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.     

Measurement of Returns to Scale and Damages to Scale for DEA-based operational and environmental assessment: How to manage desirable (good) and undesirable (bad) outputs?

Environmental assessment is increasingly important in preventing various types of pollutions. Data Envelopment Analysis (DEA) has been long used as an operational performance measure, but we have insufficiently explored the use of DEA for environmental assessment. This study explores a new use of DEA for the environmental assessment in which outputs are classified into desirable (good) and undesirable (bad) outputs. Such an output separation is important in the DEA-based environmental assessment. This study extends the use of DEA to the measurement of both Returns to Scale (RTS) for desirable outputs and Damages to Scale (DTS) for undesirable outputs. A Range-Adjusted Measure (RAM) is used as a DEA model for this study because the non-radial model can easily combine the two types of outputs in a unified treatment. All the mathematical features regarding the RAM-based RTS/DTS measurement are first discussed from the operational and environmental performance in a separate treatment. Then, this study combines the two performance measures as a unified measure. The RAM-based RTS/DTS is mathematically explored from the unified measure for operational and environmental performance.     

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.     

Theory of integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, introducing new axioms of “natural disposability” and “natural divisibility”. We derive a DEA production possibility set that satisfies the minimum extrapolation principle under our refined set of axioms. We also present a mixed integer linear programming formula for computing efficiency scores. An empirical application to Iranian university departments illustrates the approach.     

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.     

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.     

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.     

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.     

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.     

Shadow pricing of undesirable outputs in nonparametric analysis

For three decades a growing interest in the modeling of desirable and undesirable outputs has led to a theoretical and methodological debate in the nonparametric literature on production technology and efficiency. The first main discussion is about the way of modeling ‘bad/undesirables’ as inputs or outputs, or by transformation functions. The second debate concerns the implications of the weak disposability assumption in the modeling of bad outputs, in particular the possibility of assigning unexpected signs to shadow prices of bad outputs. In addition, we point out a current error in the modeling of weak disposability under a variable returns to scale technology. In this paper we introduce a hybrid model to ensure the economically meaningful jointness of good and bad outputs while constraining shadow prices of bad outputs to their expected sign. We argue that it is a sound compromise to model undesirable outputs with a meaningful primal/dual economic interpretation. Finally we propose an extension to define shadow prices for undesirable outputs following the Law of One Price (LoOP) rule.     

Network DEA approach to airports performance assessment considering undesirable outputs

In this paper, a directional distance approach is proposed to deal with network DEA problems in which the processes may generate not only desirable final outputs but also undesirable outputs. The proposed approach is applied to the problem of modelling and benchmarking airport operations. The corresponding network DEA model considers two process (Aircraft Movement and Aircraft Loading) with two final outputs (Annual Passenger Movement and Annual Cargo handled), one intermediate product (Aircraft Traffic Movements) and two undesirable outputs (Number of Delayed Flights and Accumulated Flight Delays). The proposed approach has been applied to Spanish airports data for year 2008 comparing the computed directional distance efficiency scores with those obtained using a conventional, single-process directional distance function approach. From this comparison, it can be concluded that the proposed network DEA approach has more discriminatory power than its single-process counterpart, uncovering more inefficiencies and providing more valid results.     

A new approach in modelling undesirable output in DEA model

With an increasing attention on the environment, one of the major research thrusts in Data Envelopment Analysis (DEA) based performance evaluation is the undesirable output in the conventional DEA model. There is considerable research published on the undesirable aspects of production outputs. However, the economic implications and the suitability of the DEA models for incorporating the undesirable outputs are less carefully investigated and discussed. In this paper, a comparative study is conducted of typical eco-DEA models to illustrate this issue. We propose a ratio model to evaluate the undesirable as well as the desirable outputs simultaneously. We apply the specially developed model to investigate the impact of production pollutants while conducting the efficiency evaluation in the textile industry of China. The results reveal that the production output-oriented efficiency evaluation can be significantly altered once the environmental aspects are factored into the model.     

BiLevel programming Data Envelopment Analysis with constrained resource

A new BiLevel programming Data Envelopment Analysis (DEA) approach is created to provide valuable managerial insights when assessing the performance of a system with Stackelberg-game relationships. This new approach allows us to evaluate the firm performance in decentralized decisions, which consist of the objective(s) of the leader at its first level and that is of the follower at the second level. This approach can help decentralized companies to optimize their performance using multiple inputs to produce multiples outputs in a cost-effective way, where both the system “black-box” and subsystem performance are exposed in details. We show the algorithms and solutions to our new models. We illustrate and validate the proposed new approach using two case studies: a banking chain and a manufacturing supply chain. The computation shows that subsystem being efficient at all levels results in an overall efficiency achievement in a decentralized BiLevel structure.     

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。     

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.     

非合作博弈两阶段生产系统的效率评价——基于自由处置和管理处置的视角

为了识别被动适应环境和采取创新技术主动适应环境的生产系统的效率差异,基于主从非合作框架和决策者的期望需求,分别从自由处置和管理处置的视角建立了两阶段生产系统效率评价模型,应用模型对2017年中国24省市工业生产系统效率进行了分析。结果表明:两种环境适应策略下,中国24个省市工业生产的两个子系统的效率均值都较高,主要分布在中国东部。24省市在自由处置模式下的技术差距较小,管理处置模式下的技术差距较大。24省市技术创新的重点在于减少工业废水和工业废气的排放,但是对一般工业固体废物减量化的重视程度不足。各省市工业固体废物处理无效的根源包括固体废物减量化无效、固体废物再利用和固体废物处置同时无效,以及混合无效三种方式。     

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.     

DEA with non-monotonic variables. Application to EU governments’ macroeconomic efficiency

Conventional Data Envelopment Analysis (DEA) considers monotonic variables, ie the lower the inputs and the larger the outputs, the better. There are, however, occasions when the monotonicity of a variable with respect to efficiency depends on the value of the variable, that is in a certain range of values an increase in the variable is desirable, while in another range it is a decrease of the variable that is desirable. In this paper, a DEA model that solves problems considering non-monotonic variables is proposed. An application to assess the macroeconomic efficiency of European Union Member States, as regards taxation, gross debt, GDP growth and employment is presented.     

Stepwise selection of variables in data envelopment analysis: Procedures and managerial perspectives

One of the most important steps in the application of modeling using data envelopment analysis (DEA) is the choice of input and output variables. In this paper, we develop a formal procedure for a “stepwise” approach to variable selection that involves sequentially maximizing (or minimizing) the average change in the efficiencies as variables are added or dropped from the analysis. After developing the stepwise procedure, applications from classic DEA studies are presented and the new managerial insights gained from the stepwise procedure are discussed. We discuss how this easy to understand and intuitively sound method yields useful managerial results and assists in identifying DEA models that include variables with the largest impact on the DEA results.     

Measuring environmental efficiency of thermoelectric power plants: a common equilibrium efficient frontier DEA approach with fixed-sum undesirable output

China’s rapid development in economy has intensified many problems. One of the most important issues is the problem of environmental pollution. In this paper, a new DEA approach is proposed to measure the environmental efficiency of thermoelectric power plants, considering undesirable outputs. First, we assume that the total amount of undesirable outputs of any particular type is limited and fixed to current levels. In contrast to previous studies, this study requires fixed-sum undesirable outputs. In addition, the common equilibrium efficient frontier is constructed by using different input/output multipliers (or weights) for each different decision making unit (DMU), while previous approaches which considered fixed-sum outputs assumed a common input/output multiplier for all DMUs. The proposed method is applied to measure the environmental efficiencies of 30 thermoelectric power plants in mainland China. Our empirical study shows that half of the plants perform well in terms of environmental efficiency.