Accounting for Environmental Effects and Statistical Noise in Data Envelopment Analysis

In this paper we propose a new technique for incorporating environmental effects and statistical noise into a producer performance evaluation based on data envelopment analysis (DEA). The technique involves a three-stage analysis. In the first stage, DEA is applied to outputs and inputs only, to obtain initial measures of producer performance. In the second stage, stochastic frontier analysis (SFA) is used to regress first stage performance measures against a set of environmental variables. This provides, for each input or output (depending on the orientation of the first stage DEA model), a three-way decomposition of the variation in performance into a part attributable to environmental effects, a part attributable to managerial inefficiency, and a part attributable to statistical noise. In the third stage, either inputs or outputs (again depending on the orientation of the first stage DEA model) are adjusted to account for the impact of the environmental effects and the statistical noise uncovered in the second stage, and DEA is used to re-evaluate producer performance. Throughout the analysis emphasis is placed on slacks, rather than on radial efficiency scores, as appropriate measures of producer performance. An application to nursing homes is provided to illustrate the power of the three-stage methodology.     

A hybrid DEA-MOLP model for public school assessment and closure decision in the City of Philadelphia

Data envelopment analysis (DEA) is generally used to evaluate past performance and multi objective linear programming (MOLP) is often used to plan for future performance goals. In this study, we establish an equivalence relationship between MOLP problems and combined-oriented DEA models using a direction distance function designed to account for desirable and undesirable inputs and outputs together with uncontrollable variables. This equivalence model can be effectively used to support interactive processes and performance measures designed to establish future performance goals while taking into account the preferences of decision makers (DMs). In particular, it allows DMs to consider different efficiency improvement strategies when subject to budgetary restrictions. The applicability of the proposed method and the efficacy of the procedures and algorithms are demonstrated using a case study where the performance of high schools in the City of Philadelphia is evaluated.     

Does intellectual capital matter? Assessing the profitability and marketability of IC design companies

Under a highly competitive market and a dynamic industrial environment, how to evaluate and enhance an integrated circuit (IC) design company??s good performance is important. This paper develops a two-stage data envelopment analysis (DEA) combined intellectual capital theory through financial and non-financial data to evaluate a performance process on the IC design company. It adopts a new slacks-based measure (SBM) to obtain a more accurate performance estimation and rank between companies. This paper further uses the Simar and Wilson procedure with a truncated regression to explore the impact of intellectual capital variables on performance and competitive advantage. From the study we suggest to the company in how to enhance precisely its performance to create company value and success.     

Cross redundancy and sensitivity in DEA models

Data envelopment analysis (DEA) measures the efficiency of each decision making unit (DMU) by maximizing the ratio of virtual output to virtual input with the constraint that the ratio does not exceed one for each DMU. In the case that one output variable has a linear dependence (conic dependence, to be precise) with the other output variables, it can be hypothesized that the addition or deletion of such an output variable would not change the efficiency estimates. This is also the case for input variables. However, in the case that a certain set of input and output variables is linearly dependent, the effect of such a dependency on DEA is not clear. In this paper, we call such a dependency a cross redundancy and examine the effect of a cross redundancy on DEA. We prove that the addition or deletion of a cross-redundant variable does not affect the efficiency estimates yielded by the CCR or BCC models. Furthermore, we present a sensitivity analysis to examine the effect of an imperfect cross redundancy on DEA by using accounting data obtained from United States exchange-listed companies.     

Evaluating the operational performance of knowledge-based industries: the perspective of intellectual capital

Performance evaluation is more than a quantitative concept but should also take industrial characteristics into account in order to form an accurate evaluation. In the past, evaluations of the operational performance of knowledge-based industries have missed out a significant factor, which is intellectual capital (IC). By adopting data envelopment analysis (DEA), a multiple-objective decision making method, this study aims to construct an efficiency evaluation model for the Taiwanese digital content industry based on the perspective of IC. The empirical results suggest that the scale of the digital content companies does play an important role in influencing the operating efficiency. The firms have a small amount of capital can still attain optimal efficiency, from the perspective of IC. In addition, human resource capital and customer capital are the most significant influential factors that deserve digital content firms’ attention. It is suggested that enterprises in the digital content industries should focus more on managing their IC. DEA can provide the semiconductor firms’ operations with insights into resource allocation and competitive advantage as well as help with strategic decision-making.     

Measuring the efficiency of European education systems by combining Data Envelopment Analysis and Multiple-Criteria Evaluation

Education is considered an important factor of economic growth, employment and social inclusion. However, the economic crisis has put the need to achieve educational goals in the most efficient way ever more to the fore. The main objective of this paper is to assess the spending efficiency of European compulsory educational systems, creating a ranking of countries based on the efficiency scores of their systems using a number of standard variables from the literature. To this end, we also present a methodological innovation that combines Data Envelopment Analysis (DEA) with discrete Multiple Criteria Evaluation (MCE), two methods that we consider complementary if used for providing a performance analysis. Moreover, both methods identify a set of common variables which are associated with higher levels of efficiency in educational systems (e.g. some characteristics of teachers, the stock of adults’ human capital and lower expenditures per student). The results show that findings using DEA are largely confirmed by MCE.

     

Qualitative data envelopment analysis by affinity set: a survey of subjective opinions for NPOs

Measuring the performance of Non-Profit Organizations (NPOs) is a complicated issue: data envelopment analysis (DEA) is a popular quantitative tool in the past literature. However, the subjective opinions of NPOs could disturb their actual performance, and this problem is seldom considered. In this study, we use the qualitative DEA as a tool to find the emphasized inputs and outputs for these NPOs. Most DEA models are established by the basis of quantitative data, they are difficult to describe the qualitative performance of NPOs. This paper proposes a new perspective for computing the efficiency of a Decision Making Unit based on qualitative data by affinity Set. The DEA model for qualitative data could be traced back to the work of Cook et al. early in 1993. Our contribution prevents the identical efficiency scores from the model of Cook et al., and a combinatorial optimization technique is used to solve the new problem. Finally, we found most NPOs would like to get more resources from outside; but interestingly, they don’t like to be officially monitored. Therefore, we should use the quantitative DEA on NPOs very carefully.     

Integration of network data envelopment analysis and decision-making trial and evaluation laboratory for the performance evaluation of the financial holding companies in Taiwan

Data envelopment analysis (DEA) has been constantly used to measure the technical efficiency of decision-making units (DMUs). However, the major problem of traditional DEA methods is that they do not consider the possible intermediate effects. Recently, many papers have applied network DEA models to evaluate the efficiency scores. However, the linking activity of DMUs is still hard to be recognized. Hence, we employ DEMATEL to obtain the linking activity of DMUs. Our empirical research shows that the proposed method can soundly deal with the purpose of identifying the relationship between variables and derive the reasonable result in network DEA.     

A combined machine learning algorithms and DEA method for measuring and predicting the efficiency of Chinese manufacturing listed companies

Data Envelopment Analysis (DEA) is a linear programming methodology for measuring the efficiency of Decision Making Units (DMUs) to improve organizational performance in the private and public sectors. However, if a new DMU needs to be known its efficiency score, the DEA analysis would have to be re-conducted, especially nowadays, datasets from many fields have been growing rapidly in the real world, which will need a huge amount of computation. Following the previous studies, this paper aims to establish a linkage between the DEA method and machine learning (ML) algorithms, and proposes an alternative way that combines DEA with ML (ML-DEA) algorithms to measure and predict the DEA efficiency of DMUs. Four ML-DEA algorithms are discussed, namely DEA-CCR model combined with back-propagation neural network (BPNN-DEA), with genetic algorithm (GA) integrated with back-propagation neural network (GANN-DEA), with support vector machines (SVM-DEA), and with improved support vector machines (ISVM-DEA), respectively. To illustrate the applicability of above models, the performance of Chinese manufacturing listed companies in 2016 is measured, predicted and compared with the DEA efficiency scores obtained by the DEA-CCR model. The empirical results show that the average accuracy of the predicted efficiency of DMUs is about 94%, and the comprehensive performance order of four ML-DEA algorithms ranked from good to poor is GANN-DEA, BPNN-DEA, ISVM-DEA, and SVM-DEA.     

Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis (DEA). In this study, we focus on a “big data” problem related to the considerably large dimensions of the input-output data. The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation, including principal component analysis (PCA-DEA), which is based on the idea of aggregating input and output, efficiency contribution measurement (ECM), average efficiency measure (AEC), and regression-based detection (RB), which is based on the idea of variable selection. We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test. In addition, we discuss the effect of initial variable selection in RB for the first time. Based on the results, we offer guidelines that are more reliable on how to choose an appropriate method.     

Management of nursing homes using data envelopment analysis.

Data envelopment analysis (DEA) is used to evaluate the relative technical efficiency and assist in the management of a chain of nursing homes. As with any DEA model, variables chosen are particularly important. The study looks at two possibly critical issues. The first is the appropriateness of models that include only financial and economic measures to evaluate administrators when quality care is an expected output. The second issue is the appropriateness of using noncontrollable variables, in this case operating income, to evaluate administrators. We show how efficiency scores differ when quality variables and/or operating income are included. We also demonstrate the usefulness of DEA information to both the home administrator and chain managers for improving operating efficiency.     

A multistage method to measure efficiency and its application to Japanese banking industry

When measuring technical efficiency with existing data envelopment analysis (DEA) techniques, mean efficiency scores generally exhibit volatile patterns over time. This appears to be at odds with the general perception of learning-by-doing management, due to Arrow [The economic implications of learning by doing. Review of Economic Studies 1964; 154–73]. Further, this phenomenon is largely attributable to the fundamental assumption of deterministic data maintained in DEA models, and to the difficulty such models have in incorporating environmental influences. This paper proposes a three-stage method to measure DEA efficiency while controlling for the impacts of both statistical noise and environmental factors. Using panel data on Japanese banking over the period 1997–2001, we demonstrate that the proposed approach greatly mitigates these weaknesses of DEA models. We find a stable upward trend in mean measured efficiency, indicating that, on average, the bankers were learning over the sample period. Therefore, we conclude that this new method is a significant improvement relative to those DEA models currently used by researchers, corporate management, and industrial regulatory bodies to evaluate performance of their respective interests.     

A novel method for computing single output for DEA with application in hospital efficiency

There are two main methods for measuring the efficiency of decision-making units (DMUs): data envelopment analysis (DEA) and stochastic frontier analysis (SFA). Each of these methods has advantages and disadvantages. DEA is more popular in the literature due to its simplicity, as it does not require any pre-assumption and can be used for measuring the efficiency of DMUs with multiple inputs and multiple outputs, whereas SFA is a parametric approach that is applicable to multiple inputs and a single output. Since many applied studies feature multiple output variables, SFA cannot be used in such cases. In this research, a unique method to transform multiple outputs to a virtual single output is proposed. We are thus able to obtain efficiency scores from calculated virtual single output by the proposed method that are close (or even the same depending on targeted parameters at the expense of computation time and resources) to the efficiency scores obtained from multiple outputs of DEA. This will enable us to use SFA with a virtual single output. The proposed method is validated using a simulation study, and its usefulness is demonstrated with real application by using a hospital dataset from Turkey.     

Efficiency in fundraising and distributions to cause-related social profit enterprises

Managerial efficiency is as important in social profit enterprises (SPEs) as it is for more traditional financial-profit organizations. In this regard, both donors and SPE executives use efficiency information in making decisions. Here, we suggest a linked, two-stage Data Envelopment Analysis (DEA) methodology for assessing efficiency in both charitable fundraising and cause delivery, while empirically investigating results for international aid organizations. The model allows efficiency assessment for both the fundraising and utilization of generated funds when directed for cause-related purposes. This, in particular, allows for measurement of the organization’s managerial efficiency relative to both multiple phased goals and peer organizations. Additionally, the approach provides benchmarks for identifying sources of improved performance in fundraising and program/cause service delivery. It can also project the results of changes in inputs on the amount of resources available for the charitable organization’s cause.The proposed model(s) allow the examiner to assess performance while, at the same time, identifying those instances wherein the simple ratio measures commonly used in non-profit assessment are (1) deficient, and/or (2) misleading because of the use of ‘incorrect’ variables, or the ‘hiding’ of inefficiency if/when tax form categories are filed by an SPE. Importantly, the suggested two-stage DEA methodology can be useful for any organization with multiple-linked goals.     

An insight into the specification of the input-output set for DEA-based bank efficiency measurement

Data envelopment analysis (DEA) has become one of the most widely used instruments for measuring bank efficiency. However, its application encounters many problems, which is evidenced by continuous evolvements in the DEA method so far. Our paper addresses the pitfalls of DEA in the context of measuring bank efficiency, with focus on the specification of performance factors. We aim at examining whether the input-output specification for banks in DEA applications is in consistence with the criteria upon which banks make decisions. Four bank behaviour models which are most popularly employed to determine input and output factors in DEA studies—the intermediation approach, production approach, user cost approach and value added approach—are comprehensively discussed and reviewed. The comparative reflection on the bank behaviour models and the standard DEA models shows that the input-output related pitfalls of a DEA application are associated with its implicitly fixed preference structure, flexible weight determination and limited explanatory power. Due to the pitfalls, the conventional DEA models may fail to capture bank behaviours. In such cases, DEA results can hardly reflect the performance in its true sense, i.e. how banks perform against the goals that they decide to pursue. The findings suggest focusing on (DEA-based) performance measurement from a goal-oriented perspective, i.e. from the point of view of multi criteria decision making.     

One-stage estimation of the effects of operational conditions and practices on productive performance: asymptotically normal and efficient,root-<Emphasis Type="Italic">n</Emphasis> consistent StoNEZD method

Understanding the effects of operational conditions and practices on productive efficiency can provide valuable economic and managerial insights. The conventional approach is to use a two-stage method where the efficiency estimates are regressed on contextual variables representing the operational conditions. The main problem of the two-stage approach is that it ignores the correlations between inputs and contextual variables. To address this shortcoming, we build on the recently developed regression interpretation of data envelopment analysis (DEA) to develop a new one-stage semi-nonparametric estimator that combines the nonparametric DEA-style frontier with a regression model of the contextual variables. The new method is referred to as stochastic semi-nonparametric envelopment of z variables data (StoNEZD). The StoNEZD estimator for the contextual variables is shown to be statistically consistent under less restrictive assumptions than those required by the two-stage DEA estimator. Further, the StoNEZD estimator is shown to be unbiased, asymptotically efficient, asymptotically normally distributed, and converge at the standard parametric rate of order n ^−1/2. Therefore, the conventional methods of statistical testing and confidence intervals apply for asymptotic inference. Finite sample performance of the proposed estimators is examined through Monte Carlo simulations.     

Research efficiency analysis of China's university faculty members: A modified meta-frontier DEA approach

Traditionally, data envelopment analysis (DEA) requires all decision-making units (DMUs) to have similar characteristics and experiences within the same external conditions. In many cases, this assumption fails to hold, and thus, difficulties will be encountered to some extent when measuring efficiency with a standard DEA model. Ideally, the performance of DMUs with different characteristics could be examined using the DEA meta-frontier framework. However, some of these DMUs are mixed-type DMUs that may affiliate with more than one group. Furthermore, the total number of observations of these mixed-type DMUs is limited. This is one of the common problems when studies focus on faculty research performance in higher education institutions. In general, a faculty member is affiliated with a certain department, and if the departmental assessment policy is not suitable for faculty members who are involved in interdisciplinary research, their performance could be underestimated. Therefore, the proposed model is an extension of the DEA meta-frontier framework that can assess the performance of mixed-type DMUs by constructing the reference set without the same type of DMUs. In this paper, the scientific research efficiency of faculty members at the Inner Mongolia University is used as an example to provide a better understanding of the proposed model. The proposed model is intended to provide a fair and balanced performance assessment method that reflects actual performance, especially for mixed-type DMUs.     

Measuring efficiency in education: The influence of imprecision and variability in data on DEA estimates

Many studies devoted to efficiency performance evaluation in the education sector are based on measures of central tendency at school level as, for example, the average values of students belonging to the same school. Although this is a common and accepted way of summarizing data from the original observations (students), it is not less true that this approach neglects the existing dispersion of data, which may become a serious problem if variability across schools is high. Additionally, imprecision may arise when experts on each evaluated subject select the battery of questions, with different levels of difficulty, which will be the base for the final questionnaires completed by students. This paper uses data from US students and schools participating in PISA (Programme for International Student Assessment) 2015 to illustrate that schools' efficiency measures based on aggregate data and imprecision may reflect an inaccurate picture of their performance if they are compared to measures estimated accounting for broader information provided by all students of the same school. In order to operationalize our approach, we resort to Fuzzy Data Envelopment Analysis. This methodology allows us to deal with the notion of fuzziness in some variables such as the socio-economic status of students or test scores. Our results indicate that the estimated measures of performance obtained with the fuzzy DEA approach are highly correlated with those calculated with traditional DEA models. However, we find some relevant divergences in the identification of efficient units when we account for data dispersion and vagueness.     

Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification

The appearance of strictly positive slack variables in DEA solutions causes well known computational and analytical problems studied by Olesen and Petersen (1996) and Green et al. (1996) under constant returns to scale. This paper discusses variable returns to scale and suggests the use of efficient facets (EFs) in the reference technology. It is found to give a lower bound of the efficiency scores. Most importantly, efficiency measured with respect to EFs—the EF based efficiency index—may decrease if additional variables are introduced but are disposed in production. Thus, units are penalized for disposal of incoming variables, and the EF based efficiency index captures the net efficiency of a unit. EF is found to be a useful tool also to search a suitable set of variables for efficiency measurement. Its use is demonstrated with Finnish university data and it is found to change the measured performance of the university sector quite significantly.