Introduction to the theory and application of data envelopment analysis:a foundation text with integrated software

The book aims to introduce the reader to DEA in the most accessible manner possible. It is specifically aimed at those who have had no prior exposure to DEA and wish to learn its essentials, how it works, its key uses, and the mechanics of using it. The latter will include using DEA software. Students on degree or training courses will find the book especially helpful. The same is true of practitioners engaging in comparative efficiency assessments and performance management within their organisation. Examples are used throughout the book to help the reader consolidate the concepts covered. Table of content: List of Tables. List of Figures. Preface. Abbreviations. 1. Introduction to Performance Measurement. 2. Definitions of Efficiency and Related Measures. 3. Data Envelopment Analysis Under Constant Returns to Scale: Basic Principles. 4. Data Envelopment Analysis under Constant Returns to Scale: General Models. 5. Using Data Envelopment Analysis in Practice. 6. Data Envelopment Analysis under Variable Returns to Scale. 7. Assessing Policy Effectiveness and Productivity Change Using DEA. 8. Incorporating Value Judgements in DEA Assessments. 9. Extensions to Basic DEA Models. 10. A Limited User Guide for Warwick DEA Software. Author Index. Topic Index. References.

A mathematical model for dynamic efficiency using data envelopment analysis

In this paper we propose a data envelopment analysis (DEA) based method for assessing the comparative efficiencies of units operating production processes where input-output levels are inter-temporally dependent. One cause of inter-temporal dependence between input and output levels is capital stock which influences output levels over many production periods. Such units cannot be assessed by traditional or 'static' DEA which assumes input-output correspondences are contemporaneous in the sense that the output levels observed in a time period are the product solely of the input levels observed during that same period. The method developed in the paper overcomes the problem of inter-temporal input-output dependence by using input-output 'paths' mapped out by operating units over time as the basis of assessing them. As an application we compare the results of the dynamic and static model for a set of UK universities. The paper is suggested that dynamic model capture the efficiency better than static model. © 2003 Elsevier Inc. All rights reserved.

Efficiency measurement in fuzzy additive data envelopment analysis

Performance evaluation in conventional data envelopment analysis (DEA) requires crisp numerical values. However, the observed values of the input and output data in real-world problems are often imprecise or vague. These imprecise and vague data can be represented by linguistic terms characterised by fuzzy numbers in DEA to reflect the decision-makers' intuition and subjective judgements. This paper extends the conventional DEA models to a fuzzy framework by proposing a new fuzzy additive DEA model for evaluating the efficiency of a set of decision-making units (DMUs) with fuzzy inputs and outputs. The contribution of this paper is threefold: (1) we consider ambiguous, uncertain and imprecise input and output data in DEA, (2) we propose a new fuzzy additive DEA model derived from the a-level approach and (3) we demonstrate the practical aspects of our model with two numerical examples and show its comparability with five different fuzzy DEA methods in the literature. Copyright © 2011 Inderscience Enterprises Ltd.

Introduction to data envelopment analysis and its applications

This chapter provides the theoretical foundation and background on Data Envelopment Analysis (DEA) method and some variants of basic DEA models and applications to various sectors. Some illustrative examples, helpful resources on DEA, including DEA software package, are also presented in this chapter. DEA is useful for measuring relative efficiency for variety of institutions and has its own merits and limitations. This chapter concludes that DEA results should be interpreted with much caution to avoid giving wrong signals and providing inappropriate recommendations.

Optimal design of the renewable energy map of Greece using weighted goal-programming and data envelopment analysis

Renewable energy forms have been widely used in the past decades highlighting a "green" shift in energy production. An actual reason behind this turn to renewable energy production is EU directives which set the Union's targets for energy production from renewable sources, greenhouse gas emissions and increase in energy efficiency. All member countries are obligated to apply harmonized legislation and practices and restructure their energy production networks in order to meet EU targets. Towards the fulfillment of 20-20-20 EU targets, in Greece a specific strategy which promotes the construction of large scale Renewable Energy Source plants is promoted. In this paper, we present an optimal design of the Greek renewable energy production network applying a 0-1 Weighted Goal Programming model, considering social, environmental and economic criteria. In the absence of a panel of experts Data Envelopment Analysis (DEA) approach is used in order to filter the best out of the possible network structures, seeking for the maximum technical efficiency. Super-Efficiency DEA model is also used in order to reduce the solutions and find the best out of all the possible. The results showed that in order to achieve maximum efficiency, the social and environmental criteria must be weighted more than the economic ones.

The Use of Data Envelopment Analysis as Equity Portfolio Selection Criterion in the Finnish Stock Market

This thesis examines the application of data envelopment analysis as an equity portfolio selection criterion in the Finnish stock market during period 2001-2011. A sample of publicly traded firms in the Helsinki Stock Exchange is examined in this thesis. The sample covers the majority of the publicly traded firms in the Helsinki Stock Exchange. Data envelopment analysis is used to determine the efficiency of firms using a set of input and output financial parameters. The set of financial parameters consist of asset utilization, liquidity, capital structure, growth, valuation and profitability measures. The firms are divided into artificial industry categories, because of the industry-specific nature of the input and output parameters. Comparable portfolios are formed inside the industry category according to the efficiency scores given by the DEA and the performance of the portfolios is evaluated with several measures. The empirical evidence of this thesis suggests that with certain limitations, data envelopment analysis can successfully be used as portfolio selection criterion in the Finnish stock market when the portfolios are rebalanced at annual frequency according to the efficiency scores given by the data envelopment analysis. However, when the portfolios were rebalanced every two or three years, the results are mixed and inconclusive.

Green supplier selection via Multiple Criteria Data Envelopment Analysis

An appropriate supplier selection and its profound effects on increasing the competitive advantage of companies has been widely discussed in supply chain management (SCM) literature. By raising environmental awareness among companies and industries they attach more importance to sustainable and green activities in selection procedures of raw material providers. The current thesis benefits from data envelopment analysis (DEA) technique to evaluate the relative efficiency of suppliers in the presence of carbon dioxide (CO2) emission for green supplier selection. We incorporate the pollution of suppliers as an undesirable output into DEA. However, to do so, two conventional DEA model problems arise: the lack of the discrimination power among decision making units (DMUs) and flexibility of the inputs and outputs weights. To overcome these limitations, we use multiple criteria DEA (MCDEA) as one alternative. By applying MCDEA the number of suppliers which are identified as efficient will be decreased and will lead to a better ranking and selection of the suppliers. Besides, in order to compare the performance of the suppliers with an ideal supplier, a “virtual” best practice supplier is introduced. The presence of the ideal virtual supplier will also increase the discrimination power of the model for a better ranking of the suppliers. Therefore, a new MCDEA model is proposed to simultaneously handle undesirable outputs and virtual DMU. The developed model is applied for green supplier selection problem. A numerical example illustrates the applicability of the proposed model.

Input Aggregation in Models of Data Envelopment Analysis: A Statistical Test with an Application to Indian Manufacturing

A problem frequently encountered in Data Envelopment Analysis (DEA) is that the total number of inputs and outputs included tend to be too many relative to the sample size. One way to counter this problem is to combine several inputs (or outputs) into (meaningful) aggregate variables reducing thereby the dimension of the input (or output) vector. A direct effect of input aggregation is to reduce the number of constraints. This, in its turn, alters the optimal value of the objective function. In this paper, we show how a statistical test proposed by Banker (1993) may be applied to test the validity of a specific way of aggregating several inputs. An empirical application using data from Indian manufacturing for the year 2002-03 is included as an example of the proposed test.

A Bootstrap-Regression Procedure to Capture Unit Specific Effects in Data Envelopment Analysis

The Data Envelopment Analysis (DEA) efficiency score obtained for an individual firm is a point estimate without any confidence interval around it. In recent years, researchers have resorted to bootstrapping in order to generate empirical distributions of efficiency scores. This procedure assumes that all firms have the same probability of getting an efficiency score from any specified interval within the [0,1] range. We propose a bootstrap procedure that empirically generates the conditional distribution of efficiency for each individual firm given systematic factors that influence its efficiency. Instead of resampling directly from the pooled DEA scores, we first regress these scores on a set of explanatory variables not included at the DEA stage and bootstrap the residuals from this regression. These pseudo-efficiency scores incorporate the systematic effects of unit-specific factors along with the contribution of the randomly drawn residual. Data from the U.S. airline industry are utilized in an empirical application.

Managing service productivity using data envelopment analysis

This chapter provides the theoretical foundation and background on data envelopment analysis (DEA) method. We first introduce the basic DEA models. The balance of this chapter focuses on evidences showing DEA has been extensively applied for measuring efficiency and productivity of services including financial services (banking, insurance, securities, and fund management), professional services, health services, education services, environmental and public services, energy services, logistics, tourism, information technology, telecommunications, transport, distribution, audio-visual, media, entertainment, cultural and other business services. Finally, we provide information on the use of Performance Improvement Management Software (PIM-DEA). A free limited version of this software and downloading procedure is also included in this chapter.

A new fuzzy additive model for determining the common set of weights in Data Envelopment Analysis

The main advantage of Data Envelopment Analysis (DEA) is that it does not require any priori weights for inputs and outputs and allows individual DMUs to evaluate their efficiencies with the input and output weights that are only most favorable weights for calculating their efficiency. It can be argued that if DMUs are experiencing similar circumstances, then the pricing of inputs and outputs should apply uniformly across all DMUs. That is using of different weights for DMUs makes their efficiencies unable to be compared and not possible to rank them on the same basis. This is a significant drawback of DEA; however literature observed many solutions including the use of common set of weights (CSW). Besides, the conventional DEA methods require accurate measurement of both the inputs and outputs; however, crisp input and output data may not relevant be available in real world applications. This paper develops a new model for the calculation of CSW in fuzzy environments using fuzzy DEA. Further, a numerical example is used to show the validity and efficacy of the proposed model and to compare the results with previous models available in the literature.

Fuzzy data envelopment analysis:a discrete approach

Data envelopment analysis (DEA) as introduced by Charnes, Cooper, and Rhodes (1978) is a linear programming technique that has widely been used to evaluate the relative efficiency of a set of homogenous decision making units (DMUs). In many real applications, the input-output variables cannot be precisely measured. This is particularly important in assessing efficiency of DMUs using DEA, since the efficiency score of inefficient DMUs are very sensitive to possible data errors. Hence, several approaches have been proposed to deal with imprecise data. Perhaps the most popular fuzzy DEA model is based on a-cut. One drawback of the a-cut approach is that it cannot include all information about uncertainty. This paper aims to introduce an alternative linear programming model that can include some uncertainty information from the intervals within the a-cut approach. We introduce the concept of "local a-level" to develop a multi-objective linear programming to measure the efficiency of DMUs under uncertainty. An example is given to illustrate the use of this method.

Data envelopment analysis model for the appraisal and relative performance evaluation of nurses at an intensive care unit

The appraisal and relative performance evaluation of nurses are very important and beneficial for both nurses and employers in an era of clinical governance, increased accountability and high standards of health care services. They enhance and consolidate the knowledge and practical skills of nurses by identification of training and career development plans as well as improvement in health care quality services, increase in job satisfaction and use of cost-effective resources. In this paper, a data envelopment analysis (DEA) model is proposed for the appraisal and relative performance evaluation of nurses. The model is validated on thirty-two nurses working at an Intensive Care Unit (ICU) at one of the most recognized hospitals in Lebanon. The DEA was able to classify nurses into efficient and inefficient ones. The set of efficient nurses was used to establish an internal best practice benchmark to project career development plans for improving the performance of other inefficient nurses. The DEA result confirmed the ranking of some nurses and highlighted injustice in other cases that were produced by the currently practiced appraisal system. Further, the DEA model is shown to be an effective talent management and motivational tool as it can provide clear managerial plans related to promoting, training and development activities from the perspective of nurses, hence increasing their satisfaction, motivation and acceptance of appraisal results. Due to such features, the model is currently being considered for implementation at ICU. Finally, the ratio of the number DEA units to the number of input/output measures is revisited with new suggested values on its upper and lower limits depending on the type of DEA models and the desired number of efficient units from a managerial perspective.

A taxonomy and review of the fuzzy data envelopment analysis literature:two decades in the making

Data envelopment analysis (DEA) is a methodology for measuring the relative efficiencies of a set of decision making units (DMUs) that use multiple inputs to produce multiple outputs. Crisp input and output data are fundamentally indispensable in conventional DEA. However, the observed values of the input and output data in real-world problems are sometimes imprecise or vague. Many researchers have proposed various fuzzy methods for dealing with the imprecise and ambiguous data in DEA. In this study, we provide a taxonomy and review of the fuzzy DEA methods. We present a classification scheme with four primary categories, namely, the tolerance approach, the a-level based approach, the fuzzy ranking approach and the possibility approach. We discuss each classification scheme and group the fuzzy DEA papers published in the literature over the past 20 years. To the best of our knowledge, this paper appears to be the only review and complete source of references on fuzzy DEA. © 2011 Elsevier B.V. All rights reserved.

An integer-valued data envelopment analysis model with bounded outputs

Integer-valued data envelopment analysis (DEA) with alternative returns to scale technology has been introduced and developed recently by Kuosmanen and Kazemi Matin. The proportionality assumption of their introduced "natural augmentability" axiom in constant and nondecreasing returns to scale technologies makes it possible to achieve feasible decision-making units (DMUs) of arbitrary large size. In many real world applications it is not possible to achieve such production plans since some of the input and output variables are bounded above. In this paper, we extend the axiomatic foundation of integer-valuedDEAmodels for including bounded output variables. Some model variants are achieved by introducing a new axiom of "boundedness" over the selected output variables. A mixed integer linear programming (MILP) formulation is also introduced for computing efficiency scores in the associated production set. © 2011 The Authors. International Transactions in Operational Research © 2011 International Federation of Operational Research Societies.