Data envelopment analysis with heterogeneous data: an application

The effects of data heterogeneity on the efficiency estimate by data envelopment analysis are evaluated here in terms of empirical applications in the computer industry. Scale or size variations of firms and heteroscedasticity are the two forms of heterogeneity considered here. Our empirical results show that the adverse effects of data heterogeneity can be considerably reduced by the methods suggested here.     

Chinese companies distress prediction: an application of data envelopment analysis

Bankruptcy prediction is a key part in corporate credit risk management. Traditional bankruptcy prediction models employ financial ratios or market prices to predict bankruptcy or financial distress prior to its occurrence. We investigate the predictive accuracy of corporate efficiency measures along with standard financial ratios in predicting corporate distress in Chinese companies. Data Envelopment Analysis (DEA) is used to measure corporate efficiency. In contrast to previous applications of DEA in credit risk modelling where it was used to generate a single efficiency—Technical Efficiency (TE), we assume Variable Returns to Scale, and decompose TE into Pure Technical Efficiency and Scale Efficiency. These measures are introduced into Logistic Regression to predict the probability of distress, along with the level of Returns to Scale. Effects of efficiency variables are allowed to vary across industries through the use of interaction terms, while the financial ratios are assumed to have the same effects across all sectors. The results show that the predictive power of the model is improved by this corporate efficiency information.     

Group performance evaluation, an application of data envelopment analysis

The contribution of this paper is to provide an approach for evaluating the performance of a group of decision making units (DMUs) based on the production technology. Group evaluation is an application of data envelopment analysis (DEA). DEA uses linear programming to provide a suitable technique to estimate a multiple-input/multiple-output empirical efficient function. This paper applies group evaluation to evaluate the performance of Iranian commercial banks.     

Outlier detection in data envelopment analysis: an analysis of jackknifing

This paper analyzes the resampling technique of jackknifing and its capability of detecting outliers in data envelopment analysis. It is well recognized that measured efficiency is sensitive to outliers; recent research has employed resampling techniques to estimate standard deviations in an attempt to handle outliers. Using jackknifing, each observation other than the decision making unit under analysis is deleted from the sample once and the resulting linear program is solved, leading to a distribution of efficiency estimates. From this distribution, standard deviations and confidence intervals are derived. Two types of outliers can be distinguished conceptually: those belonging to the production possibility set that are efficient, and those that do not belong but appear to due to statistical noise. This paper argues that calculation of the standard deviation is not meaningful because it is not possible to distinguish empirically between the two types of outliers.     

A distance-based measure of super efficiency in data envelopment analysis: an application to gas companies

Conventional data envelopment analysis (DEA) assists decision makers in distinguishing between efficient and inefficient decision making units (DMUs) in a homogeneous group. Standard DEA models can not provide more information about efficient units. Super-efficiency DEA models can be used in ranking the performance of efficient DMUs and overcome this obstacle. Because of the possible infeasibility, the use of super efficiency models has been restricted. This research proposes a methodology to determine a distance-based measure of super-efficiency. The proposed methodology overcomes the infeasibility problem of the existing ranking methodologies. The applicability of the proposed model is illustrated in the context of the analysis of gas companies?? performance.     

Rasch model in data envelopment analysis: application in the international tourist hotel industry

The Rasch model can be used to transform ordinal data into interval data. Rasch has seldom been incorporated in data envelopment analysis (DEA) models. Therefore, this study attempts to apply the Rasch model in DEA to analyse the performance of seven districts including Taipei; Kaoshong; Taichung; Hwalian; Scenery; Taoyuan, Hsinchu, Miaoli; Others in Taiwan containing 56 international tourist hotels during 2009 using five criteria, including average occupancy rate, average room rate, average production value per employee in the accommodation department, average production value per employee in the catering department and operating income/expenses. Furthermore, this study also compared the results with and without the Rasch-bounded DEA model. As expected of the analytical results that applying the DEA model using the bounded formulas achieves better distinguishing power than applying the model without using the bounded formulas. Furthermore, the effectiveness value of each district of Taiwan (Taipei (1.000), Kaoshong (0.3661), Taichung (0.3494), Hwalian (0.2658), Scenery (0.6476), Tyoyuan, Hsinchu, Miaoli (0.5623), others (0.3127)) during 2009 is obtained.     

Evaluating eco-efficiency with data envelopment analysis: an analytical reexamination

This paper reexamines the unintended consequences of the two widely cited models for measuring environmental efficiency—the hyperbolic efficiency model (HEM) and directional distance function (DDF). I prove the existence of three main problems: (1) these two models are not monotonic in undesirable outputs (i.e., a firm’s efficiency may increase when polluting more, and vice versa), (2) strongly dominated firms may appear efficient, and (3) some firms’ environmental efficiency scores may be computed against strongly dominated points. Using the supply-chain carbon emissions data from the 50 major U.S. manufacturing companies, I empirically compare these two models with a weighted additive DEA model. The empirical results corroborate the analytical findings that the DDF and HEM models can generate spurious efficiency estimates and must be used with extreme caution.     

Two-stage data envelopment analysis with undesirable intermediate measures: an application to air quality improvement in China

Air pollution continues to pose a major threat to human health in China and its neighbor countries including Japan. Although the general clean air trend in China is to replace older coal-fired generation with clean energy, \(60\%\) coal consumption in the overall energy use still makes it the most coal-dependent country. Improvement of the coal-fired generation efficiency is fully expected to play a vital role for the foreseeable future. Focusing on the main air pollutants, this paper presents a comprehensive study from the target region selection in China to the benefit allocation analysis for a potential collaboration between China and Japan in Integrated coal Gasification Combined Cycle (IGCC). Both radial and non-radial two-stage data envelopment analysis models with undesirable intermediate measures are applied first to evaluate the regional air quality improvement efficiencies in China (2005–2014). Due to the extremely high initial and dynamic investment for IGCC, target regions with the highest priorities to be installed with this technology are selected by k-means clustering method based on the results of two-stage data transformation model under variable returns to scale. Finally, a benefit analysis by multi-criteria allocation game with the principal performance indices from two representative IGCC power plants in China and Japan provides further insights for the mutual motivations of this kind of collaboration and uncovers some international policy implications.     

Influential DMUs and outlier detection in data envelopment analysis with an application to health care

This paper explains some drawbacks on previous approaches for detecting influential observations in deterministic nonparametric data envelopment analysis models as developed by Yang et al. (Annals of Operations Research 173:89–103, 2010). For example efficiency scores and relative entropies obtained in this model are unimportant to outlier detection and the empirical distribution of all estimated relative entropies is not a Monte-Carlo approximation. In this paper we developed a new method to detect whether a specific DMU is truly influential and a statistical test has been applied to determine the significance level. An application for measuring efficiency of hospitals is used to show the superiority of this method that leads to significant advancements in outlier detection.     

Efficiency,size, benchmarks and targets for bank branches: an application of data envelopment analysis

This paper describes an application of data envelopment analysis (DEA) to the performance assessment of Portuguese bank branches. The analysis shows how DEA can complement the profitability measure currently used at the bank. The use of an efficiency-profitability matrix enabled the characterisation of the branches' performance profile. Consistent with the bank's development objectives, the analysis focused on the relation between branch size and performance. Two alternative target setting strategies were explored. One eliminates pure technical inefficiencies by focusing on the selection of appropriate benchmarks. The other attains the branches' most productive scale size through the elimination of scale inefficiencies, with minimal changes to branches' scale size.     

Sensitivity in data envelopment analysis using an approximate inverse matrix

In this paper, sensitivity analysis of the Charnes–Cooper–Rhodes model in data envelopment analysis (DEA) is studied for the case of perturbation of all outputs and of all inputs of an efficient decision-making unit (DMU). Using an approximate inverse of the perturbed optimal basis matrix, an approximate preservation of efficiency for an efficient DMU under these perturbations is considered. Sufficient conditions for an efficient DMU to preserve its efficiency are obtained in that case. An illustrative example is provided.     

Decomposing capacity utilization in data envelopment analysis: An application to banks in India

This paper briefly reviews the existing methods of capacity utilization in nonparametric framework from economic perspectives, and then suggests an alternative in the light of limitations therein. In the spirit of work by Coelli et al. [Coelli, T.J., Grifell-Tatje, E., Perelman, S., 2002. Capacity utilisation and profitability: A decomposition of short run profit efficiency. International Journal of Production Economics 79, 261–278], we propose two methods, radial and non-radial, to decompose the input-based physical (technological) capacity utilization into various meaningful components viz., technical inefficiency, ray economic capacity utilization and optimal capacity idleness. A case study of Indian banking industry is taken as an example to illustrate the potential application of these two methods of decomposition. Our two broad empirical findings are that first, competition created after financial sector reforms generates high efficiency growth, and reduces excess capacity; second, the cost gap of the short-run cost from the actual cost is higher for the nationalized banks over the private banks indicating that the former banks, though old, do not reflect their learning experience in their cost minimizing behavior.     

Robustness of the efficient DMUs in data envelopment analysis

By means of modified versions of CCR model based on evaluation of a decision making unit (DMU) relative to a reference set grouped by all other DMUs, sensitivity analysis of the CCR model in data envelopment analysis (DEA) is studied in this paper. The methods for sensitivity analysis are linear programming problems whose optimal values yield particular regions of stability. Sufficient and necessary conditions for upward variations of inputs and for downward variations of outputs of an (extremely) efficient DMU which remains efficient are provided. The approach does not require calculation of the basic solutions and of the inverse of the corresponding optimal basis matrix. The approach is illustrated by two numerical examples.     

Sensitivity analysis of inefficient units in data envelopment analysis

One important issue in DEA which has been studied by many DEA researchers is the sensitivity of the results of an analysis to perturbations in the data.This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” in which the efficiency score of a specific inefficient DMU changes to a defined efficiency score.In what follows, we identify a new frontier, and prove the efficiency score of each arbitrary unit on it which is defined as the efficiency score.     

Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan

The efficiency of decision processes which can be divided into two stages has been measured for the whole process as well as for each stage independently by using the conventional data envelopment analysis (DEA) methodology in order to identify the causes of inefficiency. This paper modifies the conventional DEA model by taking into account the series relationship of the two sub-processes within the whole process. Under this framework, the efficiency of the whole process can be decomposed into the product of the efficiencies of the two sub-processes. In addition to this sound mathematical property, the case of Taiwanese non-life insurance companies shows that some unusual results which have appeared in the independent model do not exist in the relational model. In other words, the relational model developed in this paper is more reliable in measuring the efficiencies and consequently is capable of identifying the causes of inefficiency more accurately. Based on the structure of the model, the idea of efficiency decomposition can be extended to systems composed of multiple stages connected in series.     

Determining rates of change in data envelopment analysis

This paper presents a general method for determining rates of change of outputs with respect to inputs along efficient facets of the Pareto-optimal frontier common to several empirical production possibility sets in Data Envelopment Analysis. As a prerequisite step, a theoretical analysis is provided for identifying the efficient facets. Non-negativity of these rates of change are discussed via ‘cone direction’ developments in both the input and output spaces.     

Allocating the fixed cost: an approach based on data envelopment analysis and cooperative game

Annals of Operations Research - Allocating the fixed cost among a set of users in a fair way is an important issue both in management and economic research. Recently, Du et al. (Eur J Oper Res...     

Recent models in data envelopment analysis: Theory and applications

A critical review of the recent models of data envelopment analysis (DEA) is attempted here. Three new lines of approach involving dynamic changes in parameters, the error correction models and a stochastic sensitivity analysis are discussed in some detail. On the applications side, two new formulations are presented and discussed, e.g. a model of technical change and a cost frontier for testing economies of scale and adjustment due to risk factors. Thus the critical review of recent DEA models of productivity measurement provides new insight into the frontier of research in this field.     

Identification of Pareto-efficient facets in data envelopment analysis

In Data Envelopment Analysis (DEA), identification of the Pareto-efficient frontier of an empirical production possibility set is a prerequisite step toward determining rates of change of outputs with changes in inputs along its piecewise linear facets. These rates of change, which will be different on different facets, have important economic and managerial implications in trade-off analysis, forecasting and resource allocation. Accurate and complete identification of the component members of each facet remains an open question. Such identification is important in certain procedures for determining these rates of change. This paper develops three modifications to the pivoiing criteria of the simplex algorithm, commonly used to solve DEA problems, as alternative strategies for more completely identifying facet members of the Pareto-optimal frontier common to several production possibility sets in DEA. Experimental results from implementing these strategies are presented.