关于DEA有效性“新方法”的探讨

主要指出文献[1],[2]中所用的"新方法"不能完全区分决策单元的DEA有效性和弱DEA有效性.同时,"新方法"中所使用的DEA模型(即文献[3]中超效率DEA模型)的最优解不一定存在,这也是"新方法"使用中的一大缺陷.本文同时指出"新方法"虽然是可以扩充的,但扩充后,某些"新模型"仍然会出现上述问题.如果单纯的去评价决策单元的DEA有效性、弱DEA有效性和非弱DEA有效性时,建议还是使用传统的经典模型为好;如果需要进一步对DEA有效性再进行分析,是可以象最早提出超效率DEA模型的文献[3]中那样去应用超效率DEA模型。     

二阶段加法DEA模型的生产可能集与生产前沿面

针对二阶段加法DEA模型的中间要素的特殊性,构造生产可能集及其公理体系,由此定义生产前沿面,并建立DEA有效和生产前沿面之间的等价关系.通过构造一个多目标规划模型,建立该问题的Pareto有效解与DEA有效之间的等价关系.     

成本最小问题与(弱)DEA有效性

在文[1]的基础上,本文证明了在一定条件下对所给的决策单元、其弱DEA有效性或DEA有效性能由成本最小问题的最优解来判断.     

只有产出(投入)BC~2模型中决策单元效率的几何刻画

在DEA方法中,DEA有效和弱DEA有效的决策单元位于生产前沿面上,非弱DEA有效的DEA无效决策单元位于生产可能集的内部而非生产前沿面上.通过引入生产可能集与生产前沿面移动的思想,证明只有产出(投入)的BC²模型评价下的决策单元的最优值与相应的生产前沿面的移动值存在倒数关系,以双产出(投入)情形图示说明,明确了决策单元在生产可能集中所处的位置.     

关于弱DEA有效性的本质特征

弱DEA有效单元与偏序集的极大元之间关系密切,从偏序集理论出发刻画了四种典型DEA模型所描述的弱DEA有效性的本质特征,揭示了可能集结构变化对弱DEA有效性的影响,并对弱DEA有效性的含义给出了新的解释.最后,探讨了偏序集理论在研究DEA数据变换性质、讨论DEA模型关系、分析决策单元变更以及指标增减对弱DEA有效性影响等方面的应用.     

强DEA有效性的探讨

给出了有关强DEA有效(C2R或C2GS2)的一些必要条件,判断方法及等价的命题,特别是给出了其存在性定理、及有关强DEA有效与扩展DEA有效等价的定理.     

具有偏好锥的链式网络DEA模型

对链式网络DEA模型进行推广,将"偏好锥"引入网络DEA模型.针对中间产出重要性以及决策者评价时的偏好,建立带有产出锥和投入锥相应的两阶段生产可能集,对具有"偏好锥"的链式网络DEA模型,证明了决策单元为网络DEA有效的充要条件,给出了网络DEA有效性与各阶段弱DEA有效性的关系.另外,文章结合具体算例说明了偏好锥的变化对效率评价的影响.关于两阶段的模型以及相关结论可以推广到多阶段网络结构.     

有关Pareto解在DEA中的应用的探讨

对文[1]中有关DEA有效(C2R)的定理4,本文给出了在某种条件下的逆定理,以便简化DEA有效性(C2R)的判断.     

DEA模型在资金分配和管理中的应用

资金的合理使用,是经济活动中的一个非常重要的问题.利用DEA的理论、方法模型,探讨资金的使用效率、分配的合理性,以及最佳资金预算的确定方法.涉及的DEA模型结构属于非参数的最优化DEA模型,以及DEA平行网络结构.模型中所使用的生产可能集是可以评价是否呈现"拥挤"迹象的.     

生产函数的规模有效性和综合DEA模型C~2WY

本文运用DEA模型C~2WY证明了生产函数y=■(x)的规模有效性就是DEA有效。     

Benchmark optimization and attribute identification for improvement of container terminals

The aim of this paper is to optimize the benchmarks and prioritize the variables of decision-making units (DMUs) in data envelopment analysis (DEA) model. In DEA, there is no scope to differentiate and identify threats for efficient DMUs from the inefficient set. Although benchmarks in DEA allow for identification of targets for improvement, it does not prioritize targets or prescribe level-wise improvement path for inefficient units. This paper presents a decision tree based DEA model to enhance the capability and flexibility of classical DEA. The approach is illustrated through its application to container port industry. The method proceeds by construction of multiple efficient frontiers to identify threats for efficient/inefficient DMUs, provide level-wise reference set for inefficient terminals and diagnose the factors that differentiate the performance of inefficient DMUs. It is followed by identification of significant attributes crucial for improvement in different performance levels. The application of this approach will enable decision makers to identify threats and opportunities facing their business and to improve inefficient units relative to their maximum capacity. In addition, it will help them to make intelligent investment on target factors that can improve their firms’ productivity.     

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.     

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.     

A new DEA ranking system based on changing the reference set

This research proposes a new ranking system for extreme efficient DMUs (Decision Making Units) based upon the omission of these efficient DMUs from reference set of the inefficient DMUs. We state and prove some facts related to our model. A numerical example where the proposed method is compared with traditional ranking approaches is shown.     

Group performance evaluation, an application of data envelopment analysis

The contribution of this paper is to provide an approach for evaluating the performance of a group of decision making units (DMUs) based on the production technology. Group evaluation is an application of data envelopment analysis (DEA). DEA uses linear programming to provide a suitable technique to estimate a multiple-input/multiple-output empirical efficient function. This paper applies group evaluation to evaluate the performance of Iranian commercial banks.     

Characterizing a subset of the PPS maintaining the reference hyperplane of the radial projection point

In this paper, we characterize a subset of the production possibility set consisting of production points whose radial projection points lie on the same supporting hyperplane of the production possibility set (PPS). To this end, we consider the CCR and BCC models and establish some theoretical results by utilizing linear programming-based techniques. Determining such a subset of the PPS provides a means to perform sensitivity analysis of inefficient units. This allows us to categorize DMUs into classes with the same returns to scale. Both these issues are addressed as applications.     

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。     

企业信息化建设投入产出的相对有效性分析

本利用数据包络分析方法,讨论了企业信息化建设投入产出的相对有效性问题,并且对非DEA有效性的决策单元在投入产出方面进行了调整,使之达到相对有效。     

Sensitivity analysis of DEA models for simultaneous changes in all the data

In data envelopment analysis (DEA) efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for the basic DEA models, such as, those proposed by Charnes, Cooper and Rhodes (CCR), Banker, Charnes and Cooper (BCC) and additive models, when variations in the data are simultaneously considered for all DMUs. By means of modified DEA models, in which the specific DMU under examination is excluded from the reference set, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalises the usual sensitivity analysis approach developed in which perturbations of the data are only applied to the test DMU while all the remaining DMUs remain fixed. In our framework data are allowed to vary simultaneously for all DMUs across different subsets of inputs and outputs. We study the relations of the infeasibility of modified DEA models employed and the robustness of DEA models. It is revealed that the infeasibility means stability. The empirical applications demonstrate that DEA efficiency classifications are robust with respect to possible data errors, particularly in the convex DEA case.