指标可取区间数的决策单元的DEA评价

对输入、输出取区间数的一些决策单元,在给出有关DEA的定理的基础上,对评价它们的方法作了进一步探讨.     

某些决策单元的EDA有效性的简便判别法

本给出了判别某些决策单元EDA有效性（C^2R或C^2GS^2）的简便方法。     

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.     

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．     

考虑决策单元竞争合作动态变化的DEA博弈交叉效率方法

利用DEA方法进行相对效率评估时,决策单元通常需要考虑多重目标,且随着目标的变化,决策单元间竞争合作状态也会发生动态变化。传统竞合模型虽然考虑了决策单元间竞争与合作同时存在的现象,但忽视了竞争合作关系动态变化的过程。本文以竞争合作对策为切入点,将多目标规划中的优先因子引入传统DEA博弈交叉效率模型中,提出了带有优先等级的多目标DEA博弈交叉效率模型,即动态竞合博弈交叉效率模型。该模型充分体现了不同目标下决策单元间竞争合作关系的动态变化,其焦点由传统竞合模型对多重最优权重现象的改善,转向对最优效率得分的直接寻找。利用DEA动态竞合博弈交叉效率模型,本文对环境污染约束下2014年长三角地区制造业投入产出绩效进行了客观的评估。分析结果表明:DEA动态竞合博弈交叉效率模型收敛速度优于传统DEA博弈交叉效率模型,其交叉效率得分收敛于唯一的纳什均衡点;不同目标重要性的差异程度,对最终排名结果不产生明显影响,不需要确切指出。     

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.     

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.     

使决策单元变为DEA有效的偏差和最小法

某决策单元为非 DEA有效 ( C2 R或 C2 GS2 ) ,为了将它变为 DEA有效 ,在找出其对应点附近的一些有效前沿面的基础上 ,给出了使其对应点与这些有效前沿面上的点的输入、输出的偏差和最小的方法 .     

决策单元的变更对共协调性的影响

本文将对共协调分析的灵敏度问题进行研究,着重探讨决策单元的变更对共协调性的影响。     

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。     

A new framework for the solution of DEA models

We provide an alternative framework for solving data envelopment analysis (DEA) models which, in comparison with the standard linear programming (LP) based approach that solves one LP for each decision making unit (DMU), delivers much more information. By projecting out all the variables which are common to all LP runs, we obtain a formula into which we can substitute the inputs and outputs of each DMU in turn in order to obtain its efficiency number and all possible primal and dual optimal solutions. The method of projection, which we use, is Fourier–Motzkin (F–M) elimination. This provides us with the finite number of extreme rays of the elimination cone. These rays give the dual multipliers which can be interpreted as weights which will apply to the inputs and outputs for particular DMUs. As the approach provides all the extreme rays of the cone, multiple sets of weights, when they exist, are explicitly provided. Several applications are presented. It is shown that the output from the F–M method improves on existing methods of (i) establishing the returns to scale status of each DMU, (ii) calculating cross-efficiencies and (iii) dealing with weight flexibility. The method also demonstrates that the same weightings will apply to all DMUs having the same comparators. In addition it is possible to construct the skeleton of the efficient frontier of efficient DMUs. Finally, our experiments clearly indicate that the extra computational burden is not excessive for most practical problems.     

考虑非期望因素的决策单元排序:两阶段综合效率法

对所有平行级别上的同等类型的决策单元(DMUs)在绩效表现上的排序一直是管理决策领域研究的重要课题之一。基于数据包络分析的超效率理论和SBM模型,探讨考虑非期望因素的DMUs排序问题。首先构建新的考虑非期望因素的超效率SBM模型,此模型不仅能对有效DMUs排序,而且能够转化成线性规划问题求解,具有有界性、单调性等良好性质。然后将新模型与Tone的SBM模型结合提出了考虑非期望因素的SBM综合排序法,同时给出了相对应的多项式时间算法。该方法以SBM模型作为第一阶段完成非有效DMUs排序,以新模型作为第二阶段完成有效DMUs排序,两阶段综合即完成所有DMUs排序。研究结果表明,综合排序法能够完成对考虑非期望因素的DMUs的排序,为绩效评价的管理实践提供了重要的理论依据。选取中国2010年的30个省份为实证研究对象,应用所提出的综合效率排序法对其环境效率进行排序。分析结果与中国的现实情况的相吻合,表明该排序方法是合理的,能够完成对这些地区的环境效率进行排序,可以为决策者评价环境的绩效表现提供有效的决策支持。     

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.     

一种基于决策矩阵的DST-AHP多属性决策方法

针对层次分析法决策时存在两两判断、一致性检验次数过多和判断矩阵残缺性等问题,本文提出了一种基于决策矩阵的DST-AHP多属性决策方法。该方法结合决策矩阵的特征值,构建DST-AHP方法层次结构模型和判断矩阵,并根据判断矩阵定义不同属性下各焦元的基本概率分配函数;然后利用Dempster合成法则对基本概率分配函数值进行合成,依据合成后值对方案进行排序。最后对AHP和DST-AHP两种方法进行比较分析,说明该方法的有效性。     

On some generalization of the DEA models

Inadequate results may arise in some instances of DEA model applications. For example, a data envelopment analysis (DEA) model may show ‘a notoriously inefficient unit’ as an efficient one. In addition, too many efficient units may appear in some DEA models. An elegant and subtle approach was proposed to deal with these problems, which is based on incorporating domination cones in DEA models. Yu, Wei and Brockett suggested the generalized DEA (GDEA) model that unifies and extends most of the well-known DEA models based on using domination cones. In this paper, we propose a model that is more general than the GDEA model, on the one hand, as it covers situations that the GDEA model cannot describe. On the other hand, our model enables one to construct step-by-step any model from the family of the GDEA models by incorporating artificial units and rays in the space of inputs and outputs in the Banker, Charnes, Cooper (BCC) model, which makes the process of model construction visible and more understandable. Moreover, we show that any GDEA model can be approximated by some BCC model.     

基于目标规划的多指标群体决策

在多指标群体决策问题中,将个体决策的决策向量集结为群体决策的综合评判值是决策的关键,其中也涉及到决策专家的权威性比重问题.在五标度赋值确定专家权威性比重的基础上,以最小二乘法为工具,建立了一种群体决策的目标优化模型,从而为多指标群体决策问题提供了又一科学而合理的决策方法.     

Comparing extreme models when the sign of the extreme value index is known

In the literature on analyzing extremes, both generalized Pareto distributions and Pareto distributions are employed to infer the tail of a distribution with a known positive extreme value index. Similar studies exist for a known negative extreme value index. Intuitively, one should not employ the generalized Pareto distribution in the case of knowing the sign of the extreme value index. In this work, we show that fitting a generalized Pareto distribution is equivalent to the model in Hall (1982) in the case of a negative extreme value index, in both improving the rate of convergence and including the bias term of the asymptotic results of that reference. When the extreme value index is known to be positive, we show that fitting a generalized Pareto distribution may be preferred in some cases determined by a so-called second-order parameter and the extreme value index itself.     

一种基于相关系数矩阵的TOPSIS决策方法

在多属性决策分析中,传统的TOPSIS法是基于欧氏距离来计算各方案到正负理想点的距离,但欧氏距离没有考虑各属性之间的相关性;从这一角度出发,将相关系数矩阵与欧式距离结合,从而弥补了欧氏距离的不足,最后进行了实例分析.     

The overall efficiency of the dynamic DEA models

Central European Journal of Operations Research - This paper deals with the dynamic efficiency analysis based on Data Envelopment Analysis (DEA) models. Our aim is to formulate new dynamic DEA...     

一种多指标决策与评价的新方法

指出了多指标决策与评价投影法所用的决策矩阵无量纲化方法的不妥之处及在应用中存在的问题 ,提出了一种新方法 ,并用实例说明了该方法是可行合理的 .