DEA方法的效率悖论与数据短尾现象

通过实例分析发现许多重要DEA模型给出的评价结果都可能存在效率悖论,即随着评价标准的提高,一个决策单元的效率值反而会增大.为了探究DEA效率悖论产生的原因及解决办法,首先通过实例证明一些最重要DEA模型(包括CCR模型、BCC模型、FG模型、ST模型)给出的评价结果均可能存在效率悖论.然后,从理论上解释了DEA效率悖论产生的根源在于决策单元数据的短尾现象,并给出了判定存在数据短尾现象的方法.同时,给出了一种修正的DEA模型,该模型不仅可以克服DEA效率悖论的出现,而且还能有效提高DEA方法对效率测算的准确性.最后,应用2000-2014年的中国省级经济数据对相关模型进行了比较研究.     

A Comprehensive Dea Approach for the Resource Allocation Problem based on Scale Economies Classification

This paper is concerned with the resource allocation problem based on data envelopment analysis （DEA） which is generally found in practice such as in public services and in production process. In management context, the resource allocation has to achieve the effective-efficient-equality aim and tries to balance the different desires of two management layers： central manager and each sector. In mathematical programming context, to solve the resource allocation asks for introducing many optimization techniques such as multiple-objective programming and goal programming. We construct an algorithm framework by using comprehensive DEA tools including CCR, BCC models, inverse DEA model, the most compromising common weights analysis model, and extra resource allocation algorithm. Returns to scale characteristic is put major place for analyzing DMUs＇ scale economies and used to select DMU candidates before resource allocation. By combining extra resource allocation algorithm with scale economies target, we propose a resource allocation solution, which can achieve the effective-efficient-equality target and also provide information for future resource allocation. Many numerical examples are discussed in this paper, which also verify our work.     

四类DEA模型相互关系及其在计算中的应用

计算DEA模型效率值是采用DEA方法进行绩效评估的重要一环,研究四类DEA模型(CCR模型、BCC模型、FG模型及ST模型)之间的相互关系,有助于计算四类DEA效率值,进而判断评价对象所处的规模报酬状态及规模有效性.在四种不同规模报酬假设下,给定决策单元的DEA有效性分别由四类不同的DEA模型所定义,其输入、输出效率值具有两两相等属性.而且,CCR模型与FG模型、ST模型之间存在动态联系.鉴于此,只需要计算出CCR与BCC效率值,即可确定FG与ST效率值.     

Allocating fixed costs with considering the return to scale: A DEA approach

When the allocated fixed cost is treated as the complement of other costs, conventional data envelopment analysis (DEA) researches have ignored the effect of the return to scale (RTS) in fixed cost allocation problems. This paper first demonstrates why the RTS should be considered in fixed cost allocation problems. Then treating the fixed cost as a complementary input, the authors investigate the relationship between the allocated cost and the variable return to scale (VRS) efficiency based on the super BCC DEA model. However, the infeasibility problem may exist in this situation. To deal with it, the authors propose an algorithm. The authors find that the super BCC efficiency is a monotone non-increasing function of the allocated cost. Based on the relationship, the authors finally propose a fixed cost allocation approach in terms of principles as: (i) The fixed cost proportion allocated to inelastic DMUs should be consistent with their consumed cost proportion, and (ii) the same efficiency satisfaction degree to the rest DMUs. The optimal allocation scheme is unique. A numerical example and a real example of allocating fixed costs among 13 subsidiaries are employed to illustrate the proposed approach.     

Robust data envelopment analysis based MCDM with the consideration of uncertain data

The application of data envelopment analysis (DEA) as a multiple criteria decision making (MCDM) technique has been gaining more and more attention in recent research. In the practice of applying DEA approach, the appearance of uncertainties on input and output data of decision making unit (DMU) might make the nominal solution infeasible and lead to the efficiency scores meaningless from practical view. This paper analyzes the impact of data uncertainty on the evaluation results of DEA, and proposes several robust DEA models based on the adaptation of recently developed robust optimization approaches, which would be immune against input and output data uncertainties. The robust DEA models developed are based on input-oriented and outputoriented CCR model, respectively, when the uncertainties appear in output data and input data separately. Furthermore, the robust DEA models could deal with random symmetric uncertainty and unknown-but-bounded uncertainty, in both of which the distributions of the random data entries are permitted to be unknown. The robust DEA models are implemented in a numerical example and the efficiency scores and rankings of these models are compared. The results indicate that the robust DEA approach could be a more reliable method for efficiency evaluation and ranking in MCDM problems.     

企业规模VS效率:对中国保险企业的DEA经验研究

企业规模与效率之间的两难冲突是一个古老的经济学谜团，新古典经济学和新制度经济学没有对此形成一致的理论解释，因此成为一个经验问题。DEA（主要是CCR模型）是对规模经济问题进行经验分析的有力方法。对中国保险企业的DEA分析结果表明，规模不经济的情况在中国保险业中更具有一般性，但在程度上会受到其他因素的影响。     

基于Pareto分布的决策单元DEA效率评价

针对网络数据包络分析(DEA)应用时缺少内部数据的瓶颈,提出将决策单元内部的生产活动按照价值动因分为核心和非核心生产单元,并根据经验Pareto分布估计核心单元的输入数据,据此构建DEA效率评价模型.新模型利用输入输出数据和基于管理者经验信息获得的更多信息,据此估计生产潜力并给出相应的估计的概率,为决策单元的管理者分配资源和设定目标提供理论支持.最后利用模拟数据演示所提出的模型,并与BCC模型的结论相比较,结果显示新模型能够发现更高的生产潜力的信息,可以为决策者制订目标提供依据.     

一种DEA效率概率占优方法研究

决策单元间的效率关系研究是效率研究中的重要领域.传统DEA模型通过计算决策单元各自最优权重情景下的效率最大值,来判断决策单元间的效率排序关系.而这种最优权重往往是极端权重,没有考虑其它权重情景.采用其它权重时,决策单元的效率值和排序往往会发生较大的变化.本文考虑了所有权重情景,提出了DEA效率概率占优模型,定义了决策单元的占优效率概率和被占优效率概率.该模型能够判断任意两个决策单元的效率概率占优关系;并将效率概率占优关系从两个决策单元扩展到决策单元与决策单元集.最后将其应用于决策单元效率排序.通过实证分析发现了两条重要结论:1)考虑所有权重情景的排序与采用极端权重的CCR效率值排序不一致;2)考虑所有权重情景时,一些无效单元的效率排序比有效单元的效率排序更高.     

要素在有限范围变化的DEA模型

本文首先讨论了在数据包络分析（ＤＥＡ）中有些要素（投入或产出）只允许在有限范围变化的情况。然后从生产可能集入手，将这种对要素的限制直接反映到生产可能集中。基于此改进后的生产可能集，提出了比现有研究更广泛意义的ＤＥＡ模型。该ＤＥＡ模型实际上综合了传统的以及投入或产出固定不变的ＤＥＡ模型。此外，在进行决策单元（ＤＭＵ）效率分析时，文中给出的定理为存在投入过多及产出不足的非有效ＤＭＵ提供了改进目标以使之     

中国银行业DEA效率实证分析

采用2007年数据,运用DEA优势效率模型和劣势效率模型对我国14家商业银行的DEA综合效率进行测评,得出了国内商业银行的综合效率排名. 结果表明:国有四大商业银行的效率总体上明显不及新兴股份制商业银行.通过与2003年的数据对比, 认为尽管四大行效率有所增进,但劣势依然明显.研究还运用CCR模型进行Charnes-Cooper线性变换和对偶变换后的模型(D),分析了14家商业银行的规模效率情况, 分析结果表明:四大国有商业银行没有存在明显的规模经济.     

数据包络分析的灵敏度研究及其应用

研究并给出数据包络分析中ＣＣＲ模型的一种灵敏度分析方法，提出有效决策单元在输入／输出变动时，保持有效性不变的充分条件。实用表明，该法稳定有效。     

中国保险业DEA效率实证分析

运用DEA优势效率模型和劣势效率模型对我国9家保险公司2001年度的DEA综合效率进行测评显示:它们的效率总体上不占优势;运用CCR模型进行Charnes-Cooper线性变换和对偶变换后的模型(D),分析它们2001年的规模效率情况,结果表明大多存在非规模经济现象;运用回归模型分析综合效率、所有制形式对它们总资产报酬收益率的影响,得出总资产报酬收益率与上述两个因素显著正相关.     

基于AHP与DEA的多因素排序法

结合层次分析法(AHP)7Z数据包络分析(DEA)方法对一类多因素排序问题给出了一种合理的排序方法．该方法首先利用AHP方法给出各因素所属类的权重，再根据决策对象的状态值，运用DEA(CCR)方法求出各对象在每一类中的排序权值，最后将该值与各类的权重综合起来，即求得各对象的最终排序权值．文章中运用了一个人才选优的实际例子加以说明。     

一类基于投入约束的资源配置DEA博弈模型

结合数据包络分析(DEA)与Nash讨价还价博弈模型研究有限资源的合理配置问题。首先证明,在投入约束条件下,基于传统DEA模型的资源配置方法将陷入困境。为此,需要考虑各决策单元(DMU)对于有限资源的竞合关系,引入Nash讨价还价博弈模型,并证明最优资源配置方案具有唯一性。最终通过算例说明了本方法的合理性与可行性,与其它DEA分摊方法相比还具有一定优势。     

输入和输出DEA模型中弱DEA有效与弱Pareto之间的等价性

使用带有三个双变量 0 -1参数的综合 DEA模型 ,讨论了弱 Pareto和输入 DEA模型 (包括 C2 R输入模型、BC2 输入模型、FG输入模型、ST输入模型 )、输出 DEA模型 (包括 C2 R输出模型、BC2 输出模型、FG输出模型、ST输出模型 )之下的弱 DEA有效之间的等价性 .这些结果对于理解和解释输入 DEA模型和输出 DEA模型之下的弱 DEA有效性的概念是很重要的 .     

A Range Adjusted Measure of Super-Efficiency in Integer-Valued Data Envelopment Analysis with Undesirable Outputs

DEA(data envelopment analysis) models can be divided into two groups: Radial DEA and non-radial DEA, and the latter has higher discriminatory power than the former. The range adjusted measure(RAM) is an effective and widely used non-radial DEA approach. However, to the best of our knowledge, there is no literature on the integer-valued super-efficiency RAM-DEA model,especially when undesirable outputs are included. We first propose an integer-valued RAM-DEA mode with undesirable outputs and then extend this model to an integer-valued super-efficiency RAM-DEA model with undesirable outputs. Compared with other DEA models, the two novel models have many advantages: 1) They are non-oriented and non-radial DEA models, which enable decision makers to simultaneously and non-proportionally improve inputs and outputs; 2) They can handle integer-valued variables and undesirable outputs, so the results obtained are more reliable; 3) The results can be easily obtained as it is based on linear programming; 4) The integer-valued super-efficiency RAM-DEA model with undesirable outputs can be used to accurately rank efficient DMUs. The proposed models are applied to evaluate the efficiency of China's regional transportation systems(RTSs) considering the number of transport accidents(an undesirable output). The results help decision makers improve the performance of inefficient RTSs and analyze the strengths of efficient RTSs.     

双风险度量下封闭式基金业绩的数据包络分析

数据包络分析(Data Envelopment Analysis，DEA)是一种广泛运用于相对绩效评估的系统分析方法，将一多输入单输出DEA模型引入证券投资基金业绩评价，其中输出为基金收益，而输入则为管理费用、交易成本、标准差和VaR。随后．利用该模型对2000年以前上市的20只基金在2000年、2001年及2000～2001年间的业绩进行了评价，并发现：在所有评价期．基金安顺、兴和和金鑫的业绩相对有效．基金裕隆和景宏相对较无效，它们的相对业绩均表现出短期持续性。     

带有参数的数据包络分析C~2R模型

本文为了改进C~2R模型反映决策单元相对信息不完全的不足,提出了参数型数据包络分析模型,讨论了这个模型的有关性质,给出了阔值和有效值的概念.经过理论分析和实例验证,这两个值可更好地反映决策单元的相对信息.     

两阶段DEA分析框架下的环境效率测度与分解

本文根据传统CCR模型和两阶段DEA模型进行环境效率评价时所存在的问题,针对兼具复杂内部结构和非期望要素的生产系统,提出基于合作博弈的两阶段模型,用以评价该系统的环境效率.随后,构建基于协调效率最优的效率分解方法,客观地解决了两阶段DEA模型最优解不唯一的问题,有效衡量两个子系统各自的效率与它们之间的协调度,并从更深的层面挖掘影响生产系统环境效率的因素,为推进经济发展与环境保护协同共进提供有力工具.最后,通过对中国各地区工业生产系统水环境效率的评价来验证模型的合理性与有效性.     

Integrating dual-role variables in data envelopment analysis

Traditional data envelopment analysis (DEA) theory assumes that decision variables are regarded as inputs or outputs, and no variable can play the roles of both an input and an output at the same time. In fact, there exist some variables that work as inputs and outputs simultaneously and are called dual-role variables. Traditional DEA models cannot be used to appraise the performance of decision making units containing dual-role variables. The paper analyzes the structure and properties of the production systems comprising dual-role variables, and proposes a DEA model integrating dual-role variables. Finally the proposed model is illustrated to evaluate the efficiency of university departments.