基于公共权重的区间DEA效率评价及其排序方法研究

针对传统区间数据包络分析方法,在确定每一个决策单元区间效率的上界和下界时,存在的评价尺度不一致且计算复杂等问题,本文提出了一种同时最大化所有决策单元的效率上界和下界的公共权重区间DEA模型,并给出了一种考虑决策者偏好信息的可能度排序方法,用以解决区间效率的全排序问题。最后,以中国大陆11个沿海省份工业生产效率测算为例说明了所提方法的有效性和实用性。     

基于交叉评价策略的DEA灰色关联排序模型

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

基于交叉评价策略的DEA灰色关联排序模型北大核心

数据包络分析(DEA)是评价决策单元相对效率的有效方法,其中的交叉效率评价方法可用来对决策单元进行区分排序.针对原有模型中交叉效率值的不唯一问题,结合灰色关联分析思想,构建理想决策单元,定义各决策单元与理想决策单元的灰色关联度,以灰色关联度值最大为目标,建立优化模型来计算输入和输出指标的最佳权重,据此得出决策单元的交叉效率值,实现对决策单元的完全排序.最后通过算例来验证模型的有效性和实用性.     

含有偏好的DEA-BWM评价方法研究

针对传统的DEA模型在评估过程中并未考虑决策者对相关指标权重的偏好,将最优最差方法(BWM)嵌入到传统DEA模型中,基于决策者偏好排序的判断矩阵,构建一种含有偏好的DEA-BWM评价方法。首先在保持传统DEA方法的优势基础上,构建了CCR-BWM评价模型对各DMU进行评价。同时考虑为了便于各决策单元在统一权重基础上相互比较,构建了CSW-BWM公共权重模型。另外考虑决策单元自评和互评,构建了NCE-BWM中立型交叉效率。然后采用min-max方法分别将上述三种多目标评价模型转换为单目标线性规划进行求解。最后,选择一组算例对三种模型的有效性与合理性进行验证。     

基于LR模糊数的广义模糊DEA模型及其求解

在广义DEA模型基础上,建立基于LR模糊数的广义模糊DEA模型.通过引入LR模糊数的加权平均值,计算了待评价决策单元能体现决策者偏好的广义模糊效率和平均广义模糊效率,对待评价决策单元进行有效性排序.最后通过实例分析,表明了该模型的实用性.     

投入变量缺失系统DEA效率评价

针对投入变量缺失生产服务系统,提出一种基于DEA的相对效率评价方法.由于该系统的投入无法确知,首先需要依据产出对各决策单元(DMU)进行分组,并将其相对效率分解为组内效率与组间效率.对于组内效率,引人虚拟投入变量利用传统超效率DEA模型进行评价.而对于组间效率,则建立扩展的超效率DEA模型.最终以两类效率之积评价所有决策单元之间的相对效率.理论分析表明:投入缺失系统内决策单元有效的充要条件是其组内效率及其所在组的组间效率均有效.文章最后以基金项目评审为例进行实证分析,说明了本方法的合理性与可行性.     

一种基于虚拟决策单元的排序方法的完善和扩展

本文对文[1]中提出的基于虚拟决策单元的排序方法进行了完善和扩展。首先,根据CCR模型,给出了两类特殊的DEA模型,分别是仅有投入数据的DEA模型和仅有产出数据的DEA模型;其次,基于这两个模型,应用上述方法实现了对仅有投入(或产出)数据的决策单元的排序;第三,给出了排序方法中参数a的计算方法;最后,通过修正排序模型,有效提高了排序方法的计算精度。改进后的排序方法避免了两个决策单元因为相对效率值过小而不能排序的情形,其应用范围也进一步扩大。     

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.     

用超效率综合DEA模型来研究DEA有效性

对超效率综合DEA模型,有三个定理来判断其不可行性,其中一个定理基于加性模型来判断,并证明:当模型不可行时被评决策单元的扩展DEA有效性,由此给出了对扩展DEA有效的决策单元排序的方法,此外,对不含非阿基米德无穷小的基于输入(输出)的超效率综合DEA模型,当其最优值为1时,有一个定理来判断被评单元的DEA有效性.     

基于熵权法的DEA/AR交叉效率知识化制造模式评价

用模糊DEA/AR交叉效率方法,解决制造模式的评价与排序问题.首先,构建了四种不同的DEA/AR交叉效率模型—任意型、对抗型、友好型和博弈型.然后,应用熵权法确定每一种交叉效率模型的最终交叉效率值,目的是用保证域来避免传统模型的权重偏差,从而实现了决策单元的相对有效评价和精确排序.同时,引入奇异指数的概念来衡量最终交叉效率的合理性及可靠性.最后,通过实例验证本文模型和方法的可行性及有效性:与采用简单DEA效率模型进行评价比较,我们的方法会使得效率更加精准、排序更加合理.     

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.     

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.     

Interval cross efficiency for fully ranking decision making units using DEA/AHP approach

Data envelopment analysis (DEA) is a popular technique for measuring the relative efficiency of a set of decision making units (DMUs). Fully ranking DMUs is a traditional and important topic in DEA. In various types of ranking methods, cross efficiency method receives much attention from researchers because it evaluates DMUs by using self and peer evaluation. However, cross efficiency score is usual nonuniqueness. This paper combines the DEA and analytic hierarchy process (AHP) to fully rank the DMUs that considers all possible cross efficiencies of a DMU with respect to all the other DMUs. We firstly measure the interval cross efficiency of each DMU. Based on the interval cross efficiency, relative efficiency pairwise comparison between each pair of DMUs is used to construct interval multiplicative preference relations (IMPRs). To obtain the consistency ranking order, a method to derive consistent IMPRs is developed. After that, the full ranking order of DMUs from completely consistent IMPRs is derived. It is worth noting that our DEA/AHP approach not only avoids overestimation of DMUs’ efficiency by only self-evaluation, but also eliminates the subjectivity of pairwise comparison between DMUs in AHP. Finally, a real example is offered to illustrate the feasibility and practicality of the proposed procedure.     

基于Shephard距离函数的DEA TOPSIS方法研究

本文通过对Shephard距离函数的引入,正式构建了DEA TOPSIS决策单元排序方法的框架。本文首先定义了正(负)理想决策制定单元(DMU)以及相应的(反)生产可能集,然后在考虑正(负)理想DMU的条件下分别给出DMU的(反)效率评价模型以及对应的Shephard距离函数,然后基于评价对象到理想DMU相对接近度这一综合评价值给出了DMU的一个完全排序。最后,本文通过算例分析说明了该方法的有效性和实用性。     

A new method for complete ranking of DMUs

So far numerous models have been proposed for ranking the efficient decision-making units (DMUs) in data envelopment analysis (DEA). But, the most shortcoming of these models is their two-stage orientation. That is, firstly we have to find efficient DMUs and then rank them. Another flaw of some of these models, like AP-model (A procedure for ranking efficient units in data envelopment analysis, Management Science, 39 (10) (1993) 1261–1264), is existence of a non-Archimedean number in their objective function. Besides, when there is more than one weak efficient unit (or non-extreme efficient unit) these models could not rank DMUs. In this paper, we employ hyperplanes of the production possibility set (PPS) and propose a new method for complete ranking of DMUs in DEA. The proposed approach is a one stage method which ranks all DMUs (efficient and inefficient). In addition to ranking, the proposed method determines the type of efficiency for each DMU, simultaneously. Numerical examples are given to show applicability of the proposed method.     

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.     

基于参数设计的信噪比交叉效率评价方法

针对DEA交叉效率评价过程中没有考虑自评与互评效率的作用而主观赋予相同权重导致交叉效率评价值不准确的问题.文章基于参数设计的思想,依据试验设计中可控与不可控因素的作用机理区分自评权重和互评权重对所评价决策单元交叉效率的影响与作用,将其界定为可控与不可控因素的管理学属性,明确不同权重作用机理;引入信噪比作为衡量决策单元交叉效率评价时的性能指标,实施DEA交叉效率评价方法的改进,设计出DEA信噪比交叉效率集结方法,从而实现交叉效率的集结方式由单一考虑交叉效率波动的均值转化为综合考虑交叉效率波动情况(均值与方差),交叉效率评价值用信噪比交叉效率替代交叉效率平均值更具有统计学意义并可从管理学角度解释,评价结果也具有更高的可区分性;最后通过算例分析验证了交叉效率评价理论上的必要性和该方法的合理性与可行性,同时发现了交叉效率评价中存在CCR有效DMU序位超出了有效DMU范围现象,建议应实施同质DMU检验和评价值归一化.文章的研究也为提高DEA交叉效率测算的准确性提供一种新思路.     

The interval efficiency based on the optimistic and pessimistic points of view

Data envelopment analysis (DEA) is a data-oriented approach for evaluating the performances of a set of peer entities called decision-making units (DMUs), whose performance is determined based on multiple measures. The traditional DEA, which is based on the concept of efficiency frontier (output frontier), determines the best efficiency score that can be assigned to each DMU. Based on these scores, DMUs are classified into DEA-efficient (optimistic efficient) or DEA-non-efficient (optimistic non-efficient) units, and the DEA-efficient DMUs determine the efficiency frontier. There is a comparable approach which uses the concept of inefficiency frontier (input frontier) for determining the worst relative efficiency score that can be assigned to each DMU. DMUs on the inefficiency frontier are specified as DEA-inefficient or pessimistic inefficient, and those that do not lie on the inefficient frontier, are declared to be DEA-non-inefficient or pessimistic non-inefficient. In this paper, we argue that both relative efficiencies should be considered simultaneously, and any approach that considers only one of them will be biased. For measuring the overall performance of the DMUs, we propose to integrate both efficiencies in the form of an interval, and we call the proposed DEA models for efficiency measurement the bounded DEA models. In this way, the efficiency interval provides the decision maker with all the possible values of efficiency, which reflect various perspectives. A numerical example is presented to illustrate the application of the proposed DEA models.     

Ranking DMUs by using interval DEA cross efficiency matrix with acceptability analysis

Cross efficiency method is an extension of data envelopment analysis (DEA), and has been widely used for ranking performance of decision making units (DMUs). To eliminate the non-uniqueness of cross efficiency scores, the aggressive and benevolent strategies have been proposed as secondary goals to determine the unique cross efficiency score. The current paper aims to propose an alternative strategy which does not consider the preference of the decision maker in choosing aggressive or benevolent strategy. Instead, the paper considers all possible weight sets in weight space when computing the cross efficiency and each DMU is given an interval cross efficiency. By using the stochastic multicriteria acceptability analysis (SMAA-2) method, all DMUs in the interval cross efficiency matrix (CEM) could be fully ranked according to the acceptability indices. A numerical example about efficiency evaluation to seven academic departments in a university is illustrated.     

Ranking efficient decision making units in data envelopment analysis based on reference frontier share

Data envelopment analysis (DEA) is a powerful technique for performance evaluation of decision making units (DMUs). Ranking efficient DMUs based on a rational analysis is an issue that yet needs further research. The impact of each efficient DMU in evaluation of inefficient DMUs can be considered as additional information to discriminating among efficient DMUs. The concept of reference frontier share is introduced in which the share of each efficient DMU in construction of the reference frontier for evaluating inefficient DMUs is considered. For this purpose a model for measuring the reference frontier share of each efficient DMU associated with each inefficient one is proposed and then a total measure is provided based on which the ranking is made. The new approach has the capability for ranking extreme and non-extreme efficient DMUs. Further, it has no problem in dealing with negative data. These facts are verified by theorems, discussions and numerical examples.