Context-dependent data envelopment analysis with cross-efficiency evaluation

To address some problems with the original context-dependent data envelopment analysis (DEA), this paper proposes a new version of context-dependent DEA; this version is based on cross-efficiency evaluations. One of the problems with the original context-dependent DEA is that the attractiveness and progress measures only represent the radial distance between the decision-making unit (DMU) under evaluation and the evaluation context. This representation only shows how distinct the DMU is from a single specific DMU on the evaluation context, not from the entire evaluation context overall. Another problem is that the magnitude of attractiveness and progress scores in the original context-dependent DEA may not have significant meanings. It may not be proper to say that a DMU is more attractive simply because it has a higher attractiveness score for the same reason that the performance of inefficient DMUs cannot be compared with one another simply based on their efficiency scores. We incorporate cross-efficiency evaluations into the context-dependent DEA to overcome the preceding shortcomings of the original context-dependent DEA. We also demonstrate the proposed model's appropriateness and usefulness with an illustrative example.     

Including principal component weights to improve discrimination in data envelopment analysis

This research further develops the combined use of principal component analysis (PCA) and data envelopment analysis (DEA). The aim is to reduce the curse of dimensionality that occurs in DEA when there is an excessive number of inputs and outputs in relation to the number of decision-making units. Three separate PCA–DEA formulations are developed in the paper utilising the results of PCA to develop objective, assurance region type constraints on the DEA weights. The first model applies PCA to grouped data representing similar themes, such as quality or environmental measures. The second model, if needed, applies PCA to all inputs and separately to all outputs, thus further strengthening the discrimination power of DEA. The third formulation searches for a single set of global weights with which to fully rank all observations. In summary, it is clear that the use of principal components can noticeably improve the strength of DEA models.     

Determining common weights in data envelopment analysis based on the satisfaction degree

The traditional data envelopment analysis model allows the decision-making units (DMUs) to evaluate their maximum efficiency values using their most favourable weights. This kind of evaluation with total weight flexibility may prevent the DMUs from being fully ranked and make the evaluation results unacceptable to the DMUs. To solve these problems, first, we introduce the concept of satisfaction degree of a DMU in relation to a common set of weights. Then a common-weight evaluation approach, which contains a max–min model and two algorithms, is proposed based on the satisfaction degrees of the DMUs. The max–min model accompanied by our Algorithm 1 can generate for the DMUs a set of common weights that maximizes the least satisfaction degrees among the DMUs. Furthermore, our Algorithm 2 can ensure that the generated common set of weights is unique and that the final satisfaction degrees of the DMUs constitute a Pareto-optimal solution. All of these factors make the evaluation results more satisfied and acceptable by all the DMUs. Finally, results from the proposed approach are contrasted with those of some previous methods for two published examples: efficiency evaluation of 17 forest districts in Taiwan and R&D project selection.     

Common set of weights in data envelopment analysis: a linear programming problem

Data Envelopment Analysis is used to determine the relative efficiency of Decision Making Units as the ratio of weighted sum of outputs by weighted sum of inputs. To accomplish the purpose, a DEA model calculates the weights of inputs and outputs of each DMU individually so that the highest efficiency can be estimated. Thus, the present study suggests an innovative method using a common set of weights leading to solving a linear programming problem. The method determines the efficiency score of all DMUs and rank them too.     

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.     

Consistent weights for judgements matrices of the relative importance of alternatives

We prove that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent judgements matrices whose entries are the relative importance ratios of alternatives is the geometric mean.     

On the choice of weights profiles in cross-efficiency evaluations

In this paper, we propose a new approach to cross-efficiency evaluation that focuses on the choice of the weights profiles to be used in the calculation of the cross-efficiency scores. It has been claimed in the literature that cross-efficiency eliminates unrealistic weighting schemes in the sense that their effects are cancelled out in the summary that the cross-efficiency evaluation makes. The idea of our approach here is to try to avoid these unreasonable weights instead of expecting that their effects are cancelled out in the amalgamation of weights that is made. To do it, we extend the ideas of the multiplier bound approach to the assessment of efficiency without slacks in Ramón et al. (2010) to its use in cross-efficiency evaluations. The models used look for the profiles with the least dissimilar weights, and also guarantee non-zero weights. In particular, this approach allows the inefficient DMUs to make a choice of weights that prevent them from using unrealistic weighting schemes. We use some examples of the literature to illustrate the performance of this approach and discuss some issues of interest regarding the choice of weights in cross-efficiency evaluations.     

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.     

Prior-Ratio-Analysis procedure to improve data envelopment analysis for performance measurement

This paper proposes the use of a Prior-Ratio-Analysis procedure, analysing output/input ratio indicators, allowing the improvement in efficiency measurement by means of data envelopment analysis (DEA) methodology. This prior analysis is based on the existence of a relationship of individual ratio in the firms to DEA efficiency scores. Use of the proposed procedure allows (i) detection of efficient units whose efficiency could be overestimated and (ii) identification of certain inputs/outputs enhancing particular behaviours. Accordingly, the DEA efficiency analysis could be improved with a major understanding about the factors determining the unit efficiency, and with a measure as a true indicator for discriminating between units, and for ranking them.     

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.     

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 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 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.     

Improving the identification of returns to scale in data envelopment analysis

In order to assess the efficiencies of a set of production units, it is necessary to identify the nature of returns to scale which characterise efficient production. Some methods have been developed to test the nature of the scale elasticity across the full range of scale sizes. However these tests are heavily weighted by the majority of the units and may not identify small ranges of scale size where different returns to scale hold. This paper develops a procedure based on a combination of Data Envelopment Analysis and regression analysis to identify the ranges of scale size where the returns to scale may differ from those in other ranges for the single-output, multi-input case. We also develop a measure of scale size across different input mixes.     

A generalized model for data envelopment analysis with interval data

Data envelopment analysis (DEA) is a method to estimate the relative efficiency of decision-making units (DMUs) performing similar tasks in a production system that consumes multiple inputs to produce multiple outputs. So far, a number of DEA models with interval data have been developed. The CCR model with interval data, the BCC model with interval data and the FDH model with interval data are well known as basic DEA models with interval data. In this study, we suggest a model with interval data called interval generalized DEA (IGDEA) model, which can treat the stated basic DEA models with interval data in a unified way. In addition, by establishing the theoretical properties of the relationships among the IGDEA model and those DEA models with interval data, we prove that the IGDEA model makes it possible to calculate the efficiency of DMUs incorporating various preference structures of decision makers.     

Returns to scale in multiplicative models in data envelopment analysis

One class of models introduced in DEA is called multiplicative models, in which, as shown by Banker and Maindiratta (Manag. Sci. 32:126–135, 1986), the piecewise linear frontiers usually employed in DEA are replaced by a frontier that is piecewise Cobb-Douglas(=log  linear). Banker and Maindiratta (Manag. Sci. 32:126–135, 1986) introduced a model to identify the most productive scale size pattern, and Banker et al. (Eur. J. Oper. Res. 154:345–362, 2004) presented a two-stage method for the identification of returns to scale (RTS) in multiplicative models. In this paper it is shown that both the RTS situation and the MPSS pattern could be determined by a single model in one step. The new method is important in the computational point of view.