广义模糊DEA模型及其有效性研究

考虑到样本单元和待评价决策单元输入输出数据的模糊性,提出了广义模糊DEA模型,利用α-截集,将广义模糊DEA变换成以置信水平α为参数的参数规划,给出了待评价决策单元效率值θ~*的效率区间的计算方法,并在此基础上讨论了θ~*的隶属函数μ_(θ*).     

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。     

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.     

基于超效率DEA-IAHP的物流企业绩效评价

本文在介绍超效率数据包络分析法及区间数层次分析法的原理和模型,深入研究DEA-AHP评价方法的基础上,提出了超效率DEA-IAHP方法对物流企业绩效进行评价,改进方法引入超效率DEA方法和区间层次分析法弥补了原方法的不足,其中超效率数据包络分析法弥补了原方法不能对效率均为1的决策单元有效排序的问题,可以对所有决策单元进行总排序;区间层次分析法使用区间数判断矩阵来表达各指标因素对总目标的相对重要程度,这有效地解决了决策者因为对物流企业信息掌握不全而导致的点判断矩阵不可靠的问题,更好地体现了决策者偏好。笔者给出了应用超效率DEA-IAHP方法对物流企业进行绩效评价的基本步骤,并用实例分析体现了该方法的实用性及优越性。     

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。     

基于交叉效率DEA和熵IAHP对物流企业绩效评价

本文在研究了现有文献对物流企业绩效评价的基础上,基于超效率DEA用以计算效率值的权值只在对被评价单元最有利的特定范围内取值、忽视绩效评价的公平性和IAHP方法主观判断性较大的缺陷,提出了交叉效率DEA和熵IAHP方法。交叉效率DEA的中心思想是采用互评体系,弥补了超效率DEA方法只是选择对被评价决策单元最有效的权重忽视公平性的缺陷。熵IAHP方法是客观确定权重的熵权法和体现决策者偏好的IAHP方法的结合,这有效地解决了IAHP方法确定指标权重时主观性过大的缺陷。笔者给出了交叉效率DEA和熵IAHP模型评价物流企业绩效的基本步骤,最后通过一个实例验证了此方法的有效性和优越性。     

基于前景理论的模糊DEA交叉效率评价方法

针对模糊环境下决策单元的相对有效性评价问题，本文利用α-截集法将三角模糊数型的投入产出值转化为区间数，提出一种改进的区间交叉效率模型。随后，引入前景理论来研究区间交叉效率集结问题，定义区间参考点代替传统的单个参考点，以最大化所有决策单元的前景交叉效率为原则，构建最大化前景交叉效率模型求解集结权重。根据偏好度方法，比较区间交叉效率值。本文方法基于统一的生产前沿面来度量决策单元的效率，保证了不同决策单元之间以及不同α值下的效率可比；定义区间参考点充分考虑了决策者在模糊环境下的心理因素变化，集结决策单元的区间交叉效率值代替综合前景值，以保留尽可能多的决策信息。最后，通过例子验证方法的有效性。     

考虑投入和产出指标偏好的广义DEA模型

广义DEA是一种基于决策单元和非决策单元自由选择参考集的扩展DEA模型.传统DEA模型的最优解大多是由线性规划随机计算的,未能充分考虑投入和产出指标的重要程度.将投入和产出指标的决策者偏好引入到广义DEA模型约束条件中,首先定义投入和产出指标偏好矩阵,再将该矩阵纳入广义DEA模型的约束条件,构建了带投入和产出指标偏好的广义DEA模型(GDEA-IP).接下来给出决策单元GDEA-IP有效性与评价指标的量纲选择无关性的证明,以及决策单元为GDEA-IP弱有效和有效的理论证明.算例分析说明GDEA-IP模型的有效性,通过和其它经典模型的对比分析,进一步说明该模型比广义DEA模型具有更大的灵活性和通用性,拓展了DEA方法的理论研究.     

带有随机决策单元的广义数据包络分析方法

广义DEA方法是一种相对效率评价方法,解决了决策单元相对于任意参考系(样本单元集)的效率比较问题.在实际中,有时评价标准是确定的,决策单元的生产具有不确定性,有必要在进行生产之前基于确定性样本单元对随机性决策单元进行相对效率评价.为了解决这个问题,研究样本单元为确定值,决策单元为随机变量的广义DEA模型,分别通过期望值和机会约束将随机模型转化为确定性规划,给出决策单元GEDEA有效和GCDEA有效的概念,GEDEA有效与多目标规划Pareto有效关系,以及利用移动因子对决策单元进行有效性排序方法.     

具有阶段最终产出的广义链式网络DEA模型

传统网络DEA方法通过打开生产过程中的"黑箱",考虑生产过程的中间环节,对生产过程进行相对效率评价.但是传统网络DEA方法只能相对于决策单元集而不能相对于非决策单元集进行相对效率评价.给出能够相对于任意参考集对决策单元进行相对效率评价的基于C2R模型的具有阶段最终产出的广义链式网络DEA方法,初步讨论相应性质并进行算例演示.     

A generalized model for data envelopment analysis with interval data

Data envelopment analysis (DEA) is a method to estimate the relative efficiency of decision-making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models with interval data have been developed. The CCR model with interval data, the BCC model with interval data and the FDH model with interval data are well known as basic DEA models with interval data. In this study, we suggest a model with interval data called interval generalized DEA (IGDEA) model, which can treat the stated basic DEA models with interval data in a unified way. In addition, by establishing the theoretical properties of the relationships among the IGDEA model and those DEA models with interval data, we prove that the IGDEA model makes it possible to calculate the efficiency of DMUs incorporating various preference structures of decision makers.     

A Euclidean distance-based measure of efficiency in data envelopment analysis

Data envelopment analysis (DEA) has been proven as an excellent data-oriented performance evaluation method when multiple inputs and outputs are present in a set of peer decision-making units (DMUs). Several efficiency measures have been proposed in the DEA literature, see, for instances, radial efficiency measure of Charnes et al. (CCR)(A. Charnes. W.W. Cooper, and E. Rhodes, 1978. Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2, 429–444), Russell graph measure (J.T. Russell, and R. Sirvant. 1999. An enhanced DEA Russell graph efficiency measure. Eur. J. Oper. Res. 115, pp. 596–607) and slack-based measure of Tone (K. Tone, 2001. A slack-based measure of efficiency in DEA. Eur. J. Oper. Res. 130, p. 498–509). In this article, we will propose an Euclidean distance-based measure of efficiency. Then, in order to discriminate the performance of efficient DMUs, an alternative super-efficiency DEA model is proposed. The applicability of the models developed is illustrated in the context of the analysis of gas companies performance.     

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.     

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 robust DEA model and super-efficiency measure

Applications of traditional data envelopments analysis (DEA) models require knowledge of crisp input and output data. However, the real-world problems often deal with imprecise or ambiguous data. In this paper, the problem of considering uncertainty in the equality constraints is analyzed and by using the equivalent form of CCR model, a suitable robust DEA model is derived in order to analyze the efficiency of decision-making units (DMUs) under the assumption of uncertainty in both input and output spaces. The new model based on the robust optimization approach is suggested. Using the proposed model, it is possible to evaluate the efficiency of the DMUs in the presence of uncertainty in a fewer steps compared to other models. In addition, using the new proposed robust DEA model and envelopment form of CCR model, two linear robust super-efficiency models for complete ranking of DMUs are proposed. Two different case studies of different contexts are taken as numerical examples in order to compare the proposed model with other approaches. The examples also illustrate various possible applications of new models.     

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.     

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.     

灰变量逆DEA模型的初步研究

初步研究了变量为区间灰数的逆DEA模型。变量为区间灰数时,决策单元效率水平保持不变表达为:对决策单元的输入输出值改变前后对应的灰区间效率进行比较,前者大于等于后者与小于等于后者的可信度相等(均等于0.5)。给出了决策单元非DEA有效时,灰区间变量逆DEA模型解存在的充要条件及一般表达式,以及决策单元弱DEA有效时灰变量逆DEA模型的部分解。     

Measurement of the worst practice of decision-making units in the presence of non-discretionary factors and imprecise data

The objective of the present paper is to propose a novel pair of data envelopment analysis (DEA) models for measurement of relative efficiencies of decision-making units (DMUs) in the presence of non-discretionary factors and imprecise data. Compared to traditional DEA, the proposed interval DEA approach measures the efficiency of each DMU relative to the inefficiency frontier, also called the input frontier, and is called the worst relative efficiency or pessimistic efficiency. On the other hand, in traditional DEA, the efficiency of each DMU is measured relative to the efficiency frontier and is called the best relative efficiency or optimistic efficiency. The pair of proposed interval DEA models takes into account the crisp, ordinal, and interval data, as well as non-discretionary factors, simultaneously for measurement of relative efficiencies of DMUs. Two numeric examples will be provided to illustrate the applicability of the interval DEA models.     

A generalized model for weight restrictions in data envelopment analysis

Data envelopment analysis (DEA) is designed to maximize the efficiency of a given decision-making unit (DMU) relative to all other DMUs by the choice of a set of input and output weights. One strength of the original models is the absence of any need of a priori information about the process of transforming inputs into outputs. However, in the practical application of DEA models, this strength has also become a weakness. Incorporation of process knowledge is more a norm than an exception in practice, and typically involves placing constraints on the input and/or output weights. New DEA formulations have evolved to address this issue. However, existing formulations for weight restrictions may underestimate relative efficiency or even render a problem infeasible. A new model formulation is introduced to address this issue. This formulation represents a significant improvement over existing DEA models by providing a generalized, comprehensive treatment for weight restrictions.