Accounting for slacks to measure and decompose revenue efficiency in the Spanish Designation of Origin wines with DEA

In this paper, we show how Data Envelopment Analysis (DEA) may be used to measure and decompose revenue inefficiency, taking into account all sources of technical waste in the context of an application to assess the Spanish quality wine sector, in particular Designation of Origin (DO) wines. We try to go beyond the standard approaches, which use Shephard distance functions or directional distance functions, to provide decomposition that incorporates slacks as a source of technical inefficiency. To accomplish this, we will base our analysis on a recent approach introduced in Cooper et al. (2011a). In particular, we show how an output-oriented version of the Weighted Additive model can be used to properly identify revenue, technical, and allocative inefficiencies in Spanish DOs. In the application, we conclude that the main source of revenue inefficiency in this sector is technical waste, and that Cava can be highlighted as the DO that performs as a benchmark for more numbers of units.     

只有输出(入)的DEA改进模型及其应用

研究了只有输出(入)的DEA分析方法,针对只有输出(入)DEA模型的不足,重新定义了只有输出(入)的DEA评价方法的有效性,并改进了模型。相对已有的只有输出(入)的DEA模型,该模型充分利用了决策单元的诸输出(入),提高了DEA评价的效果。作为应用,运用新模型对武警防暴队形优选问题进行了有效性分析。     

Improving envelopment in Data Envelopment Analysis under variable returns to scale

In a Data Envelopment Analysis model, some of the weights used to compute the efficiency of a unit can have zero or negligible value despite of the importance of the corresponding input or output. This paper offers an approach to preventing inputs and outputs from being ignored in the DEA assessment under the multiple input and output VRS environment, building on an approach introduced in Allen and Thanassoulis (2004) for single input multiple output CRS cases. The proposed method is based on the idea of introducing unobserved DMUs created by adjusting input and output levels of certain observed relatively efficient DMUs, in a manner which reflects a combination of technical information and the decision maker’s value judgements. In contrast to many alternative techniques used to constrain weights and/or improve envelopment in DEA, this approach allows one to impose local information on production trade-offs, which are in line with the general VRS technology. The suggested procedure is illustrated using real data.     

On comparing the performance of primary care providers

In the past few years primary health care has been characterised as central to the development of the National Health Service in the United Kingdom. Furthermore, performance assessment is seen as a way of achieving care of high standards. Performance indicators and targets are being developed to assess primary care providers, and to develop financial incentives. However, the number of studies that have compared the performance of primary care providers is limited and the existing approaches to evaluation are open to improvement.     

Efficiency and equity in private and public education: A nonparametric comparison

We present a nonparametric approach for (1) efficiency and (2) equity evaluation in education. Firstly, we use a nonparametric (Data Envelopment Analysis) model that is specially tailored to assess educational efficiency at the pupil level. The model accounts for the fact that typically minimal prior structure is available for the behavior (objectives and feasibility set) under evaluation. It allows for uncertainty in the data, while it corrects for exogenous ‘environmental’ characteristics that are specific to each pupil. Secondly, we propose two multidimensional stochastic dominance criteria as naturally complementary aggregation criteria for comparing the performance of different school types (private and public schools). While the first criterion only accounts for efficiency, the second criterion also takes equity into consideration. The model is applied for comparing private (but publicly funded) and public primary schools in Flanders. Our application finds that no school type robustly dominates another type when controlling for the school environment and taking equity into account. More generally, it demonstrates the usefulness of our nonparametric approach, which includes environmental and equity considerations, for obtaining ‘fair’ performance comparisons in the public sector context.     

The measurement of returns to scale under a simultaneous occurrence of multiple solutions in a reference set and a supporting hyperplane

This research theoretically explores the measurement of RTS (Returns to Scale) under a possible occurrence of multiple solutions in DEA (Data Envelopment Analysis). In this study, the occurrence of multiple solutions is classified into Type I and Type II. Type I is an occurrence of multiple solutions in a reference set. Type II is an occurrence of multiple solutions on a supporting hyperplane passing on the reference set. Both Types I and II are very well known among DEA researchers, but previous research has not sufficiently explored a simultaneous occurrence of Type I and Type II in the RTS measurement. The two types of multiple solutions influence a degree of RTS in the DEA measurement. Such a quantitative issue on RTS is examined from the perspective of the Type I and Type II problems. To deal with such difficulties, a new linear programming approach is proposed to identify all efficient DMUs (Decision Making Units) that consist of a reference set, even if multiple solutions occur on the reference set. Based upon the research result, we can identify when multiple solutions of Type I and/or Type II occur on the RTS measurement and how to deal with such difficulties. Our research result makes it possible to measure a degree of scale economies (RTS) under the simultaneous occurrence of Type I and Type II.     

Review of Methods for Increasing Discrimination in Data Envelopment Analysis

We present a review of methods for increasing discrimination between efficient DMUs in Data Envelopment Analysis. These methods were classified into two groups: those that incorporate a priori information and those that do not use or minimize the use of such a priori information. We also compare these methodologies regarding their specific characteristics.     

Finding strong defining hyperplanes of Production Possibility Set

Production Possibility Set (PPS) is defined as the set of all inputs and outputs of a system in which inputs can produce outputs. Data Envelopment Analysis models implicitly use PPS to evaluate relative efficiency of Decision Making Units (DMUs). Although DEA models can determine the efficiency of a DMU, they cannot present efficient frontiers of PPS. In this paper, we propose a method for finding all Strong Defining Hyperplanes of PPS (SDHP). They are equations that form efficient surfaces. These equations are useful in Sensitivity and Stability Analysis, the status of Returns to Scale of a DMU, incorporating performance information into the efficient frontier analysis and so on.     

Efficiency analysis to incorporate interval-scale data

We develop an approach to efficiency analysis to enable us to incorporate interval-scale data in addition to ratio-scale data. Our approach introduces a measure of inefficiency and identifies efficient units as is done in Data Envelopment Analysis. The basic idea in our approach is to find the “best” hyperplane separating the units that are better and worse than each unit. “Best” is defined in such a way that the number of not-better units is maximal. The efficiency measure is defined as a proportion of not-better units to all units. The results are invariant under a strictly increasing linear re-scaling of any input- or output-variables. Thus zeroes or negative values do not cause problems for the analysis. The approach is used to analyze the data of the research evaluation exercise recently carried out at the University of Joensuu, Finland.     

Optimizing the rank position of the DMU as secondary goal in DEA cross-evaluation

Cross-efficiency evaluation is an extension of Data Envelopment Analysis (DEA) that permits not only the determination of a ranking of Decision Making Units (DMUs) but also the elimination of unrealistic weighting schemes, thereby rescinding the necessity for the inclusion of individual judgements in the models. The main deficiency of the procedure is the non-uniqueness of the optimal weights, which results in the peer evaluations dependences, for instance, on the software used to determine DMU’s efficiencies. This shortfall justifies the inclusion of secondary goals in order to determine cross-efficiency values. In this paper a new proposal of a secondary goal is studied. The idea is related with that proposed in Wu et al. (2009), in which the objective is the optimization of the rank position of the DMU under evaluation. In the procedure proposed here, an incentive to break level-pegging ties between alternatives is introduced by considering that efficiency scores induce a weak order of alternatives. The model is illustrated with a preference-aggregation application.     

权有附加约束的条件下的DEA有效性(C2R或C2GS2)

有关判别决策单元在权有附加约束的条件下是否DEA有效（C^2或C^2GS^2)，本文给出了一种基于权有附加约束条件下的加性模型的不同于文献[1]与[2]的约束与差别法。     

Nonparametric estimation of education productivity incorporating nondiscretionary inputs with an application to Dutch schools

In this paper we develop a Malmquist productivity index for public sector production characterized by the influence of environmental variables. We extend Johnson and Ruggiero (2011) to the more general case of variable returns to scale to further decompose the Malmquist productivity index into technical, efficiency, scale and environmental change. We apply our model to analyze productivity of Dutch schools using 2002–2007 data. The results indicate that the environment influences the productivity index as well as the technical, efficiency, scale and environmental change components. We see that schools with a moderate classification of environment have the highest productivity numbers. In line with expectations, schools with the worst environment also perform worse and would perform better with an improved environment.     

Ranking ranges in cross-efficiency evaluations

The existence of alternate optima for the DEA weights may reduce the usefulness of the cross-efficiency evaluation, since the ranking provided depends on the choice of weights that the different DMUs make. In this paper, we develop a procedure to carry out the cross-efficiency evaluation without the need to make any specific choice of DEA weights. The proposed procedure takes into consideration all the possible choices of weights that all the DMUs can make, and yields for each unit a range for its possible rankings instead of a single ranking. This range is determined by the best and the worst rankings that would result in the best and the worst scenarios of each unit across all the DEA weights of all the DMUs. This approach might identify good/bad performers, as those that rank at the top/bottom irrespective of the weights that are chosen, or units that outperform others in all the scenarios. In addition, it may be used to analyze the stability of the ranking provided by the standard cross-efficiency evaluation.     

Improvements by analyzing the efficient frontier in DEA

In this paper, we suggest four types of improvements for making inefficient DMUs efficient in the CCR model with the minimal change of input and output values. Moreover, we propose an algorithm for calculating such improvements by applying quadratic programming techniques. Furthermore, since all equations constructing the efficient frontiers of the CCR and BCC models are necessary to execute the algorithm, we present a procedure for calculating them.     

A Semi-Infinite Programming Model In Data Envelopment Analysis

We consider a model for data envelopment analysis with infinitely many decision-making units. The determination of the relative efficiency of a given decision-making unit amounts to the solution of a semi-infinite optimization problem. We show that a decision-making unit of maximal relative efficiency exists and that it is 100% efficient. Moreover, this decision-making unit can be found by calculating a zero of the semi-infinite constraint function. For the latter task we propose a bi-level algorithm. We apply this algorithm to a problem from chemical engineering and present numerical results     

Technological leadership and variety: A Data Envelopment Analysis for the French machinery industry

We investigate structure and structural change within the French machinery industry from 1984–1991 in order to detect the apparent technology leaders and to get an account of the technological variety within the sector. The theoretical background of the paper is found in modern approaches to the economics of innovation and technology, where the very nature of technological knowledge and the local character of technological change are seen as a fundamental reason for the use of different technologies and for the different performances of firms. We apply a procedure that allows us to take into account such different performances and variety, Data Envelopment Analysis (DEA). As one major result, we find several best-practice technologies as well as a measure of technical inefficiency, allowing us to classify firms with respect to their relative technical performance. Moreover, technology leaders can be assigned to specific technology fields. The change within and between these fields over time is investigated.     

论“打开黑箱评价”的网络DEA模型

讨论了两阶段网络DEA模型KH,复合网络DEA模型WYP,以及两个模型之间的关系.并指出了上述两个模型能够打开"黑箱".