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.     

Quadratic data envelopment analysis

Data Envelopment Analysis (DEA) offers a piece-wise linear approximation of the production frontier. The approximation tends to be poor if the true frontier is not concave, eg in case of economies of scale or of specialisation. To improve the flexibility of the DEA frontier and to gain in empirical fit, we propose to extend DEA towards a more general piece-wise quadratic approximation, called Quadratic Data Envelopment Analysis (QDEA). We show that QDEA gives statistically consistent estimates for all production frontiers with bounded Hessian eigenvalues. Our Monte-Carlo simulations suggest that QDEA can substantially improve efficiency estimation in finite samples relative to standard DEA models.     

Transconcave data envelopment analysis

Transconcave data envelopment analysis (TDEA) extends standard data envelopment analysis (DEA), in order to account for non-convex production technologies, such as those involving increasing returns-to-scale or diseconomies of scope. TDEA introduces non-convexities by transforming the range and the domain of the production frontier, thus replacing the standard assumption that the production frontier is concave with the more general assumption that the frontier is concave transformable. TDEA gives statistically consistent estimates for all monotonically increasing and concave transformable frontiers. In addition, Monte Carlo simulations suggest that TDEA can substantially improve inefficiency estimation in small samples compared to the standard Banker, Charnes and Cooper model and the full disposable hull model (FDH).     

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.     

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.     

Benefit-cost analysis using data envelopment analysis

Benefit-cost analysis is required by law and regulation throughout the federal government. Robert Dorfman (1996) declares ‘Three prominent shortcomings of benefit-cost analysis as currently practiced are (1) it does not identify the population segments that the proposed measure benefits or harms (2) it attempts to reduce all comparisons to a single dimension, generally dollars and cents and (3) it conceals the degree of inaccuracy or uncertainty in its estimates.’ The paper develops an approach for conducting benefit-cost analysis derived from data envelopment analysis (DEA) that overcomes each of Dorfman's objections. The models and methodology proposed give decision makers a tool for evaluating alternative policies and projects where there are multiple constituencies who may have conflicting perspectives. This method incorporates multiple incommensurate attributes while allowing for measures of uncertainty. An application is used to illustrate the method. This work was funded by grant N00014-99-1-0719 from the Office of Naval Research     

Data envelopment analysis applied to quality in primary health care

The performance of primary care should ultimately be judged on its effect on the health outcome of individual patients. However, for the foreseeable future, it is inconceivable that the outcome data necessary to come to a judgement on performance will be available. And in any case, specification of the statistical model necessary to analyze outcome is fraught with difficulty. This paper therefore sets out a model of primary care performance which is based on the premise that certain measurable quality indicators can act as proxies for outcome. This being the case, a model of performance can be deduced which takes into account the effect of resources and patient characteristics on outcome. The most appropriate analytic technique to make this model operational is data envelopment analysis (DEA). It is argued that DEA can handle multiple dimensions of performance more comfortably, and is less vulnerable to the misspecification bias that afflicts statistically based models. The issues are illustrated with an example from English Family Health Service Authorities.     

A multiple criteria approach to data envelopment analysis

In this paper, we present a Multiple Criteria Data Envelopment Analysis (MCDEA) model which can be used to improve discriminating power of DEA methods and also effectively yield more reasonable input and output weights without a priori information about the weights. In the proposed model, several different efficiency measures, including classical DEA efficiency, are defined under the same constraints. Each measure serves as a criterion to be optimized. Efficiencies are then evaluated under the framework of multiple objective linear programming (MOLP). The method is illustrated through three examples in which data sets are taken from previous research on DEA's discriminating power and weight restriction.     

Time substitution with application to data envelopment analysis

In this paper we analyze resource allocation distinguishing between the decision of when to begin allocation and over how many periods to apply the resources. We present analytical results for specific production technologies under different returns to scale assumptions, under capacity constraints and for production with technical change. Using a dynamic activity analysis framework we show how to compute in general optimal solutions for resource intensity use.     

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.     

Theory of integer-valued data envelopment analysis

Conventional data envelopment analysis (DEA) models assume real-valued inputs and outputs. In many occasions, some inputs and/or outputs can only take integer values. In some cases, rounding the DEA solution to the nearest whole number can lead to misleading efficiency assessments and performance targets. This paper develops the axiomatic foundation for DEA in the case of integer-valued data, introducing new axioms of “natural disposability” and “natural divisibility”. We derive a DEA production possibility set that satisfies the minimum extrapolation principle under our refined set of axioms. We also present a mixed integer linear programming formula for computing efficiency scores. An empirical application to Iranian university departments illustrates the approach.     

Equivalent solutions to additive two-stage network data envelopment analysis

In the additive approach of two-stage network data envelopment analysis (DEA), the non-linear DEA model is transformed into a parametric linear model and then solved by computing a series of linear programs. Lim and Zhu (2013; Integrated data envelopment analysis: Global vs. local optimum.European Journal of Operational Research, 229(1), 276–278) and Ang and Chen (2016; Pitfalls of decomposition weights in the additive multi-stage DEA model. Omega, 58, 139–153) propose two parametric linear approaches to solve additive two-stage network DEA model. The current study shows that the two approaches are equivalent and use the same parameter in searching for the global optimal solution.     

Variables reduction in data envelopment analysis

In real applications of data envelopment analysis (DEA), there are a number of pitfalls that could have a major influence on the efficiency. Some of these pitfalls are avoidable and the others remain problematic. One of the most important pitfalls that the researchers confront is the closeness of the number of operational units and the number of inputs and outputs. In performance measurement using DEA, the closeness of these two numbers could yield a large number of efficient units. In this article, some inputs or outputs will be aggregated and the number of inputs and outputs are reduced iteratively. Numerical examples show that in comparison to the single DEA method, our approach has the fewest efficient units. This means that our approach has a superior ability to discriminate the performance of the DMUs.     

E-DEA: Enhanced data envelopment analysis

Data envelopment analysis (DEA) has enjoyed a wide range of acceptance by researchers and practitioners alike as an instrument of performance analysis and management since its introduction in 1978. Many formulations and thousands of applications of DEA have been reported in a considerable variety of academic and professional journals all around the world. Almost all of the formulations and applications have basically centered at the concept of “relative self-evaluation”, whether they are single or multi-stage applications. This paper suggests a framework for enhancing the theory of DEA through employing the concept of “relative cross-evaluation” in a multi-stage application context. Managerial situations are described where such enhanced-DEA (E-DEA) formulations had actually been used and could also be potentially most meaningful and useful.     

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.     

Interactive classification using data envelopment analysis

In this paper, we illustrate how data envelopment analysis (DEA) can be used to aid interactive classification. We assume that the scoring function for the classification problem is known. We use DEA to identify difficult to classify cases from a database and present them to the decision-maker one at a time. The decision-maker assigns a class to the presented case and based on the decision-maker class assignment, a tradeoff cutting plane is drawn using the scoring function and decision-maker’s input. The procedure continues for finite number of iterations and terminates with the final discriminant function. We also show how a hybrid DEA and mathematical programming approach can be used when user interaction is not desired. For non-interactive case, we compare a hybrid DEA and mathematical programming based approach with several statistical and machine learning approaches, and show that the hybrid approach provides competitive performance when compared to the other machine learning approaches.