非期望产出的DEA效率评价

将非期望产出作为投入应用到传统DEA模型上,解决了非期望产出生产活动的效率评价问题.结合生产可能集,将非期望产出直接反映到生产可能集中,建立了基于投入导向的径向和非径向两种DEA模型.并对两种DEA模型效率值的大小关系、相对有效性的等价性问题进行了证明,指出非径向DEA模型更能准确的实现效率定量评价.     

基于CAR-DEA方法的环境效率评价研究

现有环境效率评价的DEA方法没有考虑多维偏好约束问题,即不同决策单元对不同期望产出和不期望产出的偏好不同. 以地区为例,不同地区对GDP、废水和废气赋予的权重偏好各不相同. 在这种情况下,由于各决策单元的偏好约束不同,形成多维偏好约束集,在传统DEA模型中容易出现无可行解现象. 针对这一问题,基于CAR-DEA方法,结合保证域理论,提出一种解决多维偏好约束集问题的环境效率评价模型. 采用中国工业系统的环境效率评价实例对提出的方法进行了分析和说明.     

不同环保意识视角下的DEA效率模型

DEA在效率分析领域具有良好的应用,随着全球气候的不断恶劣和环境的逐渐破坏,公众环保意识不断增强,在进行相关效率研究时,非期望产出越来越受到重视。以非期望产出为主要研究点,根据社会对非期望产出指标的认识规律将环保意识分为五个不同阶段,并综合考虑每个意识阶段的特征,将环境指标变动能力,环境承载能力、环境负外部性参与度、外部环境政策管理及企业生产要求纳入DEA效率分析过程中,通过对目标函数和约束条件进行不同的改进和约束,构建了不同意识阶段的DEA效率分析模型,并探讨了各阶段模型的使用范围和相互关系。最后,选取一个实例进行试算,证明各DEA模型的可行性和有效性。     

Estimating the technical efficiency of health care systems: A cross-country comparison using the directional distance function

Economic activity produces not only desirable outputs but also undesirable outputs. Undesirable outputs are usually omitted from efficiency assessments (i.e., applications of Data Envelopment Analysis) which fail to express the true production process. The directional distance function model has been used for handling asymmetrically both desirable and undesirable outputs in the assessment process. In the present paper, we apply a generalized directional distance function to measure the efficiency of the health systems of 171 countries. We incorporate both desirable and undesirable outputs into the efficiency assessment without transforming the latter type of outputs into inputs or into their inverse form, as is done in most of the extant studies that deal with the measurement of health efficiency. The methodology that we apply introduces a modified definition of the efficiency score which yields results consistent with those obtained from radial DEA models. In addition, our results are independent of the length of the direction vector.     

Efficiency analysis in multi-period systems: an application to performance evaluation in Czech higher education

Data envelopment analysis (DEA) is a non-parametric method for efficiency and performance analysis of decision making units. The paper deals with production systems where decision making units are described by their inputs and outputs in several consecutive periods. The paper presents (Park and Park in Eur J Oper Res 193(2):567–580, 2009) multi-period DEA model that is oriented on the “best” period of the unit under evaluation only. This aim of this paper is to overcome the disadvantage of this model and formulate new models of this class that allow evaluation the efficiency of decision making units within the whole production chain. The presented efficiency and super-efficiency multi-period DEA models are illustrated on a case study. The study consists in analysis of research and teaching performance of 19 Czech economic faculties in four years period from 2009 until 2012. The model considers two inputs (number of academic employees and labour costs) and two outputs for teaching efficiency (number of students and number of graduated). Research efficiency is expressed using the number of publications in various important categories and the number of so called RIV points that describe the quality of publications.     

DEA models with undesirable inputs and outputs

Data Envelopment Analysis (DEA) models with undesirable inputs and outputs have been frequently discussed in DEA literature, e.g., via data transformation. These studies were scatted in the literature, and often confined to some particular applications. In this paper we present a systematic investigation on model building of DEA without transferring undesirable data. We first describe the disposability assumptions and a number of different performance measures in the presence of undesirable inputs and outputs, and then discuss different combinations of the disposability assumptions and the metrics. This approach leads to a unified presentation of several classes of DEA models with undesirable inputs and/or outputs.     

Data envelopment analysis for environmental assessment: Comparison between public and private ownership in petroleum industry

Environmental assessment recently becomes a major policy issue in the world. This study discusses how to apply Data Envelopment Analysis (DEA) for environmental assessment. An important feature of the DEA environmental assessment is that it needs to classify outputs into desirable (good) and undesirable (bad) outputs because private and public entities often produce not only desirable outputs but also undesirable outputs as a result of their production activities. This study proposes the three types of unification for DEA environmental assessment by using non-radial DEA models. The first unification considers both an increase and a decrease in the input vector along with a decrease in the direction vector of undesirable outputs. This type of unification measures “unified efficiency”. The second unification considers a decrease in an input vector along with a decrease in the vector of undesirable outputs. This type of unification is referred to as “natural disposability” and measures “unified efficiency under natural disposability”. The third unification considers an increase in an input vector but a decrease in the vector of undesirable outputs. This type of unification is referred to as “managerial disposability” and measures “unified efficiency under managerial disposability”. All the unifications increase the vector of desirable outputs. To document their practical implications, this study has applied the proposed approach to compare the performance of national oil firms with that of international oil firms. This study identifies two important findings on the petroleum industry. One of the two findings is that national oil companies under public ownership outperform international oil companies under private ownership in terms of unified (operational and environmental) efficiency and unified efficiency under natural disposability. However, the performance of international oil companies exhibits an increasing trend in unified efficiency. The other finding is that national oil companies need to satisfy the environmental standard of its own country while international oil companies need to satisfy the international standard that is more restricted than the national standards. As a consequence, international oil companies outperform national oil companies in terms of unified efficiency under managerial disposability.     

Preference, Production and Performance in Data Envelopment Analysis

This paper attempts to provide a systematic approach to the DEA model building. To this end, we try to identify some essential aspects of DEA modelling. Three key building blocks in a DEA model are identified: they are preference order, production possibility set and performance measure. It is shown that the preferences and performance measurements used in the standard DEA models are only particular examples in this framework. It is also illustrated in this work that this methodology is useful in building new DEA models to handle nonstandard applications such as those involve non-Pareto preferences or undesirable inputs-outputs.     

Past-present-future Intertemporal DEA models

It has been well recognized that to thoroughly evaluate a firm’s performance, the evaluator must assess not only its past and present records but also future potential. However, to the best of our knowledge, there are no data envelopment analysis (DEA)-type models proposed in the literature that simultaneously take past, present and, especially, future performance indicators into account. Hence, this research aims at developing a new type of DEA model referred to as Intertemporal DEA models that can be used to fully measure a firm’s efficiency by explicitly considering its key inputs and outputs involving the past-present-future time span. In this research, the proposed Intertemporal DEA models are applied to the performance evaluation of high-tech Integrated Circuit design companies in Taiwan to demonstrate their advantages over other DEA models that ignore intertemporal efficiency.     

Undesirable outputs in efficiency valuations

Efficiency measurement is usually based on the assumption that inputs have to be minimized and outputs have to be maximized. In a growing number of applications, however, undesirable outputs are incorporated into the production model which have to be minimized. In this paper various approaches for treating such outputs in the framework of Data Envelopment Analysis (DEA) are discussed and the resulting efficient frontiers are compared. New radial measures are introduced which assume that any change of the output level will involve both undesirable and desirable outputs.     

Relationship between DEA models without explicit inputs and DEA-R models

Data envelopment analysis (DEA) is one of often used modeling tools for efficiency and performance evaluation of decision making units. Ratio DEA (DEA-R) is a group of novel mathematical models that combines standard DEA methodology and ratio analysis. The efficiency score given by standard DEA CCR model is less than or equal to that given by DEA-R model. In case of single input or single output the efficiency scores in CCR and DEA-R models are identical. The paper deals with DEA-R models without explicit inputs, i.e. models where only pure outputs or index data are taken into account. A basic DEA-R model without explicit inputs is formulated and a relation between output-oriented DEA models without explicit inputs and output-oriented DEA-R models is analyzed. Central resource allocation and slack-based measure models within DEA-R framework are examined. Finally they are used for projections of decision making units on the efficient frontier. The results of the proposed models are applied for efficiency evaluation of 15 units (Chinese research institutes) and they are discussed.     

Regulatory impact of environmental standards on the eco-efficiency of firms

In this paper, we propose an approach to implement environmental standards into Data Envelopment Analysis (DEA) and in this way to measure their regulatory impact on eco-efficiency of firms. One standard feature of basic DEA models lies in the exogeneity of inputs, desirable and undesirable outputs. Taking into account the environmental constraints, we therefore apply the bounded variable DEA model. The regulatory impact is assessed as difference in eco-efficiency scores before and after fictive introduction of an environmental standard. Furthermore, we distinguish between weak and strong disposability of undesirable outputs and develop corresponding models. Assessing the regulatory impact of environmental standards in advance provides support for environmental policymakers in choosing appropriate instruments and in adjusting the intensity of regulation.     

An extended slacks-based measure model for data envelopment analysis with negative data

Data envelopment analysis (DEA) is a non-parametric approach based on linear programming that has been widely applied for evaluating the relative efficiency of a set of homogeneous decision-making units (DMUs) with multiple inputs and outputs. The original DEA models use positive input and output variables that are measured on a ratio scale, but these models do not apply to the variables in which negative data can appear. However, with the widespread use of interval scale data and undesirable data, the emphasis has been directed towards the simultaneous consideration of the positive and negative data in DEA models. In this paper, using the slacks-based measure, we propose an extended model to evaluate the efficiency of DMUs, even if some variables are measured on an interval scale and some on a ratio scale. Moreover, the extended model allows for the presence of all interval-scale variables, which are capable of taking both negative and positive values.     

Modeling undesirable factors in data envelopment analysis

Data envelopment analysis is a mathematical programming technique for identifying efficient frontiers for peer decision making units with multiple inputs and multiple outputs. These performance factors (inputs and outputs) are classified into two groups: desirable and undesirable. Obviously, undesirable factors in production process should be reduced to improve the performance. In the current paper, we present a data envelopment analysis (DEA) model in which can be used to improve the relative performance via increasing undesirable inputs and decreasing undesirable outputs.     

Negative features of hyperbolic and directional distance models for technologies with undesirable outputs

In data envelopment analysis for environmental performance measurement the undesirable outputs are taken into account. Ones of the standard approaches for dealing with the undesirable outputs are the hyperbolic and the directional distance measures. They both allow a simultaneous expansion of desirable outputs and a contraction of undesirable outputs by means of a single parameter. To meet environmental requirements, a technology with no disposability of undesirable outputs is often considered and the outputs are assumed to be only weakly disposable. We show that the combination of this type of technology with the hyperbolic measure, (or with its linearization, which is a special type of the directional distance model) may lead to a misleading efficiency score of the unit under evaluation. We derive the dual of the hyperbolic model under the environmental technology and describe some of its properties. Then, we use the hyperbolic and directional distance dual models for developing a second-phase method. This enables to detect the misleading scores of the decision making units. We illustrate the results on a real world data set.     

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.     

DEA environmental assessment: Measurement of damages to scale with unified efficiency under managerial disposability or environmental efficiency

This study proposes a use of Data Envelopment Analysis (DEA) for environmental assessment. Firms usually produce not only desirable but also undesirable outputs as a result of their economic activities. The concept of disposability on undesirable outputs is separated into natural and managerial disposability. Natural disposability is an environmental strategy in which firms decrease their inputs to reduce a vector of undesirable outputs. Given the reduced input vector, they attempt to increase desirable outputs as much as possible. Managerial disposability involves the opposite strategy of increasing an input vector. The concept of disposability expresses an environmental strategy that considers a regulation change on undesirable outputs as a new business opportunity. Firms attempt to improve their unified (operational and environmental) performance by utilizing new technology and/or new management. Considering the two disposability concepts, this study discusses how to measure unified efficiency under managerial disposability and then discusses how to measure environmental efficiency. The proposed uses of DEA can serve as an empirical basis for measuring new economic concepts such as “Scale Damages (SD)”, corresponding to scale economies for undesirable outputs, and “Damages to Scale (DTS)”, corresponding to returns to scale for undesirable outputs.     

Applying inverse DEA and cone constraint to sensitivity analysis of DMUs with undesirable inputs and outputs

In this paper, the inverse data envelopment analysis (DEA) with the preference of cone constraints will be discussed in a way that in the decision-making units, the undesirable inputs and outputs exist simultaneously. Supposing that the efficiency level does not change, if the unit under assessment increases the level of the desirable outputs and decreases the level of the undesirable outputs, how will it affect the amount of the desirable input level and the undesirable input level? To answer this question, the application of the inverse DEA with preference of cone constraints is suggested. The suggested approach, while maintaining the efficiency level, increases the level of its undesirable input and decreases the level of its desirable input by selection of strongly efficient solutions or some weakly efficient solutions of the multiple objective linear programming (MOLP) model. While maintaining the efficiency level, the suggested approach by selection of strongly efficient solution or some of the weakly efficient solutions of the MOLP model can increase the undesirable input level and decrease the desirable input level. Similarly, the suggested approach can be applied if the decision-making unit increases its undesirable input level and decreases the desirable input level so that the undesirable output level decreases and the desirable output level increases while maintaining the efficiency level. As an illustration, two numerical examples are rendered.     

考虑服务水平的商业银行综合效率评价研究

商业银行是我国银行体系的主体,提高银行的经营效率和服务水平是当前金融改革的重点。已有的研究较多关注于银行的收益,对银行的非期望产出如呆坏账及服务水平等关注较少。本文运用多个处理非期望产出的DEA模型,对2008年中国商业银行的效率进行了评价分析。文章在改进熵DEA方法的基础上,利用指标体系对商业银行的综合效率进行了测度并对比了处于多模型条件下模型的区分度问题。研究结果显示,呆坏账、服务水平(等待时间)等非期望产出对商业银行的效率意义重大;股份制商业银行的效率普遍高于国有商业银行,因此国有商业银行的股份制改造是一个积极的方向。最后,根据实证分析的结果提出的效率改进建议对商业银行的自身发展和管理当局的改革规划都具有重要的指导意义。     

Incorporating performance measures with target levels in data envelopment analysis

Data envelopment analysis (DEA) is a technique for evaluating relative efficiencies of peer decision making units (DMUs) which have multiple performance measures. These performance measures have to be classified as either inputs or outputs in DEA. DEA assumes that higher output levels and/or lower input levels indicate better performance. This study is motivated by the fact that there are performance measures (or factors) that cannot be classified as an input or output, because they have target levels with which all DMUs strive to achieve in order to attain the best practice, and any deviations from the target levels are not desirable and may indicate inefficiency. We show how such performance measures with target levels can be incorporated in DEA. We formulate a new production possibility set by extending the standard DEA production possibility set under variable returns-to-scale assumption based on a set of axiomatic properties postulated to suit the case of targeted factors. We develop three efficiency measures by extending the standard radial, slacks-based, and Nerlove–Luenberger measures. We illustrate the proposed model and efficiency measures by applying them to the efficiency evaluation of 36 US universities.