Efficiency measurement using independent component analysis and data envelopment analysis

Efficiency measurement is an important issue for any firm or organization. Efficiency measurement allows organizations to compare their performance with their competitors’ and then develop corresponding plans to improve performance. Various efficiency measurement tools, such as conventional statistical methods and non-parametric methods, have been successfully developed in the literature. Among these tools, the data envelopment analysis (DEA) approach is one of the most widely discussed. However, problems of discrimination between efficient and inefficient decision-making units also exist in the DEA context (Adler and Yazhemsky, 2010). In this paper, a two-stage approach of integrating independent component analysis (ICA) and data envelopment analysis (DEA) is proposed to overcome this issue. We suggest using ICA first to extract the input variables for generating independent components, then selecting the ICs representing the independent sources of input variables, and finally, inputting the selected ICs as new variables in the DEA model. A simulated dataset and a hospital dataset provided by the Office of Statistics in Taiwan’s Department of Health are used to demonstrate the validity of the proposed two-stage approach. The results show that the proposed method can not only separate performance differences between the DMUs but also improve the discriminatory capability of the DEA’s efficiency measurement.     

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.     

A new methodology for evaluating sustainable product design performance with two-stage network data envelopment analysis

Sustainable product design has been considered as one of the most important practices for achieving sustainability. To improve the environmental performances of a product through product design, however, a firm often needs to deal with some difficult technical trade-offs between traditional and environmental attributes which require new design concepts and engineering specifications. In this paper, we propose a novel use of the two-stage network Data Envelopment Analysis (DEA) to evaluate sustainable product design performances. We conceptualize “design efficiency” as a key measurement of design performance in terms of how well multiple product specifications and attributes are combined in a product design that leads to lower environmental impacts or better environmental performances. A two-stage network DEA model is developed for sustainable design performance evaluation with an “industrial design module” and a “bio design module.” To demonstrate the applications of our DEA-based methodology, we use data of key engineering specifications, product attributes, and emissions performances in the vehicle emissions testing database published by the US EPA to evaluate the sustainable design performances of different automobile manufacturers. Our test results show that sustainable design does not need to mean compromise between traditional and environmental attributes. Through addressing the interrelatedness of subsystems in product design, a firm can find the most efficient way to combine product specifications and attributes which leads to lower environmental impacts or better environmental performances. This paper contributes to the existing literature by developing a new research framework for evaluating sustainable design performances as well as by proposing an innovative application of the two-stage network DEA for finding the most eco-efficient way to achieve better environmental performances through product design.     

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.     

Hedge fund performance appraisal using data envelopment analysis

In this paper we apply data envelopment analysis (DEA) to evaluate the performance of hedge fund classifications. The purpose of alternative investment strategies such as hedge funds is to offer absolute returns, so using passive benchmarks to measure their performance could be ineffective. With the increasing number of hedge funds available, institutional investors, pension funds, and high net worth individuals urgently need a trustworthy efficiency appraisal method. DEA can achieve this. An important benefit of the DEA measure is that benchmarks are not required, thereby alleviating the problem of using traditional benchmarks to examine non-normal distribution of hedge fund returns. We suggest that DEA be used as a complimentary technique (or method) for the selection of efficient hedge funds and funds of hedge funds for investors. Using DEA can shed light and further validate hedge fund manager selection with other methodologies.     

Joint use of DEA and constrained canonical correlation analysis for efficiency valuations involving categorical variables

The research on efficiency valuations has used two distinct approaches. One is the nonparametric approach known as data envelopment analysis (DEA), the other is the parametric approach based on regression analysis or its extension such as constrained canonical correlation analysis (CCCA). Interestingly, a recent study has employed a hybrid approach that cross-fertilizes DEA and CCCA to compensate for the drawbacks of the two methods and capture their positive aspects. This approach first applies DEA to select efficient units and then utilizes CCCA to identify a smooth efficient frontier with the selected efficient units only. We extend it to incorporate a categorical variable that reflects an environmental effect on efficiency performance. The need for considering a categorical variable arises in practice for an equitable efficiency valuation, as illustrated by managerial performance evaluation of the branches of a fast-food company, where the location of branches such as commercial or noncommercial area significantly affects their performance. We demonstrate various possible ways to handle such a categorical variable in the framework of a hybrid approach and characterize each of the methods. Based on this study, we suggest one method that simultaneously utilizes an extension of DEA, referred to as DEA with categorical variable, and CCCA employing a dummy variable, as in multiple regressions with dummy variables. Through an application to the branches of a fast-food company, we show the efficacy of the suggested method in terms of penalizing the advantageous location effect and compensating for the disadvantageous location effect. We also provide some discussions on the limitations underlying the hybrid approach in order to guide a proper use of this approach to the other potential applications.     

Assessing the performance of biogas plants with multi-criteria and data envelopment analysis

This paper performs an assessment of 41 agricultural biogas plants located in Austria to determine their relative performance in terms of economic, environmental, and social criteria and corresponding indicators. The comparison of these renewable energy conversion plants is based on two complementary analyses. Data envelopment analysis (DEA) was conducted to provide measures of radial efficiency relative to the observed frontier of production possibilities. Multi-criteria decision analysis (MCDA), using the IRIS/ELECTRE TRI methodology, was conducted to obtain a different perspective on the results, and as a tool that would enable to incorporate managerial preferences easily. To be able to use IRIS while keeping the spirit behind DEA, the evaluation criteria were defined as different output/input efficiency ratios, and no information about criteria weights was introduced at the outset. The results suggest that MCDA, and the use of IRIS in particular, constitutes a useful approach that can be applied in a complementary way to DEA.     

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.     

Reconciling ratio analysis and DEA as performance assessment tools

The assessment of operational performance remains a fundamental challenge both in practice and in theory. Data envelopment analysis (DEA) is one method developed in production economic theory and applied by researchers to study groups of enterprises. In practice, individual enterprises almost universally rely on simple output–input ratios. Each approach has its strengths and weaknesses, but the theoretical connection between the two has not been fully articulated. This paper uses the framework of DEA to establish a mathematical relationship between DEA efficiency scores and corresponding ratio analysis. The relationship can be expressed as a product of seven components: technical efficiency, technical change, scale efficiency, input slack factor, input substitution factor, output slack factor and output substitution factor.     

Analysis of hedge fund strategies using slack-based DEA models

Hedge funds have made a significant impact on the performance of world financial markets in recent times. Our objective in this paper is to develop a robust framework for the evaluation of hedge funds by incorporating a maximum number of performance measures through public data sources. We analyse the hedge fund strategies (styles) using a variety of classical risk-return measures with the help of slack-based Data Envelopment Analysis (DEA) models to determine a unique performance indicator. The main thrust is to investigate the risk return profile of 4730 hedge funds classified under 18 different strategies using multiple inputs and outputs. The originality of the work lies in applying Slack-Based DEA to decipher the risk-return profile of these strategies using advanced risk-return measures such as Value at Risk, drawdown, lower and higher partial moments and skewness. We find that the correlation between the ranking of hedge fund strategies based on Sharpe ratio and the DEA models is very low; at the same time, there is a significant correlation between rankings obtained by the application of DEA using different sets of input/output measures. We have also compared the DEA rankings with other traditional financial ratios such as modified Sharpe ratio, Sortino ratio and Calmar ratio. The paper also studies the impact of events such as the Asian financial crisis on the performance of hedge funds. The study around the event shows that only a relatively small number of strategies performed better during times of turmoil.     

Measuring dynamic efficiency: Theories and an integrated methodology

Almost all dynamic production systems are subject to lagged productive effects, which are an often-ignored latent source of interference in the efficiency measuring process. Existing data envelopment analysis (DEA) approaches rely on a static production environment. They can easily lead to biased evaluation results due to the erroneous assumption. To tackle this issue, this paper develops a dynamic DEA model that allows intertemporal effects in efficiency measuring. Specifically, the dynamic DEA model incorporates dynamic factors via a linear parametric formulation. Our model can be applied in place of static DEA models to a wide range of applications, such as analyzing longitudinal firm performance and productivity changes. As for the empirical efficiencies, we demonstrate how the lag parameters in the dynamic model can be estimated by the panel vector autoregressive model (PVAR). We use our methodology to evaluate advertising efficiencies of several major automobile and pharmaceutical firms in North America. The result shows that using static DEA in dynamic production can lead to both rank reversals and changes in efficiency scores.     

Context-dependent data envelopment analysis with cross-efficiency evaluation

To address some problems with the original context-dependent data envelopment analysis (DEA), this paper proposes a new version of context-dependent DEA; this version is based on cross-efficiency evaluations. One of the problems with the original context-dependent DEA is that the attractiveness and progress measures only represent the radial distance between the decision-making unit (DMU) under evaluation and the evaluation context. This representation only shows how distinct the DMU is from a single specific DMU on the evaluation context, not from the entire evaluation context overall. Another problem is that the magnitude of attractiveness and progress scores in the original context-dependent DEA may not have significant meanings. It may not be proper to say that a DMU is more attractive simply because it has a higher attractiveness score for the same reason that the performance of inefficient DMUs cannot be compared with one another simply based on their efficiency scores. We incorporate cross-efficiency evaluations into the context-dependent DEA to overcome the preceding shortcomings of the original context-dependent DEA. We also demonstrate the proposed model's appropriateness and usefulness with an illustrative example.     

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.     

DEA and the discriminant analysis of ratios for ranking units

The purpose of this study is to develop a new method which provides for given inputs and outputs the best common weights for all the units that discriminate optimally between the efficient and inefficient units as pregiven by the Data Envelopment Analysis (DEA), in order to rank all the units on the same scale. This new method, Discriminant Data Envelopment Analysis of Ratios (DR/DEA), presents a further post-optimality analysis of DEA for organizational units when their multiple inputs and outputs are given. We construct the ratio between the composite output and the composite input, where their common weights are computed by a new non-linear optimization of goodness of separation between the two pregiven groups. A practical use of DR/DEA is that the common weights may be utilized for ranking the units on a unified scale. DR/DEA is a new use of a two-group discriminant criterion that has been presented here for ratios, rather than the traditional discriminant analysis which applies to a linear function. Moreover, non-parametric statistical tests are employed to verify the consistency between the classification from DEA (efficient and inefficient units) and the post-classification as generated by DR/DEA.     

A non-radial DEA approach to measuring environmental performance

Data envelopment analysis (DEA) has gained great popularity in environmental performance measurement because it can provide a synthetic standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. Past studies about the application of DEA to environmental performance measurement often follow the concept of radial efficiency measures. In this paper, we present a non-radial DEA approach to measuring environmental performance, which consists of a non-radial DEA-based model for multilateral environmental performance comparisons and a non-radial Malmquist environmental performance index for modeling the change of environmental performance over time. A case study of OECD countries using the proposed non-radial DEA approach is also presented. It is found that the environmental performance of OECD countries as a whole has been improved from 1995 to 1997.     

Output–input ratio analysis and DEA frontier

Data envelopment analysis (DEA) is a mathematical programming technique for identifying efficient frontiers for peer decision making units (DMUs). The ability of identifying frontier DMUs prior to the DEA calculation is of extreme importance to an effective and efficient DEA computation. In this paper, we present mathematical properties which characterize the inherent relationships between DEA frontier DMUs and output–input ratios. It is shown that top-ranked performance by ratio analysis is a DEA frontier point. This in turn allows identification of membership of frontier DMUs without solving a DEA program. Such finding is useful in streamlining the solution of DEA.     

Estimation of potential gains from mergers in multiple periods: a comparison of stochastic frontier analysis and Data Envelopment Analysis

A new dynamic Data Envelopment Analysis (DEA) approach is created to provide valuable managerial insights when assessing the merger performance. This new approach allows us to dynamically evaluate the pre-merger firms and the post-merger firm in a multi-period situation. A case study of bank branch merger is conducted to illustrate and validate the proposed approach. Both stochastic frontier analysis and data envelopment analysis are used and compared leading to highly correlated results. The computation show that merger results in an overall efficiency achievement in a banking industry.     

Avoiding infeasibility in DEA models with weight restrictions

The flexibility of weights assigned to inputs and outputs is a key aspect of DEA modeling. However, excessive weight variability and implausible weight values have led to the development of DEA models that incorporate weight restrictions, reflecting expert judgment. This in turn has created problems of infeasibility of the corresponding linear programs. We provide an existence theorem that establishes feasibility conditions for DEA multiplier programs with weight restrictions. We then propose a linear model that tests for feasibility and a nonlinear model that provides minimally acceptable adjustments to the original restrictions that render the program feasible. The analysis can be applied to restrictions on weight ratios, or to restrictions on virtual inputs or outputs.     

Pricing decision-making units

In this note we extend the standard DEA paradigm to address the question of how one can price DMUs (decision-making units). To do this we use an adjoint transformation to the technology generated by these DMUs which links to traditional linear programming theory of the firm and is similar to pricing portfolios in financial markets. We also provide a numerical example illustrating the practicality of the proposed method.     

DEA models for resource reallocation and production input/output estimation

This paper discusses the “inverse” data envelopment analysis (DEA) problem with preference cone constraints. An inverse DEA model can be used for a decision making unit (DMU) to estimate its input/output levels when some or all of its input/output entities are revised, given its current DEA efficiency level. The extension of introducing additional preference cones to the previously developed inverse DEA model allows the decision makers to incorporate their preferences or important policies over inputs/outputs into the production analysis and resource allocation process. We provide the properties of the inverse DEA problem through a discussion of its related multi-objective and weighted sum single-objective programming problems. Numerical examples are presented to illustrate the application procedure of our extended inverse DEA model. In particular, we demonstrate how to apply the model to the case of a local home electrical appliance group company for its resource reallocation decisions.