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

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

Data envelopment analysis with missing data

A first systematic attempt to use data containing missing values in data envelopment analysis (DEA) is presented. It is formally shown that allowing missing values into the data set can only improve estimation of the best-practice frontier. Technically, DEA can automatically exclude the missing data from the analysis if blank data entries are coded by appropriate numerical values.     

Data envelopment analysis with stochastic data

Data envelopment analysis (DEA) has proven to be a useful technique in evaluating the efficiency of decision making units that produce multiple-outputs using multiple-inputs. However, the ability to estimate efficiency reliably is hampered in the presence of measurement error and other statistical noise. A main and legitimate criticism of all deterministic models is the inability to separate out measurement error from inefficiency, both of which are unobserved. In this paper, we consider panel data models of efficiency estimation. One DEA model that has been used averages cross-sectional efficiency estimates across time and has been shown to work relatively well. In this paper, it is shown that this approach leads to biased efficiency estimates and provide an alternative model that corrects this problem. The approaches are compared using simulated data for illustrative purposes.     

Data envelopment analysis with imprecise data

In original data envelopment analysis (DEA) models, inputs and outputs are measured by exact values on a ratio scale. Cooper et al. [Management Science, 45 (1999) 597–607] recently addressed the problem of imprecise data in DEA, in its general form. We develop in this paper an alternative approach for dealing with imprecise data in DEA. Our approach is to transform a non-linear DEA model to a linear programming equivalent, on the basis of the original data set, by applying transformations only on the variables. Upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations. It is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post-DEA model and the endurance indices. We then proceed still further in formulating another post-DEA model for determining input thresholds that turn an inefficient unit to an efficient one.     

Data envelopment analysis and university selection

This paper is concerned with the process of performance measurement undertaken by different stakeholders in the UK higher education sector, focusing on the perspective of the potential student. The appropriateness of the Times League Table in guiding applicants choices is considered, and a case study of applicants at a comprehensive school reported on. The contribution of data envelopment analysis as a decision support technique which can produce customised individual league tables to inform the potential student in his/her choice is illustrated.     

Multiple objective data envelopment analysis as applied to the Indian Pharmaceutical Industry

The change of Intellectual Property Protection (IPP) from a softer process patenting to a stronger product patenting in Indian Pharmaceutical Industry (IPI) is attracting many global drug majors to source their production from India, which is the fourth largest producer of pharmaceuticals in the world. In this paper, the interests of different stake holders like the buyers (multinational enterprises), who are searching for efficient partners and the vendors (Indian drug producers) that are competing for the contracts, are analysed for a suitable efficiency evaluation criterion. The primary objective of this paper is to study how various firms in the IPI with different business strategies, competing for the same opportunities can find suitable benchmarking peer groups to meet the challenges of a dynamic business environment using data envelopment analysis (DEA). A multiple objective DEA model that determines suitable peer groups for inefficient companies is discussed along with more traditional DEA models. The proposed model has the flexibility to include inputs like R&D expenditure and outputs like Exports that are not homogeneously distributed across the firms and address the interests of various stake holders like buyers and vendors simultaneously.     

Data envelopment scenario analysis with imprecise data

In the existing DEA models, we have a centralized decision maker (DM) who supervises all the operating units. In this paper, we solve a problem in which the centralized DM encounters limited or constant resources for total inputs or total outputs. We establish a DEA target model that solves and deals with such a situation. In our model, we consider the decrease of total input consumption and the increase of total output production; however, in the existing DEA models, total output production is guaranteed not to decrease. Considering the importance of imprecise data in organizations, we define our model so as to deal with interval and ordinal data. A numerical illustration is provided to show the application of our model and the advantages of our approach over the previous one.     

Data envelopment analysis models of investment funds

This paper develops theory missing in the sizable literature that uses data envelopment analysis to construct return-risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it. It identifies relationships between diversification, coherent measures of risk and stochastic dominance. It shows how the iterative procedure makes a practical difference using monthly returns of 30 hedge funds over the same time period. It discusses possible shortcomings of the procedure and offers directions for future research.     

Data envelopment scenario analysis for setting targets to electricity generating plants

The development of viable and challenging performance measurement systems in multi-unit organisations receives increased attention in recent years. Performance is no longer viewed as a static phenomenon that reflects the past history of operating systems. There is increasing appreciation for the value of performance scenarios which can be used to guide management for the expected performance consequences of alternative policies. In this paper we demonstrate how data envelopment analysis can be used to develop policy making scenarios that would enable managers to identify the response of productive units such as power plants to different priorities regarding demand of services, costs and pollution emissions.     

Data envelopment analysis,operational research and uncertainty

This paper discusses a number of applications of data envelopment analysis and the nature of uncertainty in those applications. It then reviews the key approaches to handling uncertainty in data envelopment analysis (DEA) (imprecise DEA, bootstrapping, Monte Carlo simulation and chance constrained DEA) and considers their suitability for modelling the applications. The paper concludes with suggestions about the challenges facing an operational research analyst in applying DEA in real-world situations.     

Data envelopment analysis with nonlinear virtual inputs and outputs

An underlying assumption in DEA is that the weights coupled with the ratio scales of the inputs and outputs imply linear value functions. In this paper, we present a general modeling approach to deal with outputs and/or inputs that are characterized by nonlinear value functions. To this end, we represent the nonlinear virtual outputs and/or inputs in a piece-wise linear fashion. We give the CCR model that can assess the efficiency of the units in the presence of nonlinear virtual inputs and outputs. Further, we extend the models with the assurance region approach to deal with concave output and convex input value functions. Actually, our formulations indicate a transformation of the original data set to an augmented data set where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. To underline the usefulness of such a new development, we revisit a previous work of one of the authors dealing with the assessment of the human development index on the light of DEA.     

Data envelopment analysis with heterogeneous data: an application

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

On the quality of the data envelopment analysis model

The user of data envelopment analysis (DEA) has little available guidance on model quality. The technique offers none of the misspecification tests or goodness of fit statistics developed for parametric statistical methods. Yet, if a DEA model is to guide managerial policy, the quality of the model is of crucial importance. This paper suggests four alternative purposes of DEA modelling, and offers four measures of the quality of a DEA model which reflect those purposes. Using Monte Carlo simulation methods, it explores the performance of DEA under a wide variety of assumptions. It notes that four issues will have an important influence on model results: the distribution of true efficiencies in the study sample; the size of the sample; the number of inputs and outputs included in the analysis; and the degree of correlation between inputs and outputs. The paper concludes that any judgement about the reliability of model results must be dependent on the objective of the analysis.     

Preface to topics in data envelopment analysis

This paper serves as an introduction to a series of three papers which are directed to different aspects of DEA (Data Envelopment Analysis) as follows: (1) uses and extensions of window analyses' to study DEA efficiency measures with an illustrative applications to maintenance activities for U.S. Air Force fighter wings, (2) a comparison of DEA and regression approaches to identifying and estimating, sources of inefficiency by means of artificially generated data, and (3) an extension of ordinary (linear programming) sensitivity analyses to deal with special features that require attention in DEA. Background is supplied in this introductory paper with accompanying proofs and explanations to facilitate understanding of what DEA provides in the way of underpinning for the papers that follow. An attempt is made to bring readers abreast of recent progress in DEA research and uses. A synoptic history is presented along with brief references to related work, and problems requiring attention are also indicated and possible research approaches also suggested.This research was partly supported by the National Science Foundation and USARI Contract MDA 903-83-K0312, with the Center for Cybernetic Studies, the University of Texas at Austin. It was also partly supported by the IC² Institute at the University of Texas at Austin. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Data envelopment analysis based decision model for optimal operator allocation in CMS

This paper presents a decision making approach based on data envelopment analysis (DEA) for determining the most efficient number of operators and the efficient measurement of labor assignment in cellular manufacturing system (CMS). The DEA approach is performed by employing the average lead time, the average operator utilization as the output variables and using the number of operators, transfer batch size, demand level as the input variables. Both inputs and outputs are procured by means of simulation of CMS. The objective is to determine the labor assignment in CMS environment.     

Data envelopment analysis of mutual funds based on second-order stochastic dominance

Although data envelopment analysis (DEA) has been extensively used to assess the performance of mutual funds (MF), most of the approaches overestimate the risk associated to the endogenous benchmark portfolio. This is because in the conventional DEA technology the risk of the target portfolio is computed as a linear combination of the risk of the assessed MF. This neglects the important effects of portfolio diversification. Other approaches based on mean–variance or mean–variance–skewness are non-linear. We propose to combine DEA with stochastic dominance criteria. Thus, in this paper, six distinct DEA-like linear programming (LP) models are proposed for computing relative efficiency scores consistent (in the sense of necessity) with second-order stochastic dominance (SSD). The aim is that, being SSD efficient, the obtained target portfolio should be an optimal benchmark for any rational risk-averse investor. The proposed models are compared with several related approaches from the literature.     

Data envelopment analysis with common weights: the compromise solution approach

A characteristic of data envelopment analysis (DEA) is to allow individual decision-making units (DMUs) to select the factor weights that are the most advantageous for them in calculating their efficiency scores. This flexibility in selecting the weights, on the other hand, deters the comparison among DMUs on a common base. In order to rank all the DMUs on the same scale, this paper proposes a compromise solution approach for generating common weights under the DEA framework. The efficiency scores calculated from the standard DEA model are regarded as the ideal solution for the DMUs to achieve. A common set of weights which produces the vector of efficiency scores for the DMUs closest to the ideal solution is sought. Based on the generalized measure of distance, a family of efficiency scores called ‘compromise solutions’ can be derived. The compromise solutions have the properties of unique solution and Pareto optimality not enjoyed by the solutions derived from the existing methods of common weights. An example of forest management illustrates that the compromise solution approach is able to generate a common set of weights, which not only differentiates efficient DMUs but also detects abnormal efficiency scores on a common base.     

A data envelopment approach to decision analysis

A decision aid to assist the development of a linear valuation function for multiple attribute problems is proposed, based on a linear programming formulation using a constraint set structured in a similar manner to data envelopment analysis (DEA). Value functions which favour each decision option are calculated, and efficient, potentially optimal, options identified. These are used to help a decision maker progressively to articulate preferences, indicators of his/her values, in an interactive, structurally flexible manner. As preference indications are provided, candidate value functions and hitherto efficient options inconsistent with his/her declarations are eliminated, thus proceeding towards an explicit value function and, if needed a corresponding complete option order.