Data Envelopment Analysis Literature Research Articles

Robust data envelopment analysis with variable budgeted uncertainty

Including uncertainty in data envelopment analysis (DEA) is vital to achieving stable and reliable performance evaluations for the field of operational research as business environments are becoming increasingly volatile and unpredictable. Robust DEA models with budgeted uncertainty have been drawing particular attention in the DEA literature for modelling uncertainties, aiming to obtain robust efficiency scores in a way that guarantees the feasibility of solutions. A concern with such robust DEA models – which has been largely ignored in the literature – is that incorporating high uncertainty levels might result in too conservative efficiency measures, possibly reducing the decision support value of such information. To address this concern, this paper tackles uncertainties by employing variable budgeted uncertainty, which is a generalisation of the budgeted uncertainty. We introduce a novel robust DEA model with variable budgeted uncertainty that is less conservative than extant robust DEA models. Furthermore, we suggest a solution for specifying the probabilistic bounds for constraint violations of the uncertain parameters in robust DEA models. A comparison of the introduced robust DEA model with existing robust DEA models based on a numerical example shows an average reduction in the price of robustness by approximately 20%. Finally, the usefulness and applicability of the suggested model are demonstrated by using a large-scale data set in the context of grocery retailing.

Enchanting performance measurement and management with data envelopment analysis: Insights from bibliometric data visualization and analysis

While the breadth of applicative uses of data envelopment analysis (DEA) has increased over time, this non-parametric frontier methodology has proven effective for measuring how efficient decision-making units (DMUs) are. One of its uses is performance measurement in various organizations — from universities and banks to investment funds and entrepreneurial small and medium-sized enterprises. Following a search inquiry in the Scopus and Web of Science databases, we found no bibliometric analysis and keyword co-occurrence network visualization of just the use of DEA for performance management. With this study, we attempt to investigate the DEA literature for performance measurement and management, considering articles in scientific peer-reviewed journals, which are indexed in the Web of Science database. The analysis and visualization of the bibliometric data are based on 89 articles from the start of the century onward. We present the annual trends of published articles, journals, authors, and countries leading the scientific discussion and citation analysis. A detailed keyword visualization analysis was performed and is discussed in this article alongside the paths for future hotspots of the use of DEA for performance management. The findings have implications for both the academic community and practitioners, business leaders, managers, and policy-makers.

A generalized robust data envelopment analysis model based on directional distance function

In the literature of data envelopment analysis, the directional distance function (DDF) model is commonly used to measure efficiency improvement, as it allows the decision-maker to choose an appropriate direction that permits input contraction and output expansion. However, choosing the right direction is challenging in empirical research. Additionally, efficiency measurement becomes problematic when input and output data are uncertain. To address these issues, we present an equivalent DDF model in multiplier form and use the robust optimization approach to construct a technology in order to develop a generalized robust-DDF measure of efficiency. Among the three commonly used predefined directions (input-oriented, output-oriented, and proportional) considered in this study, we define the robust direction as the one with the minimum price that decision-maker must pay to be immune to data uncertainty. To demonstrate the usefulness of our proposed robust direction measure, we apply it a real-life data on life insurance companies in India over eight years (2011–12–2018–19). Our results show that the proportional direction exhibits the lowest price of robustness and is therefore the most appropriate for measuring potential efficiency improvement. Additionally, the increasing efficiency trend in the life insurance industry confirms the evidence of increased work intensity due to competition resulting from insurance reforms, supporting the competition and X-efficiency hypothesis.

Predicting the performance of MSMEs: a hybrid DEA-machine learning approach

AbstractMicro, small and medium enterprises (MSMEs) dominate the business landscape and create more than half of employment worldwide. How we can apply big data analytical tools such as machine learning to examine the performance of MSMEs has become an important question to provide quicker results and recommend better and more reliable solutions that improve performance. This paper proposes a novel method for estimating a common set of weights (CSW) based on regression analysis for data envelopment analysis (DEA) as an important analytical and operational research technique, which (i) allows for measurement evaluations and ranking comparisons of the MSMEs, and (ii) helps overcome the time-consuming non-convexity issues of other CSW DEA methodologies. Our hybrid approach used several econometric and machine learning techniques (such as Tobit, least absolute shrinkage and selection operator, and Random Forest regression) to empirically explain and predict the performance of more than 5400 Vietnamese MSMEs (2010‒2016), and showed that the machine learning techniques are more efficient and accurate than the econometric ones. Our study, therefore, sheds new light on the two-stage DEA literature, especially in terms of predicting performance in the era of big data to strengthen the role of analytics in business and management.

Data envelopment analysis for scale elasticity measurement in the stochastic case: with an application to Indian banking

In the nonparametric data envelopment analysis literature, scale elasticity is evaluated in two alternative ways: using either the technical efficiency model or the cost efficiency model. This evaluation becomes problematic in several situations, for example (a) when input proportions change in the long run, (b) when inputs are heterogeneous, and (c) when firms face ex-ante price uncertainty in making their production decisions. To address these situations, a scale elasticity evaluation was performed using a value-based cost efficiency model. However, this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data. Therefore, in this study, we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty. An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years (1998–2005) was made to compare inferences about their efficiency and scale properties. The key findings are as follows: First, both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints. However, both models yield the same results at a tolerance level of 0.5, implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks. Second, the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart. Third, public banks exhibit higher efficiency than private and foreign banks. Finally, public and old private banks mostly exhibit either decreasing or constant returns to scale, whereas foreign and new private banks experience either increasing or decreasing returns to scale. Although the application of our proposed stochastic model is illustrative, it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs, which have ample potential for reaping scale and scope benefits.

Evaluation of groups using cooperative game with fuzzy data envelopment analysis

<abstract><p>Data Envelopment Analysis (DEA) is a prominent technique for evaluating the performance and ranking of a set of decision-making units (DMUs) that transform multiple inputs into multiple outputs. However, one of the challenges of the primary DEA models is facing imprecise data in real practical problems. To address this issue, fuzzy DEA have been proposed, which have been successfully applied in many real fields. On the other hand, in some real-world DEA applications, the primary objective of performance evaluation is the ranking of a group that consists of several DMUs that are typically under the control of a centralized management. In this paper, we try to use the theory of cooperative games and Shapley value method as a fair method to solve such games in order to rank groups in DEA. In this way, the resulting rank for groups is based on the average marginal shares of groups in different coalitions that are formed based on the theory of cooperative games. We applied the proposed method to rank groups of airlines considering fuzzy data. To the best of authors' knowledge, so far, no method has been presented in DEA literature for ranking groups in fuzzy environment and using game theory techniques.</p></abstract>

A new method based on finding the weak and strong defining supporting hyperplanes to recognize the anchor points

One of the main important issues in Data Envelopment Analysis (DEA) is to recognize the set of anchor points which is the subset of the extreme efficient points of the production possibility set (PPS). An anchor point is an extreme efficient point which is located on the intersection of the strong efficient frontier and the weak efficient frontier. In the other word, each anchor point delineate the strong efficient frontier from the weak efficient frontier. So, if a decision making unit (DMU) is an anchor point, then there is at least one supporting hyperplane whose the gradient vector has some of zero components, and so some input\output factor does not play any role in the performance of the unit under evaluation. The concept of anchor point was used in DEA for the generation of unobserved DMUs in order to extend the DEA efficient frontier and so, this concept plays a critical role in the DEA theory and its applications. Given the importance of the anchor pints in the DEA literature, this study focuses on finding the anchor points and presents a new method to search the anchor points of the PPS under the variable returns to scale (VRS) assumption. For this purpose, we use the definition of the anchor points and present an approach to find the anchor points of the PPS. The proposed method is based on finding the weak and strong defining supporting hyperplanes passing through the unit under evaluation. The main advantage of the proposed method is that it exactly uses the definition of the anchor points to provide the approach and it is very simple to use and the anchor points can be easily identified by solving two simple models. In addition, the proposed approach is such that in addition to determining the anchor points, it also finds two important defining supporting hyperplanes on the PPS, which can be used in many problems in DEA. The potentially of the proposed method is illustrated by some numerical examples, reported in the literature to compare the proposed method with the existing methods.

Assessing most productive scale size with fuzzy stochastic data envelopment analysis

Classic data envelopment analysis (DEA) is a linear programming method for evaluating the relative efficiency of decision making units (DMUs) that uses multiple inputs to produce multiple outputs. In the classic DEA model inputs and outputs of DMUs are deterministic, while in the real world, are often fuzzy, random, or fuzzy-random. Many researchers have proposed different approaches to evaluate the relative efficiency with fuzzy and random data in DEA. In many studies, the most productive scale size (mpss) of decision making units has been estimated with fuzzy and random inputs and outputs. Also, the concept of fuzzy random variable is used in the DEA literature to describe events or occurrences in which fuzzy and random changes occur simultaneously. This paper has proposed the fuzzy stochastic DEA model to assess the most productive scale size of DMUs that produce multiple fuzzy random outputs using multiple fuzzy random inputs with respect to the possibility-probability constraints. For solving the fuzzy stochastic DEA model, we obtained a nonlinear deterministic equivalent for the probability constraints using chance constrained programming approaches (CCP). Then, using the possibility theory the possibilities of fuzzy events transformed to the deterministic equivalents with definite data. In the final section, the fuzzy stochastic DEA model, proposed model, has been used to evaluate the most productive scale size of sixteen Iranian hospitals with four fuzzy random inputs and two fuzzy random outputs with symmetrical triangular membership functions.

Subsampling bootstrap in network DEA

Data Envelopment Analysis (DEA), provides an empirical estimation of the production frontier, based on an observed sample of decision making units (DMUs). Except for the single input-single output case, the asymptotic distribution of the DEA estimator can only be approximated through bootstrapping approaches. Therefore, bootstrapping techniques have been widely applied in the DEA literature to make statistical inference for the cases when the production process has a single-stage structure. However, in many cases, the transformation of inputs into outputs has an inner structure that needs to be considered. This paper examines the applicability of the subsampling bootstrap procedure in the approximation of the asymptotic distribution of the DEA estimator when the production process has a network structure, and in the presence of undesirable factors. Evidence on the performance of subsampling bootstrap is obtained through Monte Carlo experiments for the case of two-stage series structures, where overall and stage efficiency estimates are calculated using the additive decomposition approach. Results indicate great sensitivity both to the sample and subsample size, as well as to the data generating process. Subsampling methodology is then applied to construct confidence interval estimates for the overall and stage efficiency scores of railways in 22 European countries, where the railway transport process is decomposed into two stages and the railway noise pollution problem is considered as an undesirable output.

Weight profiles in cross-efficiency evaluation based on hypervolume maximization

In this paper, we propose and discuss a new model in order to obtain the weight profiles to be used in the calculation of cross-efficiency scores in Data Envelopment Analysis (DEA). In the standard DEA literature, total flexibility in the selection of weights has been strongly criticized due to the fact that some inputs and/or outputs may have no contribution (zero weights) to the efficiency scores. Although cross evaluation somewhat mitigates the effect of these unrealistic weighting schemes on the amalgamation of weights that standard DEA models produce, we propose a method that ensures strictly positive and balanced weights to be used in cross-efficiency evaluation. In particular, we propose an optimization model based on hypervolume maximization as a method for selecting a suitable weight profile for each evaluated unit to be used in cross-efficiency. The model is solved through Second-Order Cone Programming (SOCP). As a result, the solution obtained is unique and the Production Possibility Set (PPS) is not modified. Another advantage of the proposed method, among others, is that it does not need subjective expert opinions or full-dimension efficient facets of the polyhedral PPS, but if available, it can be easily incorporated into the model. The approach introduced is illustrated through a numerical example. We also present some theoretical results.

New Approach in Fixed Resource Allocation and Target Setting Using Data Envelopment Analysis with Common Set of Weights

One of the mathematical programming techniques is data envelopment analysis (DEA), which is used for evaluating the efficiency of a set of similar decision-making units (DMUs). Fixed resource allocation and target setting with the help of DEA is a subject that has gained much attention from researchers. A new model was proposed by determining a common set of weights (CSW). All DMUs were involved with the aim of achieving higher efficiency in every DMU after the procedure. The minimum resources and targets allocated to each DMU were commensurate to the efficiency of that DMU and the share of DMU in the input resources and the output productions. To examine the proposed method, other methods in the DEA literature were examined as well, and then, the efficiency of the method was demonstrated through a numerical example.

The generalized range adjusted measure in data envelopment analysis: Properties, computational aspects and duality

The measurement of technical efficiency is a topic of great interest in microeconomics and engineering. Data Envelopment Analysis (DEA) is one of the existing techniques for measuring technical efficiency. One of the challenges related to DEA is to introduce a “well-defined” efficiency measure. Overall, it means that the technical efficiency measure should satisfy a list of mathematical and economical properties. Regarding this point, an unresolved question in the DEA literature to date, is whether any measure can satisfy both Indication, also called Pareto-efficiency identification, and uniqueness of the projection point generated by the corresponding efficiency optimization model. With this issue in mind, this paper introduces a new family of measures, inspired on the Range-Adjusted Measure (RAM), which satisfy a list of six properties. This family of measures will be called Generalized Range-Adjusted Measure (GRAM). Additionally, we show in this paper how GRAM can be implemented from a computational point of view and we also provide an economical interpretation of its dual program in terms of (shadow) profit maximization. Finally, an empirical example extracted from the literature serves to illustrate the new methodology.

A box-uncertainty in DEA: A robust performance measurement framework

The problem of assessment of Decision Making Units (DMUs) by using Data Envelopment Analysis (DEA) may not be straightforward due to the data uncertainty. Several studies have been developed to incorporate uncertainty into input/output values in the DEA literature. On the other hand, while traditional DEA models focus more on crisp data, there exist many applications in which data is reported in form of intervals. This paper considers the box-uncertainty in data which means that each input/output value is selected from a symmetric box. This specific type of uncertainty has been addressed as Interval DEA approaches. Our proposed model deals with efficiency evaluation of DMUs with imprecise data in a robust optimization. We assume that inputs and outputs are reported in the form of intervals and propose the robust counterpart problem for the envelopment form of the DEA model. Further, we also develop two ranking methods which have more benefits compared to some existing approaches. An illustrative example is provided to show how the proposed approaches work. An application on hospital efficiency in East Virginia is used to show the usefulness of the proposed approaches.

Implementing strategic disposability for performance evaluation: Innovation, stability, profitability and corporate social responsibility in Chinese banking

The current paper estimates the overall inefficiency indicator of a bank under a network Data Envelopment Analysis (DEA) in the presence of undesirable inputs and outputs. We primarily contribute to the DEA literature in four ways. First, we decompose banks’ overall inefficiency performance indicator into five component indicators, namely, the sub-indicators of innovation, two kinds of stability, profitability and corporate social responsibility. Second, since the proposed model, which is an absolute value optimization problem, does not give the overall inefficiency score directly, we introduce a two-step procedure to obtain all sub-indicator scores and the overall inefficiency score. Third, we extend the by-production framework by proposing not only a concept and interpretation of “strategic disposability” for an intermediate undesirable output in estimating the stability sub-indicators, but also another concept of “strategic disposability” for an intermediate undesirable input in gauging the sub-indicator related to corporate social responsibility. Our results show that 1) the Chinese banking industry has a high level of innovation inefficiency and profitability inefficiency is higher than primary business stability inefficiency, strategic management stability inefficiency and corporate social responsibility inefficiency for all the bank ownership types except the state-owned commercial banks; 2) state-owned commercial banks have a higher level of corporate social responsibility inefficiency compared to the other inefficiencies; 3) state-owned commercial banks, rural commercial banks and joint-stock commercial banks are the best three performers with different ownership types performing well in different perspectives; 4) all different ownership types experience a level of performance volatility over the examined period.

Inverse Frontier-based Benchmarking for Investigating the Efficiency and Achieving the Targets in the Vietnamese Education System

This paper extends the theory of inverse frontier-based benchmarking to address the issue of effectiveness when investigating the efficiency of household expenditure in the case of the Vietnamese education system. Enhancing the conventional efficiency measurement approach by Data Envelopment Analysis (DEA), our study focuses on the derivation of meaningful benchmarks – in terms of the required level of inputs and outputs – for performance improvement. The proposed inverse optimization problem identifies the essential household education expenditures for 63 provincial education systems at different efficiency levels while the university entrance threshold for exam results is satisfied as an effectiveness constraint. The results strongly recommend including this constraint into the action plans of improving the educational achievements in all provinces across Vietnam. Besides revealing policy implications in the specific case, the proposed approach adds to current DEA literature by suggesting complementary measures such as effectiveness and feasibility to strengthen performance assessment.

Evaluating Health System Efficiency using Data Envelopment Analysis: A case of Indian Healthcare System

Purpose-With increased demand and restricted healthcare resources, it becomes important to take a step back and evaluate the efficiency of healthcare delivery. The present study aims to evaluate the health system efficiency of India by benchmarking it against its peers in BRICS countries and against OECD countries. Design/Methodology/Approach: The input and output variables required for measuring the efficiency of healthcare system were identified. A Data Envelopment Analysis (DEA) approach was used and efficiency frontier identified with the rankings of the BRICS and OECD countries. India is thus benchmarked against its peers (BRICS) and against OECD countries. Finding: India was found to operate at the efficiency frontier along with China, Russia, Brazil, and South Africa, however it ranked fourth. When benchmarked against OECD countries, India operates on the efficiency frontier along with Canada, Greece, Japan, Korea, Mexico, Spain, Sweden, Switzerland, Turkey, Great Britain, Chile and Israel. Countries like Germany, United States of America, Czech Republic, Slovakia and Lithuania operate at a lower healthcare efficiency and need to use their resources wisely. Practical/Research Implications: Developing countries like India can look to improve its healthcare system delivery by replicating best practices of healthcare systems from its peers and the top 10 OECD countries. Majority of the OECD countries in the top 10 have implemented universal health coverage, have higher physician and nurse density and higher hospital bed ratios. They are inclined towards branded drugs vis-à-vis generics and have follow evidence based medicine. From a theoretical perspective, it adds to the body of literature of DEA and health system efficiency. Originality/Value: This is a pioneer study that benchmarks India against its peers and against OECD countries drawing unique insights about healthcare efficiency

A literature review of DEA efficiency methodology in defence sector

PropósitoLa mejora de la eficiencia de la gestión pública conduce a un aumento de la calidad de los servicios, impulsando la confianza en las instituciones y generando así un efecto multiplicador. El presente trabajo tiene por objeto actualizar la literatura sobre la metodología frontera de medición de la eficiencia DEA, aplicada al sector de la Defensa.Diseño/metodología/enfoqueA través de este estudio, se relacionan dos áreas principales de investigación: Economía de la Defensa y Análisis de Eficiencia y Productividad. Los métodos frontera para medir la eficiencia técnica se agrupan en paramétricos, no paramétricos y semiparamétricos. La revisión de la literatura DEA en el sector seleccionado permite identificar tres campos de trabajo principales que se discuten en detalle.ResultadosLa investigación empírica existente apenas ha aplicado métodos bootstrap para eliminar el sesgo de las estimaciones. Ningún trabajo empírico ha aplicado un análisis de determinantes de la eficiencia mediante la inclusión de variables exógenas.Originalidad/valorLas repercusiones de la eficiencia en la gestión son numerosas. Se propone una línea de investigación para examinar en qué medida las mejoras de la eficiencia repercuten en la reputación y, por consiguiente, en la imagen y la confianza en las instituciones. También se considera el vínculo entre la Economía de la Defensa y la Economía de la Corrupción.

Project Portfolio Selection under Uncertainty: A DEA Methodology using Predicted and Actual Frontiers

Project portfolio management (PPM) is an important area of interest in many organizations. There is a wide literature on each of many different aspects of PPM. The central purpose of the current paper is to focus on a specific sub-area of PPM, namely the project portfolio selection (PPS) problem. Specifically, we develop a new methodology that will aid management in choosing from a set of candidate project proposals, a subset of those project proposals that align with strategic objectives of the organization. Research methodology is based on the data envelopment analysis (DEA) construct to compare a set of decision making units (such as proposed projects) to arrive at an efficiency score for each member of this competing set, derive the best performers, generate an efficiency frontier and quantify inefficiency in the non-best performers. While DEA has been applied in numerous settings, the unique feature of the project portfolio application is the presence of two sets of data, namely pre-implementation “estimates”, and post-implementation “actuals”. Our methodology is unique in that it uses the idea of dual DEA frontiers based on such before and after data for a set of past projects. Dual frontier concept makes not only an important practical contribution to the PPS literature, but as well it opens new directions and provides an innovative advancement in the DEA literature. The requisite data is not publicly available. We believe, however, that the stand-alone methodology makes an important contribution to both the DEA and PPS literature.

Agricultural loan efficiency in centralized bank supply chains with fairness concern: a DEA-based analysis

PurposeDue to the rapid development and innovation in the Internet-based technology, conventional banks are under pressure and have to compete with Internet-based finance. This has made banks adopt measures to improve operational efficiency and reduce input and increase output.Design/methodology/approachThe authors had proposed a two-stage fairness concern efficiency model based on the classical theory of data envelopment analysis (DEA) and performed an empirical study to measure agricultural loan efficiency in the 20 major Chinese banks.FindingsThe findings of the empirical analysis are as follows: (1) peer-induced fairness concern has no impact on deposit efficiency in a centralized bank supply chain; (2) The China Merchants Bank (CMB) has the third lowest deposit efficiency; (3) monotonicity of loan efficiency with input allocation depends on a bank's ownership structure; (4) efficiency ranks are strongly affected by the fairness concern; (5) most Chinese banks show a low agricultural loan efficiency.Originality/valueThis paper contributes to the literature in several ways. First, to the best of the authors’ knowledge, this is the first attempt to analyze agricultural loan efficiency for a bank supply chain system with the fairness concern. This work reveals the hidden factor that restricts loan efficiency of Chinese banks. Second, the proposed fairness concern two-stage DEA model has shown good ability for full ranking. It can provide a new perspective to the classical DEA literature for ranking decision-making units (DMUs). Third, the authors have demonstrated empirical bank efficiency for the 20 major Chinese banks.

A nonparametric framework to detect outliers in estimating production frontiers

In a large number of organizations, there is an ongoing need to evaluate performance. There is also a need to estimate the production frontier of best performers in such environments. Part of the difficulty in constructing this frontier is that massive amounts of data are generated daily with the result being that the set of best performers is constantly changing. Furthermore, measurement errors can influence datasets as well as the estimation of a production frontier. Outliers can also substantially affect the estimated production frontier. Efforts have been made in the past three decades to deal with datasets that might include such outliers; these methods are mostly semiautomatic or require significant computation time when a large dataset is involved. The few existing research on large datasets also focuses on the computational process of measuring a production frontier without identifying the possible influence of outliers to the estimated frontier. In the current paper, for the first time in the literature of data envelopment analysis (DEA), we develop an automatic framework with the computational capability and accuracy needed when big datasets (with multiple inputs and multiple outputs) are considered. Several examples, simulation experiments, and real-life applications are discussed to demonstrate the power of the proposed framework. A data analysis with illustrative graphs is provided to clearly show the methodology. In terms of estimating the production frontier, the method is robust, user-friendly, and substantially decreases the requirement of user judgment while at the same time allowing for the incorporation of such judgement.