Sensitivity and stability analysis in data envelopment analysis

One of the topics of interest in data envelopment analysis (DEA) is sensitivity and stability and stability analysis of the specific decision making unit (DMU), which is under evaluation. In DEA, efficient DMUs are of primary importance as they define the efficient frontier. In this paper, we develop a new sensitivity analysis approach for the CCR, BCC and Additive models, when variations in the data are considered for a specific efficient DMU and the data for the remaining DMUs are assumed fixed.     

Sensitivity and stability analysis in fuzzy data envelopment analysis

As a useful management and decision tool, data envelopment analysis (DEA) has become a pop area of research. One of the topics of interests in DEA is sensitivity and stability analysis of decision making units (DMUs). Due to the uncertainty of the data in real life, this paper will give some DEA models in fuzzy environment. It is followed by a series analysis of sensitivity and stability for all DMUs. Finally a numerical example will be presented to give an illustration of the sensitivity and stability analysis.     

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.     

Dominance stochastic models in data envelopment analysis

In this paper stochastic models in data envelopment analysis (DEA) are developed by taking into account the possibility of random variations in input-output data, and dominance structures on the DEA envelopment side are used to incorporate the modelbuilder's preferences and to discriminate efficiencies among decision making units (DMUs). The efficiency measure for a DMU is defined via joint dominantly probabilistic comparisons of inputs and outputs with other DMUs and can be characterized by solving a chance constrained programming problem. Deterministic equivalents are obtained for multivariate symmetric random errors and for a single random factor in the production relationships. The goal programming technique is utilized in deriving linear deterministic equivalents and their dual forms. The relationship between the general stochastic DEA models and the conventional DEA models is also discussed.     

Sensitivity analysis of inefficient units in data envelopment analysis

One important issue in DEA which has been studied by many DEA researchers is the sensitivity of the results of an analysis to perturbations in the data.This paper develops a procedure for performing a sensitivity analysis of the inefficient decision making units (DMUs). The procedure yields an exact “Necessary Change Region” in which the efficiency score of a specific inefficient DMU changes to a defined efficiency score.In what follows, we identify a new frontier, and prove the efficiency score of each arbitrary unit on it which is defined as the efficiency score.     

Measures of inefficiency in data envelopment analysis and stochastic frontier estimation

This paper discusses recent work in developing scalar measures of inefficiency which (a) comprehend all inefficiencies, including non-zero slacks, and (b) are readily interpretable and easily used in a wide variety of contexts. The opening section of the paper discusses some of the varied contexts in which uses of DEA are now being reported. This provides background for some of these measures. The closing section turns to simulation studies of DEA-regression combinations and possible inefficiency measures. Serious problems of bias in SF (Stochastic Frontier) regression approaches are identified. Extensions and modifications are suggested which can make a development of other inefficiency measures worthwhile for SF extensions to input-specific and multiple output evaluations.     

Sensitivity in data envelopment analysis using an approximate inverse matrix

In this paper, sensitivity analysis of the Charnes–Cooper–Rhodes model in data envelopment analysis (DEA) is studied for the case of perturbation of all outputs and of all inputs of an efficient decision-making unit (DMU). Using an approximate inverse of the perturbed optimal basis matrix, an approximate preservation of efficiency for an efficient DMU under these perturbations is considered. Sufficient conditions for an efficient DMU to preserve its efficiency are obtained in that case. An illustrative example is provided.     

An input relaxation measure of efficiency in stochastic data envelopment analysis

We introduce stochastic version of an input relaxation model in data envelopment analysis (DEA). The input relaxation model, recently developed in DEA, is useful to resource management [e.g. G.R. Jahanshahloo, M. Khodabakhshi, Suitable combination of inputs for improving outputs in DEA with determining input congestion, Appl. Math. Comput. 151(1) (2004) 263–273]. This model allows more changes in the input combinations of decision making units than those in the observed inputs of evaluating decision making units. Using this extra flexibility in input combinations we can find better outputs. We obtain a non-linear deterministic equivalent to this stochastic model. It is shown that under fairly general conditions this non-linear model can be replaced by an ordinary deterministic DEA model. The model is illustrated using a real data set.     

Super-efficiency in stochastic data envelopment analysis: An input relaxation approach

This paper addresses super-efficiency issue based on input relaxation model in stochastic data envelopment analysis. The proposed model is not limited to using the input amounts of evaluating DMU, and one can obtain a total ordering of units by using this method. The input relaxation super-efficiency model is developed in stochastic data envelopment analysis, and its deterministic equivalent, also, is derived which is a nonlinear program. Moreover, it is shown that the deterministic equivalent of the stochastic super-efficiency model can be converted to a quadratic program. As an empirical example, the proposed method is applied to the data of textile industry of China to rank efficient units. Finally, when allowable limits of data variations for evaluating DMU are permitted, the sensitivity analysis of the proposed model is discussed.     

Proactive data envelopment analysis: Effective production and capacity expansion in stochastic environments

Demand fluctuations that cause variations in output levels will affect a firm’s technical inefficiency. To assess this demand effect, a demand-truncated production function is developed and an “effectiveness” measure is proposed. Often a firm can adjust some input resources influencing the output level in an attempt to match demand. We propose a short-run capacity planning method, termed proactive data envelopment analysis, which quantifies the effectiveness of a firm’s production system under demand uncertainty. Using a stochastic programming DEA approach, we improve upon short-run capacity expansion planning models by accounting for the decreasing marginal benefit of inputs and estimating the expected value of effectiveness, given demand. The law of diminishing marginal returns is an important property of production function; however, constant marginal productivity is usually assumed for capacity expansion problems resulting in biased capacity estimates. Applying the proposed model in an empirical study of convenience stores in Japan demonstrates the actionable advice the model provides about the levels of variable inputs in uncertain demand environments. We conclude that the method is most suitable for characterizing production systems with perishable goods or service systems that cannot store inventories.     

随机DEA期望值模型的一些性质

为判别决策单元在随机DEA期望值模型下的随机有效性,首次提出了随机期望无效、随机期望弱有效、随机期望有效以及随机期望超有效的概念．并给出了三个命题用于判别不同显著性水平下随机期望效率与期望效率的关系．在此基础上,得到了两个重要的性质：（1）当期望效率保持不变时,随机期望效率为显著性水平的增函数;（2）当显著性水平保持不变时,随机期望效率为期望效率的增函数．最后,利用随机模拟和一个算例对上述结论进行了验证．     

Chance constrained programming approaches to technical efficiencies and inefficiencies in stochastic data envelopment analysis

This paper replaces ordinary DEA formulations with stochastic counterparts in the form of a series of chance constrained programming models. Emphasis is on technical efficiencies and inefficiencies which do not require costs or prices, but which are nevertheless basic in that the achievement of technical efficiency is necessary for the attainment of ‘allocative’, ‘cost’ and other types of efficiencies.     

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).     

Non-discretionary inputs in data envelopment analysis

The technique for efficiency measurement known as Data Envelopment Analysis (DEA) has been extended to allow non-discretionary inputs that affect production. Several methods exist for measuring efficiency while controlling for these fixed factors of production. This paper reviews these approaches, providing a discussion of strengths and weaknesses and highlighting potential limitations. In addition, a new approach is developed that overcomes existing weaknesses. To facilitate comparison, an analysis using simulated data is performed. The results show that the new approach improves existing models and performs relatively well.     

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.     

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