基于带有虚拟单元聚类分析的广义DEA方法

广义DEA方法是相对于样本单元对决策单元进行评价,如何选择样本单元对于评价的结果有一定的影响.有时可以选择决策单元集的子集作为样本单元集,这样更容易被决策者所接受.通过构造符合一定条件的虚拟决策单元与所有决策单元一起采取最短距离法进行聚类分析,用包含虚拟决策单元的类作为样本单元集,可以使评价结果与传统DEA方法相比能够进一步体现出相对效率之间的差异.     

模糊数据包络分析方法有效性分析

传统数据包络分析(DEA)模型只能用来评价具有精确投入和产出数据的决策单元.然而在实践中决策单元的投入产出数据可能存在一定模糊性.为了评价具有模糊投入产出数据的决策问题,研究工作者提出了模糊数据包络分析模型,并给出了相应的有效性定义.对于不同研究者提出的有效性定义方式有众多地方需要改进.通过这些改进提出了相关模型及新的有效性定义方式,并给出了相关实例.     

基于样本评价的广义数据包络分析方法

传统DEA方法是一种依据自评体系评价的方法,而无法自主选择参照系.为了解决DEA方法可以同时依据自评体系和其它参照系进行评价问题,首先给出了广义DEA有效的概念.然后,给出了一类基于样本单元评价的广义数据包络分析模型,包括面向输入的广义DEA模型、面向输出的广义DEA模型以及加性广义DEA模型.最后,分析了上述这些模型与传统DEA模型之间的关系,探讨了广义DEA有效与相应多目标规划Pareto有效之间的关系,并给出了决策单元的投影性质以及决策单元的有效性排序方法.     

基于聚类分析的数量差异较大决策单元DEA有效性评价

传统DEA方法对每个决策单元基于决策单元集进行相对效率评价,如果它们之间在数量上存在较大差异,得到的评价结果可能无法体现数量规模的影响.为了解决这类问题,首先利用聚类分析方法按一定标准将决策单元进行分类,然后利用传统和广义DEA方法对决策单元按类进行自评和他评,最后根据各类决策单元的数量规模情况进行赋权进而给出决策单元...     

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.     

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.     

广义与传统BC~2模型效率评价差异及其几何刻画

传统DEA方法相对于决策单元全体对决策单元进行评价,广义DEA方法相对于样本单元全体对决策单元进行评价.由于参照系的不同,对不同决策单元的相对效率评价结果可能不同.针对这种情况,对基于BC2模型的只有投入或只有产出的传统和广义DEA模型进行说明,并通过样本前沿面的移动对广义DEA模型中相对效率值进行几何刻画.     

带有随机因素的逆DEA模型

本文讨论含有随机因素的逆 DEA模型 .逆 DEA模型解决的问题是 :对于某个决策单元 (DMU ) ,若增加其输入 ,在保持相对效率水平不变的情况下 ,估计 (预测 )输出应增加多少 .因此逆 DEA模型可用于短期预测问题 .带有随机因素的逆 DEA模型 ,是将该问题转化成机会约束的多目标规划问题 ,在某些特殊情况下 ,成为机会约束的线性规划问题 .     

基于C~2R模型的广义链式网络DEA模型

传统网络DEA方法是将传统DEA方法评价过程中的"黑箱"打开,考虑输入到输出的中间环节,对生产过程中的各个环节分别评价。传统网络DEA方法获得的是相对于有效决策单元评价的结果,但有时可能要相对于非有效决策单元或者非决策单元进行评价,传统网络DEA方法无法解决该类问题。为此给出相对于非有效决策单元或者非决策单元进行评价的基于C~2R模型的广义链式网络DEA模型,并探讨相关性质.     

聚类分析在确定广义DEA方法样本单元集中的应用

利用基于BC~2模型的只有输出的DEA模型(D-BC_O~2)来评价决策单元的有效性时,得到的效率值有时会与定性分析存在一定的差异.为了解决这类问题,引入只有产出的广义DEA模型(DG-BC_O~2),并利用聚类分析方法确定样本单元集,给出(DG_(cluster)模型来评价决策单元的有效性.最后通过2009年中国各省市人均经济发展数据进行演示,说明利用聚类分析方法确定样本单元集具有一定的可行性.     

Cross-ranking of Decision Making Units in Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a mathematical model that evaluates the relative efficiency of Decision Making Units (DMUs) with multiple input and output. In some applications of DEA, ranking of the DMUs are important. For this purpose, a number of approaches have been introduced. Among them is the cross-efficiency method. The method utilizes the result of the cross-efficiency matrix and averages the cross-efficiency scores of each DMU. Ranking is then performed based on the average efficiency scores. In this paper, we proposed a new way of handling the information from the cross-efficiency matrix. Based on the notion that the ranking order is more important than individual efficiency score, the cross-efficiency matrix is converted to a cross-ranking matrix. A cross-ranking matrix is basically a cross-efficiency matrix with the efficiency score of each element being replaced with the ranking order of that efficiency score with respect to the other efficiency scores in a column. By so doing, each DMU assume the role of a decision maker and how they voted or ranked the other DMUs are reflected in their respective column of the cross-ranking matrix. These votes are then aggregated using a preference aggregation method to determine the overall ranking of the DMUs. Comparison with an existing cross-efficiency method indicates a relatively better result through usage of the proposed method.     

A Complete Efficiency Ranking of Decision Making Units in Data Envelopment Analysis

The efficiency measures provided by DEA can be used for ranking Decision Making Units (DMUs), however, this ranking procedure does not yield relative rankings for those units with 100% efficiency. Andersen and Petersen have proposed a modified efficiency measure for efficient units which can be used for ranking, but this ranking breaks down in some cases, and can be unstable when one of the DMUs has a relatively small value for some of its inputs. This paper proposes an alternative efficiency measure, based on a different optimization problem that removes the difficulties.     

IDEA (Imprecise Data Envelopment Analysis) with CMDs (Column Maximum Decision Making Units)

IDEA (Imprecise Data Envelopment Analysis) extends DEA so it can simultaneously treat exact and imprecise data where the latter are known only to obey ordinal relations or to lie within prescribed bounds. AR-IDEA extends this further to include AR (Assurance Region) and the like approaches to constraints on the variables. In order to provide one unified approach, a further extension also includes cone-ratio envelopment approaches to simultaneous transformations of the data and constraints on the variables. The present paper removes a limitation of IDEA and AR-IDEA which requires access to actually attained maximum values in the data. This is accomplished by introducing a dummy variable that supplies needed normalizations on maximal values and this is done in a way that continues to provide linear programming equivalents to the original problems. This dummy variable can be regarded as a new DMU (Decision Making Unit), referred to as a CMD (Column Maximum DMU).     

A Comparison of Data Envelopment Analysis and Artificial Neural Networks as Tools for Assessing the Efficiency of Decision Making Units

This paper is concerned with the comparison of two popular non-parametric methodologies—data envelopment analysis and artificial neural networks—as tools for assessing performance. Data envelopment analysis has been established since 1978 as a superior alternative to traditional parametric methodologies, such as regression analysis, for assessing performance. Neural networks have recently been proposed as a method for assessing performance. In this paper, we use a simulated production technology of two inputs and one output for testing the success of the two methods for assessing efficiency. The two methods are also compared on their practical use as performance measurement tools on a set of bank branches, having multiple input and output criteria. The results demonstrate that, despite their differences, both methods offer a useful range of information regarding the assessment of performance.     

Relationships between Data Envelopment Analysis and Multicriteria Decision Analysis

We contrast the different approaches of Data Envelopment Analysis (DEA) and Multiple Criteria Decision Making (MCDM) to superficially similar problems. The concepts of efficiency and Pareto optimality in DEA and MCDM are compared, and a link is demonstrated between the ratio efficiency definition in DEA and a distance measure in input–output space based on linear value functions. The problem of weight sensitivity is discussed in terms of value measurement theory, highlighting the assumptions needed during model formulation in order to justify the use of value judgements to constrain weight flexibility in DEA. Finally, we propose a stochastic approach, in which a probability distribution on efficiencies can be derived for each decision making unit, as a basis for comparison.     

一种新的带有参数的DEA有效单元排序模型

本文对数据包络分析中的有效单元排序方法进行了研究, 从一个新 的角度,定义最优有效和最劣无效, 提出了一种带有参数的有效单元排序模型.本文还给出并证明了此模型的一些性质, 并与其他排序模型进行了比较, 证明了本文模型的优越性. 最后用一个实例, 检验了此模型的可行性.     

Data Envelopment Analysis with Preference Structure

It is important to consider the decision making unit (DMU)'s or decision maker's preference over the potential adjustments of various inputs and outputs when data envelopment analysis (DEA) is employed. On the basis of the so-called Russell measure, this paper develops some weighted non-radial CCR models by specifying a proper set of ‘preference weights’ that reflect the relative degree of desirability of the potential adjustments of current input or output levels. These input or output adjustments can be either less or greater than one; that is, the approach enables certain inputs actually to be increased, or certain outputs actually to be decreased. It is shown that the preference structure prescribes fixed weights (virtual multiplier bounds) or regions that invalidate some virtual multipliers and hence it generates preferred (efficient) input and output targets for each DMU. In addition to providing the preferred target, the approach gives a scalar efficiency score for each DMU to secure comparability. It is also shown how specific cases of our approach handle non-controllable factors in DEA and measure allocative and technical efficiency. Finally, the methodology is applied with the industrial performance of 14 open coastal cities and four special economic zones in 1991 in China. As applied here, the DEA/preference structure model refines the original DEA model's result and eliminates apparently efficient DMUs.