A slacks-based inefficiency measure for a two-stage system with bad outputs

We model the performance of DMUs (decision-making units) using a two-stage network model. In the first stage of production DMUs use inputs to produce an intermediate output that becomes an input to a second stage where final outputs are produced. Previous black box DEA models allowed for non-radial scaling of outputs and inputs and accounted for slacks in the constraints that define the technology. We extend these models and build a performance measure that accounts for a network structure of production. We use our method to estimate the performance of Japanese banks, which use labor, physical capital, and financial equity capital in a first stage to produce an intermediate output of deposits. In the second stage, those deposits become an input in the production of loans and securities investments. The network estimates reveal greater bank inefficiency than do the estimates that treat the bank production process as a black box with all production taking place in a single stage.     

Efficiency in the generation of social welfare in Mexico: A proposal in the presence of bad outputs

One of the main goals of any country is to secure the general welfare of society, entailing positive levels of education, health and income, coupled with low levels of social inequality. The following paper studies the efficient use of economic and social resources to generate social welfare in the presence of bad outputs in the states of Mexico during 2010. A two-level data envelopment analysis model was used to determine how efficient the 32 states of the Mexican Republic were, considering as model variables the socioeconomic indicators of the three dimensions of human development (education, health and income), and the data on poverty or inequity in the country. The analysis of the results reveals that only 5 of the 32 units studied were efficient in generating welfare and in reducing poverty, while the rest need to increase their welfare levels and especially reduce inequity in education and income using the economic and social resources they possess.     

Slacks-based inefficiency approach for general networks with bad outputs: An application to the banking sector

In this paper the efficiency assessment of general networks of processes that produce both desirable and undesirable outputs is addressed. This problem arises in many contexts (e.g. transportation, energy generation, etc.). A general networks slacks-based inefficiency (GNSBI) measure can be computed using a simple linear program that takes into account the weak disposability of the bad outputs. The slacks-based inefficiency (SBI) of each process is also calculated. Target values for all inputs, outputs (both desirable and undesirable) and even intermediate products are also provided. The proposed approach is rather general and can accommodate many different network topologies and returns to scale assumptions. Two applications to the banking sector are presented: one to assess banks efficiencies and another to assess bank branches.     

Evaluating cost efficiency in central administrative services in UK universities

This paper describes an attempt to evaluate cost efficiency in UK university central administration. The funding councils of higher education institutions have progressively evolved elaborate systems for measuring university performance in teaching quality and research. Indeed, funding of universities is linked to their performance in research. The allocation of resources between academic and administrative activities, on the other hand, has so far not been subject to scrutiny. Yet, expenditure on administration is typically some 30% of that allocated to academic activities. This paper sets up a data envelopment analysis (DEA) framework to identify practices leading to cost-efficient central administrative services in UK universities. The problems in defining the unit of assessment and the relationship between the inputs and the outputs are clearly demonstrated.     

评价相对效率的投入-产出型DEA

传统DEA只能在固定投入或产出的条件下,从产出或投入角度测算决策单元相对效率,因而不能综合地反映决策单元的投入产出效果.基于双目标规划,本文将提出从投入及产出角度评价决策单元相对效率的投入-产出型DEA,并研究其相对有效性.最后以沪市16家高科技上市公司为应用实例,研究其相对经营效率.     

DEA控制投影模型及其应用

考虑到输入输出要素的有限取值范围,本文提出了DEA控制投影模型,并给出了在特定情形下非CRS有效单元有现实意义的投影。在工程应用中,本文采用所提出的模型,对182家创新型企业的技术创新能力与竞争力的调查数据进行了分析。研究结果表明,利用该控制投影模型得到的有效性分类不仅与传统CRS模型的有效性分类完全一致,而且其按行业分竞争力投影结果为企业审计竞争力提供了科学的高标,具有较强的工程应用价值。     

基于标杆管理的DEA算法对公共部门的绩效评价

传统的部门绩效考评中考核权重具有相当的主观性,对于部门考核特别是对于公共管理部门等非赢利部门的绩效考核是不很合理的。基于此,本文提出数据包络分析(DEA)的一种改进算法,此算法既避免了权重的非正常影响,又克服了DEA算法本身的"相对有效性"的缺陷。运用此方法对公共部门进行绩效考核,理论上比较完善,考核结果与实际结果也很吻合。同时此方法还能对非DEA有效的部门,给出改进方向和方法。     

多层次结构DEA模型及其应用

在评价实践中,评价者通常倾向采用一组指标或指标体系对DMUs展开相对全面的评价,不同层次指标的重要性也往往不同。然而,标准DEA模型在DMUs有限条件下经常会面临无法直接处理过多的评价指标,也无法直接处理多层次指标的问题。本文从DEA模型中的序结构和测度出发,构建了符合多层次指标体系特点,能相对全面地体现评价者价值导向,且具有合理区分能力的多层次结构DEA模型,并以15个机构基础研究的投入-产出评价为例展开了应用分析。     

Evolving the latent variable model as an environmental DEA technology

This article tests several nonparametric DEA models for their ability to accurately decompose CO₂ emissions change using a Malmquist styled decomposition framework. This production oriented activity analysis involves panel data and two data sets from the literature for comparison. A new Latent Variable radial input-oriented technology is introduced that is closely associated with a Koopmans Efficient Slacks Based Model. The Latent Variable technology simultaneously reduces inputs and undesirable outputs in a single Multiple Objective Linear Program. This production theoretic methodology is adapted to preserve both scale efficiency and causality within the envelopment framework. Finally, the application studies demonstrate the internal consistency of the Latent Variable reduction coefficients, which overturns previous results and paves the way for further research into undesirable externalities.     

Multi-valued measures in DEA in the presence of undesirable outputs

Data envelopment analysis (DEA) evaluates the relative efficiency of a set of comparable decision making units (DMUs) with multiple performance measures (inputs and outputs). Classical DEA models rely on the assumption that each DMU can improve its performance by increasing its current output level and decreasing its current input levels. However, undesirable outputs (like wastes and pollutants) may often be produced together with desirable outputs in final products which have to be minimized. On the other hands, in some real-world situations, we may encounter some specific performance measures with more than one value which are measured by various standards. In this study, we referee such measures as multi-valued measures which only one of their values should be selected. For instance, unemployment rate is a multi-valued measure in economic applications since there are several definitions or standards to measure it. As a result, selecting a suitable value for a multi-valued measure is a challenging issue and is crucial for successful application of DEA. The aim of this study is to accommodate multi-valued measures in the presence of undesirable outputs. In doing so, we formulate two individual and summative selecting directional distance models and develop a pair of multiplier- and envelopment-based selecting approaches. Finally, we elaborate applicability of the proposed method using a real data on 183 NUTS 2 regions in 23 selected EU-28 countries.     

环保项目有效性评价的数据包络分析方法

利用数据包络分析(DEA)方法评价环保项目有效性时,输入、输出数据中可能同时存在环境因素,不符合传统的DEA模型要求,需要对这些数据进行转换。本文讨论了"不好的"数据平移转换法、输入和输出因素转换法、倒数转换法,建立了三种DEA模型,对建立的DEA模型一致性进行了分析,拓宽了以前DEA模型的应用范围。一个例子验证了这三种方法在评价环保项目有效性时是一致的。     

Two-level DEA approaches in research evaluation

It is well known that the discrimination power of data envelopment analysis (DEA) models will be much weakened if too many input or output indicators are used. It is a dilemma if decision makers wish to select comprehensive indicators, which often have some hierarchical structures, to present a relatively holistic evaluation using DEA. In this paper we show that it is possible to develop DEA models that utilize hierarchical structures of input–output data so that they are able to handle quite large numbers of inputs and outputs. We present two approaches in a pilot evaluation of 15 institutes for basic research in the Chinese Academy of Sciences using the DEA models.     

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.     

DEA with streaming data

DEA can be interpreted as a tool for the identification of “frontier outliers” among data points. These are points that are potentially interesting because they exhibit extreme properties in that the values of their attributes, either alone or combined, are at the upper or lower limits of the data set to which they belong. A real challenge for this type of frontier analysis arises when data stream in at high rates and the DEA analysis needs to be performed quickly. This paper extends DEA into this dynamic data environment. The purpose is to propose a formal theoretical framework to handle streaming data and to answer the question of how fast data can be processed using this new framework. Potential applications involving large data sets include auditing, appraisals, fraud detection, and security. In such settings the situation is likely to be dynamic with the data domain constantly changing as new entities arrive in the course of time. New specialized tools to adapt DEA to deal with streaming data will be explored.     

一个新的考虑非期望产出的非径向-双目标DEA模型

如何实现对环境效率更准确的定量评价,是国际上从事DEA研究的学者们当前关注的问题之一。在传统DEA效率模型的基础上,综合考虑评价过程中期望产出与非期望产出之间的差异以及实际生产过程中人们追求期望产出最大化和非期望产出最小化的双重目标,构建非期望产出的非径向-双目标DEA环境效率评价模型,通过线性加权和法转化为一个求最大值的单目标线性规划问题。研究结果表明,这种新模型不仅可以分析DEA有效性与Pa-reto最优之间的关系,还利用决策单元的投影获得投入和产出的可调整量,从而提高考虑非期望产出的环境效率评价的精度。实证分析结果与现实情况的高度吻合,说明这种新的非径向-双目标DEA环境效率模型是有效的。     

Set-valued DEA production games

In this paper, a generalization of the linear production model is considered on the basis of a DEA-inspired technology in which the maximization of the production levels is formulated as a multi-objective linear programming problem. When multiple decision-makers cooperate by pooling their resources and sharing their technologies in the production process, the final production must then be divided between the agents involved, and a multi-commodity game arises. Such a game is referred to as a set-valued DEA production game. It is shown that, by adopting two different excess functions to measure the dissatisfaction of the coalitions, two different core concepts emerge, namely the preference core and the dominance core. Moreover, we provide the procedure to determine allocations in the respective least cores and show how to compute the nucleolus in the case of the excess function leading to the preference core. Finally, the results are illustrated with a case study.     

DEA for non-homogenous parallel networks

In practice, systems are often composed of a group of sub-units. Each sub-unit has a set of performance metrics that are classified as inputs and outputs in data envelopment analysis (DEA). Conventional DEA views such a system as a “black-box”, other DEA-based models are developed to investigate the inner structure, either with a serial structure where components are connected by intermediate products, or with a parallel system under the key assumption that all sub-units are associated with the same type of inputs and outputs (in differing amounts) without the links. In many applications, however, this property of identical input/output factors may not hold. For example, factories may have various manufacturing lines whose inputs and outputs differ from one another. The current paper proposes a series of DEA models to accommodate settings where non-homogenous sub-units operate in parallel network structures with intermediate measures or links. Both the overall performance of the entire parallel network system and efficiency decomposition for each sub-unit can be evaluated through our method.     

基于决策者满意度的区间DEA的求解

定义了一种反映决策者满意度的区间数序关系,基于此将区间DEA中的区间不等式约束转化为确定型约束。研究了区间DEA模型向确定型DEA模型转化过程中的数据一致性问题。在保持数据一致性的前提下,根据决策者给出的满意度水平,将区间DEA转化为确定型DEA并进行求解。最后给出算例,并总结和分析了决策单元的DEA效率值随满意度水平变化的规律。     

基于分段参数型DEA前沿面的投入—产出型技术效率

由传统DEA模型可以直接测算投入固定(产出固定)的条件下,面向产出(投入)的技术效率。尽管加型DEA模型同时考虑了投入和产出的松弛,但却不能像传统模型一样直接测算投入—产出型技术效率。为了直接由加性模型测算投入产出型技术效率,本文将利用DEA有效决策单元建立分段参数型DEA生产前沿面,并根据古典技术效率的定义,解决投入产出型技术效率的测算问题。研究发现,这种效率实质上是产出型技术效率与投入配置效率的乘积。由于同时考虑了投入和产出的技术无效性,与其它类型的技术效率相比,这种投入产出型技术效率的可分性更强。     

Estimation of portfolio efficiency via DEA

Traditional DEA models and nonlinear (diversification) DEA models are often used in performance evaluation of portfolios. However, the diversification models are usually very complicated to compute except the very basic models. And the classic DEA models still need to be further justified and tested, since it is not clear whether they are over-linearised according to the diversification models. The existing studies on performance evaluation via the classic DEA models generally focus on the selection of inputs and outputs. In this work, we investigate theoretical foundation of DEA models for portfolios from a perspective of sampling portfolio. We show the classic DEA provides an effective and practical way to approximate the portfolio efficiency (PE). We further verify this approach through different portfolio models with various frictions and bounds on the market. Through the comprehensive simulations carried out in this study, we show that with adequate data sets, the classic DEA models can effectively sample portfolios to take into account sufficient diversification, and thus can be used as an effective tool in computing the PE for their performance assessments. This study can be viewed as a justification of the classic DEA performance assessments and the way to introduce other efficiency notions (like allocation efficiency, scale efficiency, etc) into assessment of portfolios.