判断决策单元是否(弱)DEA有效并克服现有的模型及[1]中模型在解决上述问题时的不足之处,本文将讨论的新模型是由CCR模型与CCGSS模型变来的,且定理的证明不同于[1]．还讨论了文中新模型的最优解的存在性,此外,研究了所有决策单元的输入输出的变化对某决策单元有效性的影响．     

技术有效的决策单元与DEA有效性(C~2GS~2)

对李光金、阎洪先生所定义的技术有效的决策单元,证明了它是DEA有效(C~2GS~2)的,而且讨论了将非有效的决策单元转变为有效.     

On finding the most BCC-efficient DMU: A new integrated MIP–DEA model

This paper proposes a new integrated mixed integer programing – data envelopment analysis (MIP–DEA) model to improve the integrated DEA model which was introduced by Toloo & Nalchigar [M. Toloo, S. Nalchigar. A new integrated DEA model for finding most BCC–efficient DMU. Appl. Math. Model. 33 (2009) 597–60]. In this study some problems of applying Toloo & Nalchigar’s model are addressed. A new integrated MIP–DEA model is then introduced to determine the most BCC-efficient decision making unit (DMU). Moreover, it is mathematically proved that the new model identifies only a single BCC-efficient DMU by a common set of optimal weights. To show applicability of proposed models, a numerical example is used which contains a real data set of nineteen facility layout designs (FLDs).     

基于SMAA和公共权重的决策单元效率评价与排序

在数据包络分析(DEA)中,公共权重模型是决策单元效率评价与排序的常用方法之一。与传统DEA模型相比,公共权重模型用一组公共的投入产出权重评价所有决策单元,评价结果往往更具有区分度且更为客观。本文考虑决策单元对排序位置的满意程度,提出了基于最大化最小满意度和最大化平均满意度两类新的公共权重模型。首先,基于随机多准则可接受度分析(SMAA)方法,计算出每个决策单元处于各个排名位置的可接受度;然后,通过逆权重空间分析,分别求得使最小满意度和平均满意度最大化的一组公共权重;最后,利用所求的公共权重,计算各决策单元的效率值及相应的排序。算例分析验证了本文提出的基于SMAA的公共权重模型用于决策单元效率评价与排序的可行性。     

Performance ranking of units considering ideal and anti-ideal DMU with common weights

A characteristic of traditional DEA CCR mode is that it allows DMUs to measure their maximum efficiency score with the most favorable weights. Thus, it would have some shortcomings, for example, the efficiencies of different DMUs obtained by different sets of weights may be unable to be compared and ranked on the same basis. Besides, there are always more than one DMU to be evaluated as efficient because of the flexibility in the selection of weights; it would cause the situation that all DMUs cannot be fully discriminated. With the research gaps, in this paper, we propose two models considering ideal and anti-ideal DMU to generate common weights for performance evaluation and ranking. Finally, two examples of Asian lead frame firms and flexible manufacturing systems are illustrated to examine the validity of the proposed methods.     

A new integrated DEA model for finding most BCC-efficient DMU

In many applications of widely recognized technique, DEA, finding the most efficient DMU is desirable for decision maker. Using basic DEA models, decision maker is not able to identify most efficient DMU. Amin and Toloo [Gholam R. Amin, M. Toloo, Finding the most efficient DMUs in DEA: an improved integrated model. Comput. Ind. Eng. 52 (2007) 71–77] introduced an integrated DEA model for finding most CCR-efficient DMU. In this paper, we propose a new integrated model for determining most BCC-efficient DMU by solving only one linear programming (LP). This model is useful for situations in which return to scale is variable, so has wider range of application than other models which find most CCR-efficient DMU. The applicability of the proposed integrated model is illustrated, using a real data set of a case study, which consists of 19 facility layout alternatives.     

An epsilon-free approach for finding the most efficient unit in DEA

Data envelopment analysis (DEA), considering the best condition for each decision making unit (DMU), assesses the relative efficiency and partitions DMUs into two sets: efficient and inefficient. Practically, in traditional DEA models more than one efficient DMU are recognized and these models cannot rank efficient DMUs. Some studies have been carried out aiming at ranking efficient DMUs, although in some cases only discrimination of the most efficient unit is desirable. Furthermore, several investigations have been done for finding the most CCR-efficient DMU. The basic idea of the majority of them is to introduce an integrated model which achieves an optimal common set of weights (CSW). These weights help us identify the most efficient unit in an identical condition.     

Robustness of the efficient DMUs in data envelopment analysis

By means of modified versions of CCR model based on evaluation of a decision making unit (DMU) relative to a reference set grouped by all other DMUs, sensitivity analysis of the CCR model in data envelopment analysis (DEA) is studied in this paper. The methods for sensitivity analysis are linear programming problems whose optimal values yield particular regions of stability. Sufficient and necessary conditions for upward variations of inputs and for downward variations of outputs of an (extremely) efficient DMU which remains efficient are provided. The approach does not require calculation of the basic solutions and of the inverse of the corresponding optimal basis matrix. The approach is illustrated by two numerical examples.     

链式网络DEA模型

数据包络分析(DEA)是评价决策单元(DMU)相对有效性的一种工具,现已得到广泛的应用.传统的DEA不考虑系统内部结构,而是将系统作为一个"黑箱"来度量效率.针对多阶段网络结构提出一个新的网络DEA模型—链式网络DEA模型.研究网络决策单元的网络DEA有效性及各个阶段的弱DEA有效性之间的关系,给出了网络DEA有效的充分必要条件.若网络决策单元不是网络DEA有效的,根据模型可以指出系统在哪些阶段是无效的.