The linear formulation of the ZSG-DEA models with different production technologies

The zero sum gains data envelopment analysis models (ZSG-DEA models) are non-linear. In this paper, we first show that the ZSG-DEA models can be transformed to linear or parametric linear models and discuss the feasible domains of the parameters. Second, we show that the linear formulations of ZSG-DEA models under the equal output reduction strategy and the proportional output reduction strategy in a single output case are equivalent to the output-oriented super-efficiency model under variable returns-to-scale (VRS) assumption. As a matter of course, the models may encounter infeasibility. Third, we propose the linear transformations of ZSG-DEA models under constant returns-to-scale (CRS) assumption and compare them with the VRS models. In the end, we evaluate the participant countries at the Olympic Games by the linear equivalent models with multiple outputs under different weight restrictions. Our results are compared with the efficiencies obtained from the original ZSG-DEA model with an aggregated output under both CRS and VRS assumptions. It is found that the original method with aggregated output tends to underestimate the efficiencies of DMUs.     

General and multiplicative non-parametric corporate performance models with interval ratio data

The increasing intensity of global competition has led organizations to utilize various types of performance measurement tools for improving the quality of their products and services. Data envelopment analysis (DEA) is a methodology for evaluating and measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. All the data in the conventional DEA with input and/or output ratios assumes the form of crisp numbers. However, the observed values of data in real-world problems are sometimes expressed as interval ratios. In this paper, we propose two new models: general and multiplicative non-parametric ratio models for DEA problems with interval data. The contributions of this paper are fourfold: (1) we consider input and output data expressed as interval ratios in DEA; (2) we address the gap in DEA literature for problems not suitable or difficult to model with crisp values; (3) we propose two new DEA models for evaluating the relative efficiencies of DMUs with interval ratios, and (4) we present a case study involving 20 banks with three interval ratios to demonstrate the applicability and efficacy of the proposed models where the traditional indicators are mostly financial ratios.     

Measuring ecological efficiency with data envelopment analysis (DEA)

The measurement of ecological efficiency provides some important information for the companies’ environmental management. Ecological efficiency is usually measured by comparing environmental performance indicators. Data envelopment analysis (DEA) shows a high potential to support such comparisons, as no explicit weights are needed to aggregate the indicators. In general, DEA assumes that inputs and outputs are ‘goods’, but from an ecological perspective also ‘bads’ have to be considered. In the literature, ‘bads’ are treated in different and sometimes arbitrarily chosen ways. This article aims at the systematic derivation of ecologically extended DEA models. Starting from the assumptions of DEA in production theory and activity analysis, a generalisation of basic DEA models is derived by incorporating a multi-dimensional value function f. Extended preference structures can be considered by different specifications of f, e.g. specifications for ecologically motivated applications of DEA.     

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.     

Sensitivity analysis of DEA models for simultaneous changes in all the data

In data envelopment analysis (DEA) efficient decision making units (DMUs) are of primary importance as they define the efficient frontier. The current paper develops a new sensitivity analysis approach for the basic DEA models, such as, those proposed by Charnes, Cooper and Rhodes (CCR), Banker, Charnes and Cooper (BCC) and additive models, when variations in the data are simultaneously considered for all DMUs. By means of modified DEA models, in which the specific DMU under examination is excluded from the reference set, we are able to determine what perturbations of the data can be tolerated before efficient DMUs become inefficient. Our approach generalises the usual sensitivity analysis approach developed in which perturbations of the data are only applied to the test DMU while all the remaining DMUs remain fixed. In our framework data are allowed to vary simultaneously for all DMUs across different subsets of inputs and outputs. We study the relations of the infeasibility of modified DEA models employed and the robustness of DEA models. It is revealed that the infeasibility means stability. The empirical applications demonstrate that DEA efficiency classifications are robust with respect to possible data errors, particularly in the convex DEA case.     

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.     

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.     

Decomposition of technical and scale efficiencies in two-stage production systems

Conventional data envelopment analysis (DEA) models are used to measure the technical and scale efficiencies of a system when it is considered as a whole unit. This paper extends the efficiency measurement to two-stage systems where each stage has one process and all the outputs from the first process become the inputs of the second. An input-oriented DEA model for the first process is developed to separate the process efficiency into the input technical and scale efficiencies, and an output-oriented model is developed for the second process to separate the process efficiency into the output technical and scale efficiencies. Combining the two models, the system efficiency is expressed as the product of the overall technical and scale efficiencies, where the overall technical and scale efficiencies are the products of the corresponding efficiencies of the two processes, respectively. The detailed decomposition allows the sources of inefficiency to be identified.     

Multiobjective data envelopment analysis

Data envelopment analysis (DEA) is popularly used to evaluate relative efficiency among public or private firms. Most DEA models are established by individually maximizing each firm's efficiency according to its advantageous expectation by a ratio. Some scholars have pointed out the interesting relationship between the multiobjective linear programming (MOLP) problem and the DEA problem. They also introduced the common weight approach to DEA based on MOLP. This paper proposes a new linear programming problem for computing the efficiency of a decision-making unit (DMU). The proposed model differs from traditional and existing multiobjective DEA models in that its objective function is the difference between inputs and outputs instead of the outputs/inputs ratio. Then an MOLP problem, based on the introduced linear programming problem, is formulated for the computation of common weights for all DMUs. To be precise, the modified Chebychev distance and the ideal point of MOLP are used to generate common weights. The dual problem of this model is also investigated. Finally, this study presents an actual case study analysing R&D efficiency of 10 TFT-LCD companies in Taiwan to illustrate this new approach. Our model demonstrates better performance than the traditional DEA model as well as some of the most important existing multiobjective DEA models.     

Identifying the efficiency status in network DEA

Data envelopment analysis (DEA) is commonly employed to evaluate the efficiency performance of a decision making unit (DMU) that transforms exogenous inputs into final outputs. In such a black-box DEA approach, details of an internal production process of the DMU are typically ignored and hence the locations of inefficiency are not adequately provided. In view of this, DEA researchers have recently developed various network approaches by looking into the black box, where the inputs that enter the box and the outputs that come out of it are only considered. However, most of these network approaches evaluate divisional efficiency by using an optimal solution of their respective optimization problem. If such an optimal solution is used in the case when there are multiple optima, then managerial guidance based on this solution alone may be inappropriate because more appropriate targets from the viewpoint of management may be ignored. Taking this fact into account, therefore, we propose a network approach for identifying the efficiency status of each DMU and its divisions. This approach provides a practical computational procedure.     

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.     

On relations between DEA-risk models and stochastic dominance efficiency tests

In this paper, several concepts of portfolio efficiency testing are compared, based either on data envelopment analysis (DEA) or the second-order stochastic dominance (SSD) relation: constant return to scale DEA models, variable return to scale (VRS) DEA models, diversification-consistent DEA models, pairwise SSD efficiency tests, convex SSD efficiency tests and full SSD portfolio efficiency tests. Especially, the equivalence between VRS DEA model with binary weights and the SSD pairwise efficiency test is proved. DEA models equivalent to convex SSD efficiency tests and full SSD portfolio efficiency tests are also formulated. In the empirical application, the efficiency testing of 48 US representative industry portfolios using all considered DEA models and SSD tests is presented. The obtained efficiency sets are compared. A special attention is paid to the case of small number of the inputs and outputs. It is empirically shown that DEA models equivalent either to the convex SSD test or to the SSD portfolio efficiency test work well even with quite small number of inputs and outputs. However, the reduced VRS DEA model with binary weights is not able to identify all the pairwise SSD efficient portfolios.     

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.     

Benchmarking with quality-adjusted DEA (Q-DEA) to seek lower-cost high-quality service: Evidence from a U.S.bank application

Benchmarking is a widely cited method to identify and adopt best-practices as a means to improve performance. Data envelopment analysis (DEA) has been demonstrated to be a powerful benchmarking methodology for situations where multiple inputs and outputs need to be assessed to identify best-practices and improve productivity in organizations. Most DEA benchmarking studies have excluded quality, even in service-sector applications such as health care where quality is a key element of performance. This limits the practical value of DEA in organizations where maintaining and improving service quality is critical to achieving performance objectives. In this paper, alternative methods incorporating quality in DEA benchmarking are demonstrated and evaluated. It is shown that simply treating the quality measures as DEA outputs does not help in discriminating the performance. Thus, the current study presents a new, more sensitive, quality-adjusted DEA (Q-DEA), which effectively deals with quality measures in benchmarking. We report the results of applying Q-DEA to a U.S. bank's 200-branch network that required a method for benchmarking to help manage operating costs and service quality. Q-DEA findings helped the bank achieve cost savings and improved operations while preserving service quality, a dimension critical to its mission. New insights about ways to improve branch operations based on the best-practice (high-quality low-cost) benchmarks identified with Q-DEA are also described in the paper. This demonstrates the practical need and potential benefits of Q-DEA and its efficacy in one application, and also suggests the need for further research on measuring and incorporating quality into DEA benchmarking. The review process of this paper was handled by the Edit-in-Chief Peter Hammer.     

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.     

DEA model with shared resources and efficiency decomposition

Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.     

A new proposed model of restricted data envelopment analysis by correlation coefficients

The concept of efficiency in data envelopment analysis (DEA) is defined as weighted sum of outputs/weighted sum of inputs. In order to calculate the maximum efficiency score, each decision making unit (DMU)’s inputs and outputs are assigned to different weights. Hence, the classical DEA allows the weight flexibility. Therefore, even if they are important, the inputs or outputs of some DMUs can be assigned zero (0) weights. Thus, these inputs or outputs are neglected in the evaluation. Also, some DMUs may be defined as efficient even if they are inefficient. This situation leads to unrealistic results. Also to eliminate the problem of weight flexibility, weight restrictions are made in DEA. In our study, we proposed a new model which has not been published in the literature. We describe it as the restricted data envelopment analysis ((ARIII(COR))) model with correlation coefficients. The aim for developing this new model, is to take into account the relations between variables using correlation coefficients. Also, these relations were added as constraints to the CCR and BCC models. For this purpose, the correlation coefficients were used in the restrictions of input–output each one alone and their combination together. Inputs and outputs are related to the degree of correlation between each other in the production. Previous studies did not take into account the relationship between inputs/outputs variables. So, only with expert opinions or an objective method, weight restrictions have been made. In our study, the weights for input and output variables were determined, according to the correlations between input and output variables. The proposed new method is different from other methods in the literature, because the efficiency scores were calculated at the level of correlations between the input and/or output variables.     

Improving data envelopment analysis by the use of production trade-offs

Production technologies in data envelopment analysis (DEA) are described in terms of inputs and outputs. Production trade-offs represent simultaneous changes to the inputs and outputs that are possible in the technology under consideration. Recently, a method for their incorporation in DEA models has been developed. It was shown that the use of production trade-offs not only improves the discrimination of DEA models but also preserves the traditional meaning of efficiency as a radial improvement factor for inputs and outputs. This new paper follows the above development and provides an example of its use in the assessment of efficiency of university departments. The paper avoids excessive technical detail which can be found in the previous publication and instead focuses on the implementation of this new technique.     

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.     

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.