基于证据推理和前景理论的交叉效率排序方法研究

针对由交叉效率评价策略和交叉效率集结方法的多样性而造成评价结果不一致的问题,提出利用证据推理方法和前景理论,综合各个交叉效率评价策略的评价结果,实现对决策单元的统一评价。首先,分别将选用的交叉效率评价策略以及各个评价策略中的他评效率设置成一级指标和二级指标,依据算数平均和前景理论分别确定一、二级指标的权重;其次,依据他评效率确定二级指标置信度,利用证据推理方法将各个交叉效率评价策略的他评效率综合转换成决策单元被评价为有效的置信度。决策者可通过比较决策单元被识别为有效的置信度的大小来判断决策单元交叉效率的大小,进而实现对决策单元的排序;最后,通过案例验证和说明本文提出方法的有效性和实用性。     

基于多种DEA模型和Gini准则的效率评价方法——兼对我国高校运营绩效的评价

针对多种数据包络分析（Data Envelopment Analysis,简称DEA）模型会产生不同绩效评价结果的问题,提出基于Gini准则科学地融合各DEA模型结果的方法。首先基于Gini准则定义信息纯度以衡量各DEA模型结果的确定性并赋予权重,然后通过加权融合最终得出客观唯一的综合效率。此外,根据评价者的偏好信息或先验知识,进一步提出交互式多DEA模型-Gini准则方法。以前学者仅从单一角度出发选择DEA模型评价高校的运营绩效,考虑到从不同角度出发的多种DEA模型可以给出高校更加全面客观的运营绩效评价,利用以上方法对2011年国内25所理工类高校的运营绩效进行了实证分析,结果验证了以上方法可以合理有效的衡量各高校的运营绩效表现,对于高校运营绩效的评价研究具有实际指导意义。     

基于最近距离投影的DEA两阶段效率评价方法研究

数据包络分析是进行效率评价最重要的方法之一。传统的数据包络分析理论主要寻找有效前沿面上的最远距离投影，在极大化无效性指数的同时也面临着效率改进的巨大难度和高额成本。对于具有两阶段内部生产结构的决策单元，本文从考虑最小改进难度的视角出发，提出了最近距离投影的两阶段效率评价方法。该方法首先得到所有强有效决策单元的线性组合，且这些组合均占优于被评价的两阶段决策单元。然后建立了两阶段范围调整效率评价模型，在确定具有最近投影距离的占优组合的同时，得到了两阶段评价效率。最后，本文运用我国32家上市银行的年度数据对所提出方法进行了应用验证。     

Hierarchical network systems: An application to high-technology industry in China

In real world situations, there is a hierarchical structure exists in a specific organization and each component has its network process. However, such hierarchical network system has not been well studied in previous literature, and misleading results often are produced. The current paper discusses a data envelopment analysis (DEA) modelling technique for a network structure where a hierarchical system consists of components having two-stage series processes. An additive network DEA is proposed to evaluate the performance of this type of network structure. The overall and divisional efficiencies of the system and each component can be derived, and the relationship between system efficiency, divisional efficiency and the ones of components is discussed. The newly developed additive network DEA is nonlinear and cannot be converted into a linear program. A semidefinite programming (SDP) approach is developed for effectively solving this model and the global solution can be guaranteed. Another linear multiplicative network DEA also developed for this hierarchical system. The two newly developed models are illustrated with a case of the performance evaluation of high-technology industry in China.     

Directional distance based diversification super-efficiency DEA models for mutual funds

Current data envelopment analysis (DEA) models with diversification cannot discriminate the performance of efficient mutual funds. Based on the directional distance function and diversification DEA models, this paper proposes two diversification super-efficiency models for discriminating the performance of efficient mutual funds on financial market. The proposed diversification super-efficiency models as well as the corresponding diversification DEA models are feasible and can deal with negative values in risk measures, transaction costs and return measures. The proposed methods generate bounded super-efficiency scores for all the funds. Under the assumption of discrete return distributions, all the models in the proposed diversification super-efficiency methods can be transformed into linear programming (LP) problems by choosing proper risk and return measures. To demonstrate the validity and practicality of the proposed diversification super-efficiency methods, we apply them to evaluate the performance of mutual funds in the American market. The empirical results show that the proposed diversification super-efficiency models can distinguish efficient funds well and the linear combination of efficient funds might be inefficient. Moreover, the backtesting results show that the proposed diversification super-efficiency models generally have a good practice value for the actual portfolio selection.     

Efficiency measurement for hierarchical network systems

The conventional data envelopment analysis (DEA) models for measuring the relative efficiency of a set of decision making units (DMUs), without considering the operations of the component processes, often produce misleading results, and network models have thus been recommended. This paper discusses the development of a network DEA model for systems with a hierarchical structure. It is shown that the hierarchical structure is equivalent to a parallel structure, with the components being the units at the bottom of the hierarchy. Due to the characteristics of a parallel system, the efficiency of a hierarchical system is thus a weighted average of those of the units at the bottom of the hierarchy. A hypothetic example shows that the proposed model is able to distinguish the order of the efficient DMUs evaluated by the conventional DEA model. Moreover, it provides the efficiencies of the functions of the DMU, which enables managers to identify areas of weakness, and thus better focus efforts to improve overall performance.     

存在保证域的模糊超效率DEA模型

模糊DEA模型是用于解决存在模糊数据的决策单元(DMUs)效率评价问题的,然而现有的模糊DEA模型分辨率低,本文构建了存在保证域的模糊超效率DEA模型,并给出了一种基于截集的求解方法并进行了证明,该模型有效地解决了输入和输出全部或部分为模糊数的决策单元全排序问题。最后给出了一个银行效率评价的实例说明了方法的有效性。     

Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: Specific application to determining optimal resource levels in surgical services

Simulation is a powerful tool for modeling complex systems with intricate relationships between various entities and resources. Simulation optimization refers to methods that search the design space (i.e., the set of all feasible system configurations) to find a system configuration (also called a design point) that gives the best performance. Since simulation is often time consuming, sampling as few design points from the design space as possible is desired. However, in the case of multiple objectives, traditional simulation optimization methods are ineffective to uncover the efficient frontier. We propose a framework for multi-objective simulation optimization that combines the power of genetic algorithm (GA), which can effectively search very large design spaces, with data envelopment analysis (DEA) used to evaluate the simulation results and guide the search process. In our framework, we use a design point's relative efficiency score from DEA as its fitness value in the selection operation of GA. We apply our algorithm to determine optimal resource levels in surgical services. Our numerical experiments show that our algorithm effectively furthers the frontier and identifies efficient design points.     

Incorporating cost and environmental factors in quality function deployment using data envelopment analysis

Quality function deployment (QFD) is an important tool available to organizations for efficient product design and development. Traditionally, QFD rates the design requirements (DRs) with respect to customer needs, and aggregates the ratings to get relative importance scores of DRs. An increasing number of studies stress on the need to incorporate additional factors, such as cost and environmental impact, while calculating the relative importance of DRs. However, there is a paucity of methodologies for deriving the relative importance of DRs when several additional factors are considered. In this paper, data envelopment analysis (DEA) is suggested for the purpose. It is proved that the relative importance values computed by DEA coincide with traditional QFD calculations when only the ratings of DRs with respect to customer needs are considered, and when only one additional factor, namely cost, is considered. DEA provides a general framework facilitating QFD computations when more factors need to be considered. The calculations are explained using a step-by-step procedure and illustrations. The proposed QFD–DEA methodology is applied to the design of security fasteners for a Chinese company. Though traditional QFD calculations consider the ratings as cardinal numbers, DEA has the flexibility to treat the ratings as qualitative variables. This aspect is illustrated in a separate section.     

DEA and ranking with the network-based approach: a case of R&D performance

This study enhances the network-based approach, which is a novel method to increase discrimination in data envelopment analysis. The enhancements include removing the bias caused by a scale difference among organizations and highlighting the approach's ability to identify the strengths and weaknesses of each organization. The former makes the approach applicable to both the constant returns of scale (CRS) and the variable returns of scale (VRS) models. The network-based approach applies the centrality concept developed in social network analysis to discriminate efficient decision making organizations as determined by standard data envelopment analysis (DEA). More specifically, the results of data envelopment analysis are transformed into a directed and weighted network in which each node represents a decision making organization and the link between a pair of node represents the referencing relationship between the pair. The centrality value for each efficient organization provides the base for discrimination and ranking. This network-based approach suggests aggregating DEA results of different input/output combinations such that the merits of each organization under various situations can be considered. The final ranking of this approach favors organizations that have their strengths evenly spread and tends to screen out specialized efficient organizations. As a real world example, the approach is applied to evaluate and rank the R&D (research and development) performance of Taiwan's government-supported research institutes. The cross-organizations and within-organization strengths for each efficient research institute are identified after applying the approach. A two-stage R&D evaluation model separates the R&D process into the technology development and technology diffusion stage. The resulting performance map differentiates the research institutes into four categories—Achievers, Marketers, Innovators, and Underdogs.     

Ranking efficient units in DEA

Super-efficiency data envelopment analysis (DEA) model can be used in ranking the performance of efficient decision making units (DMUs). Because of the infeasibility problem associated with the super-efficiency DEA model, ranking has been restricted to the model where constant returns to scale and proportional changes in all inputs or all outputs are assumed. In fact, when super-efficiency is used as an efficiency stability measure, infeasibility means the highest super-efficiency. However, if super-efficiency is interpreted as input saving or output surplus achieved by a specific efficient DMU, infeasibility does not necessarily mean the highest super-efficiency. In order to obtain a complete ranking of efficient DMUs when the two assumptions are relaxed, a modified super-efficiency DEA model is proposed to overcome the infeasibility problem and to correctly capture the super-efficiency represented by the input saving or the output surplus. The current paper suggests using both input- and output-oriented super-efficiency models to characterize the super-efficiency when infeasibility occurs. As a result, we can rank the efficient DMUs if infeasibility occurs. The approach is applied to 20 largest Japanese companies and 15 US cities, respectively.     

A modified DEA cross efficiency method with negative data and its application in supplier selection

Basic Data Envelopment Analysis (DEA) models are designed for non-negative data. However, negative data is inevitably used in many real-world issues. Also, multiple units with a maximum relative performance score (equal to one) can be obtained due to the benevolent view of evaluating Decision Making Units (DMUs) consistent performance. Therefore, the researchers proposed ranking models to differentiate efficient units. Cross efficiency is one of the most useful tools for DMUs ranking in the DEA. There are two major drawbacks to implementing this process. First, it gives different results in the presence of other optimal solutions; second, it does not provide a compelling reason to use the arithmetic mean to aggregate the results of the cross efficiency matrix. In this paper, first a new non-radial model is proposed to evaluate the performance of DMUs in the presence of negative data and then based on this model a new secondary goal model is proposed to eliminate the first drawback in the cross efficiency method. Also, to solve the second drawback in this method, a hybrid Multi-Attribute Decision Making (MADM)-DEA process with the help of fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje method is proposed. Finally, to show the applicability of the proposed methods, the results are used to select the supplier in a real-world problem.

     

A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.     

Two-stage DEA models with undesirable input-intermediate-outputs

Data envelopment analysis (DEA) is a non-parametric approach for measuring the relative efficiencies of peer decision making units (DMUs). Many studies have examined DEA efficiencies of two-stage systems, where all the outputs from the first stage are the only inputs to the second stage. Although single-stage DEA models with undesirable input-outputs have been extensively studied, there still lacks of more systematical investigation on two-stage DEA with undesirable variables. For instance, depending on its operating model, even whether an intermediate variable is desirable or undesirable can be questionable for a particular two-stage system. Furthermore, most of the existing studies on two-stage systems focus on the case where only the final outputs are undesirable. In this work, we try to systematically examine two-stage DEA models with undesirable input-intermediate-outputs. Particularly, we utilize the free-disposal axioms to construct the production possibility sets (PPS) and the corresponding DEA models with undesirable variables. The proposed models are then used to illustrate some theoretical perspectives by using the data of China׳s listed banks.     

Cross-benchmarking for performance evaluation: Looking across best practices of different peer groups using DEA

In benchmarking, organizations look outward to examine others’ performance in their industry or sector. Often, they can learn from the best practices of some of them and improve. In order to develop this idea within the framework of Data Envelopment Analysis (DEA), this paper extends the common benchmarking framework proposed in Ruiz and Sirvent (2016) to an approach based on the benchmarking of decision making units (DMUs) against several reference sets. We refer to this approach as cross-benchmarking. First, we design a procedure aimed at making a selection of reference sets (as defined in DEA), which establish the common framework for the benchmarking. Next, benchmarking models are formulated which allow us to set the closest targets relative to the reference sets selected. The availability of a wider spectrum of targets may offer managers the possibility of choosing among alternative ways for improvements, taking into account what can be learned from the best practices of different peer groups. Thus, cross-benchmarking is a flexible tool that can support a process of future planning while considering different managerial implications.     

资源约束型两阶段生产系统的DEA效率评价模型

经典的数据包络分析(DEA)模型将决策单元看作"黑箱",忽视决策单元的内部过程,必然会高估决策单元的效率。本文研究了一种资源约束型两阶段生产系统的DEA效率评价方法,针对此类生产过程的内部过程,研究其内部运行机制对整体效率的影响。本文提出的模型实质上是一类特殊的网络DEA模型,其评价原理有别于已有的研究成果,但更有助于管理者确定生产过程的非有效来源及其效率改进方向。实例证实本文方法的合理性。     

THE ANALYSIS OF OUTLYING DATA POINTS USING ROBUST REGRESSION: A MULTIVARIATE PROBLEM-BANK IDENTIFICATION MODEL*

Because the eight largest bank failures in United States history have occurred since 1973 [24], the development of early-warning problem-bank identification models is an important undertaking. It has been shown previously [3] [5] that M-estimator robust regression provides such a model. The present paper develops a similar model for the multivariate case using both a robustified Mahalanobis distance analysis [21] and principal components analysis [10]. In addition to providing a successful presumptive problem-bank identification model, combining the use of the M-estimator robust regression procedure and the robust Mahalanobis distance procedure with principal components analysis is also demonstrated to be a general method of outlier detection. The results from using these procedures are compared to some previously suggested procedures, and general conclusions are drawn.     

两种改进的超效DEA模型

对DEA有效决策单元不能排序是传统DEA模型的一大缺点。该问题也成为DEA领域研究的热点。AP模型是最常用的区分DEA有效决策单元效率值大小的超效模型,但在实际应用中却出现了无解或解不稳定的情况。国外学者新近提出的MAJ模型、LJK模型则有效解决了这两个问题,但却存在模型区分能力不强的缺点。本文分析了这两种模型缺点产生的原因、予以改进并给出理论证明。标准数据集的实验显示改进效果显著,尤其是改进后的LJK模型表现优异。     

Efficiency decomposition in network data envelopment analysis with slacks-based measures

Conventional data envelopment analysis (DEA) treats the production system as a black box when measuring efficiency, ignoring its internal structure. By taking the operations of the component processes of the system into consideration, several network DEA models have been developed. Of these, the slacks-based measure (SBM) approach has attracted much attention for its ability to provide suitable efficiency measures, especially for weakly efficient production units. This paper proposes a general SBM model for network systems, and is able to decompose the system efficiency into a weighted average of the process efficiencies. This relationship holds for all types of network structure. An example shows that the network model has stronger discriminating power than the conventional black-box model, and the system efficiency is indeed a weighted average of the process efficiencies. The decomposition of the system efficiency helps identify key factors to improve the performance of a production unit.