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DEA and its appropriate applications are heavily dependent on the data set that is used as an input to the productivity model. As we now know there are numerous models based on DEA. However, there are certain characteristics of data that may not be acceptable for the execution of DEA models. In this chapter we shall look at some data requirements and characteristics that may ease the execution of the models and the interpretation of results. The lessons and ideas presented here are based on a number of experiences and considerations for DEA. We shall not get into the appropriate selection and development of models, such as what is used for input or output data, but focus more on the type of data and the numerical characteristics of this data. [ABSTRACT FROM AUTHOR]

In data envelopment analysis (DEA), the input and output data from all of the decision making units (DMUs) to be compared are required. If, for any reason, some data are missing, then the associated DMU must be eliminated to make the approach applicable. This study proposes a fuzzy set approach to deal with missing values. The value of a DMU in an input (or output) which is missing is represented by a triangular fuzzy number constructed from the values of other DMUs in that input (or output). A fuzzy DEA model is then used to calculate the efficiencies, which are usually also fuzzy numbers. We use a problem with complete data to investigate the effect of this approach when 1%, 2%, and 5% of the values are missing. While the conventional DMU-deletion method will overestimate the efficiencies of the remaining DMUs, the fuzzy set approach produces results which are very close to those calculated from complete data. The average error in estimating the true efficiency is less than 0.3%. Most importantly, the fuzzy set approach is able to calculate the efficiencies of all DMUs, including those with some values missing. [ABSTRACT FROM AUTHOR]

Conventional Data Envelopment Analysis (DEA) models consider that inputs and outputs are continuous (i.e. real-valued) amounts. However, there are many applications in which one or more inputs and/or outputs are necessarily integer quantities. Commonly, in these situations, the non-integer targets are rounded off. However, rounding off may easily lead to an infeasible target (i.e. out of the Production Possibility Set) or to a dominated operation point. In this chapter, a general framework to handle integer inputs and outputs is presented and a number of integer DEA models reviewed. We illustrate the working of the proposed approach with on a problem from the literature. [ABSTRACT FROM AUTHOR]

In standard data envelopment analysis (DEA), it is assumed that the input versus output status of each of the chosen analysis measures is known. In some situations, however, certain measures can play either input or output roles. Consider using the number of interns on staff in a study of hospital efficiency. Such a factor clearly constitutes an output measure for a hospital, being one form of training provided by the organization, but at the same time is an important component of the hospital's total staff complement, hence is an input. This chapter presents DEA models to accommodate such flexible measures. Both an individual DMU model and an aggregate model are suggested as methodologies for deriving the most appropriate designations for flexible measures. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is a methodology for identifying the efficient frontier of decision making units (DMUs). Context-dependent DEA refers to a DEA approach where a set of DMUs is evaluated against a particular evaluation context. Each evaluation context represents an efficient frontier composed by DMUs in a specific performance level. The context-dependent DEA measures the attractiveness and the progress when DMUs exhibiting poorer and better performance are chosen as the evaluation context, respectively. This chapter also presents a slack-based context-dependent DEA approach. In DEA, nonzero input and output slacks are very likely to present after the radial efficiency score improvement. The slack-based context-dependent DEA allows us to fully evaluate the inefficiency in a DMU's performance. [ABSTRACT FROM AUTHOR]

This chapter describes network DEA models, where a network consists of sub-technologies. A DEA model typically describes a technology to a level of abstraction necessary for the analyst's purpose, but leaves out a description of the sub-technologies that make up the internal functions of the technology. These sub-technologies are usually treated as a "black box", i.e., there is no information about what happens inside them. The specification of the sub-technologies enables the explicit examination of input allocation and intermediate products that together form the production process. The combination of sub-technologies into networks provides a method of analyzing problems that the traditional DEA models cannot address. We apply network DEA methods to three examples; a static production technology with intermediate products, a dynamic production technology, and technology adoption (or embodied technological change). The data and GAMS code for two examples of network DEA models are listed in appendices. [ABSTRACT FROM AUTHOR]

Standard data envelopment analysis (DEA) models cannot be used directly to measure the performance of a supply chain and its members, because of the existence of the intermediate measures connecting those members. This observation is true for any situations where DMUs contain multi-stage processes. This chapter presents several DEA-based approaches in a seller-buyer supply chain context. Some DEA models are developed under the assumption that the relationship between the seller and buyer is treated as leader-follower and cooperative, respectively. In the leader-follower (or non-cooperative) structure, the leader is first evaluated using the standard DEA model, and then the follower is evaluated by a new DEA-based model which incorporates the DEA efficiency information for the leader. In the cooperative structure, one maximizes the joint efficiency that is modeled as the average of the seller's and buyer's efficiency scores, and both supply chain members are evaluated simultaneously. [ABSTRACT FROM AUTHOR]

The purpose of this chapter is to present data envelopment analysis (DEA) as a two-dimensional plot that permits an easy, graphical explanation of the results. Due to the multiple dimensions of the problem, graphical presentation of DEA results has proven somewhat elusive up to now. Co-Plot, a variant of multidimensional scaling, places each decision-making unit in a two-dimensional space in which the location of each observation is determined by all variables simultaneously. The graphical display technique exhibits observations as points and variables (ratios) as arrows, relative to the same center-of-gravity. Observations are mapped such that similar decision-making units are closely located on the plot, signifying that they belong to a group possessing comparable characteristics and behavior. In this chapter, we will analyze 19 Finnish Forestry Boards using Co-Plot to examine the original data and then to present the results of various weight-constrained DEA models, including that of PCA-DEA. [ABSTRACT FROM AUTHOR]

Data envelopment analysis (DEA) is firmly anchored in efficiency and productivity paradigms. This research claims new application domains for DEA by releasing it from these moorings. The same reasons why efficient entities are of interest in DEA apply to the geometric equivalent in general point sets since they are based on the data's magnitude limits relative to the other data points. A framework for non-parametric frontier analysis is derived from a new set of first principles. This chapter deals with the extension of data envelopment analysis to the general problem of mining oriented outliers. [ABSTRACT FROM AUTHOR]

The purpose of this chapter is to present the combined use of principal component analysis (PCA) and data envelopment analysis (DEA) with the stated aim of reducing 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. Various PCA-DEA formulations are developed in the chapter utilizing the results of principal component analyses to develop objective, assurance region type constraints on the DEA weights. The first set of models applies PCA to grouped data representing similar themes, such as quality or environmental measures. The second set of models, if needed, applies PCA to all inputs and separately to all outputs, thus further strengthening the discrimination power of DEA. A case study of municipal solid waste managements in the Oulu district of Finland, which has been frequently analyzed in the literature, will illustrate the different models and the power of the PCA-DEA formulation. In summary, it is clear that the use of principal components can noticeably improve the strength of DEA models. [ABSTRACT FROM AUTHOR]

This chapter highlights the usefulness of the directional distance function in measuring the impact of the EU Nitrate directive, which prevents the free disposal of organic manure and nitrogen surplus. Efficiency indices for the production and environmental performance of farms at an individual level are proposed, together with an evaluation of the impact caused by the said EU regulation. An empirical illustration, based on a sample of French pig farms located in Brittany in 1996, is provided. This chapter extends the previous approach to good and bad outputs within the framework of the directional distance function, by introducing a by-product (organic manure), which becomes a pollutant once a certain level of disposability is exceeded. In this specific case, the bad output is the nitrogen surplus - resulting from the nutrient balance of each farm - that is spread on the land. This extension to the model allows us to explicitly introduce the EU regulation on organic manure, which sets a spreading limit of 170kg/ha. Our results show that the extended model provides greater possibilities for increasing the level of production, and thus the revenue of each farm, while decreasing the bad product (nitrogen surplus) and complying with the mandatory standard on the spreading of organic manure. [ABSTRACT FROM AUTHOR]

The standard Data Envelopment Analysis (DEA) models rely on the assumption that inputs are minimized and outputs are maximized. However, when some inputs or outputs are undesirable factors (e.g., pollutants or wastes), these outputs (inputs) should be reduced (increased) to improve inefficiency. This chapter discusses the existing methods of treating undesirable factors in DEA. Under strongly disposable technology and weakly disposable technology, there are at least three approaches of treating undesirable outputs in the DEA literature. The first approach is the hyperbolic output efficiency measure that increases desirable outputs and decreases undesirable outputs simultaneously. Based on the classification invariance property, a linear monotone decreasing transformation is used to treat the undesirable outputs. A directional distance function is used to estimate the efficiency scores based on weak disposability of undesirable outputs. This chapter also presents an extended DEA model in which undesirable outputs and non-discretionary inputs are considered simultaneously. [ABSTRACT FROM AUTHOR]

A motivating factor for Data Envelopment Analysis (DEA) was the measurement of technical efficiency in public sector applications with unknown input prices. Many applications, including public sector production, are also characterized by heterogeneous producers who face different technologies. This chapter discusses existing approaches to measuring performance when non-discretionary inputs affect the transformation of discretionary inputs into outputs. The suitability of the approaches depends on underlying assumptions about the relationship between non-discretionary inputs and outputs. One model treats non-discretionary inputs like discretionary inputs but uses a non-radial approach to project inefficient decision making units (DMUs) to the frontier holding non-discretionary inputs fixed. A potential drawback is the assumption that convexity holds with respect to non-discretionary inputs and outputs. Alternatively, the assumption of convexity can be relaxed by comparing DMUs only to other DMUs with similar environments. Other models use multiple stage models with regression to control for the effect that non-discretionary inputs have on production. [ABSTRACT FROM AUTHOR]

In this chapter we present an overview of the different existing approaches dealing with the treatment of negative data in DEA. We discuss both the classical approaches and the most recent contributions to this problem. The focus is mainly on issues such as translation invariance and units invariance of the variables, classification invariance of the units, as well as efficiency measurement and target setting [ABSTRACT FROM AUTHOR]

The standard Data Envelopment Analysis (DEA) method requires that the values for all inputs and outputs are known exactly. When some inputs and output are imprecise data, such as interval or bounded data, ordinal data, and ratio bounded data, the resulting DEA model becomes a non-linear programming problem. Such a DEA model is called imprecise DEA (IDEA) in the literature. There are two approaches in dealing with such imprecise inputs and outputs. One approach uses scale transformations and variable alternations to convert the non-linear IDEA model into a linear program. The other identifies a set of exact data from the imprecise inputs and outputs and then uses the standard linear DEA model. This chapter focuses on the latter IDEA approach that uses the standard DEA model. This chapter shows that different results are obtained depending on whether the imprecise data are introduced directly into the multiplier or envelopment DEA model. Because the presence of imprecise data invalidates the linear duality between the multiplier and envelopment DEA models. The multiplier IDEA (MIDEA), developed based upon the multiplier DEA model, presents the best efficiency scenario whereas the envelopment IDEA (EIDEA), developed based upon the envelopment DEA model, presents the worst efficiency scenario. Weight restrictions are often redundant if they are added into MIDEA. Alternative optimal solutions on the imprecise data can be determined using the recent sensitivity analysis approach. The approaches are illustrated with both numerical and real world data sets. [ABSTRACT FROM AUTHOR]

In data envelopment analysis (DEA), performance evaluation is generally assumed to be based upon a set of quantitative data. In many real world settings, however, it is essential to take into account the presence of qualitative factors when evaluating the performance of decision making units (DMUs). Very often rankings are provided from best to worst relative to particular attributes. Such rank positions might better be presented in an ordinal, rather than numerical sense. The chapter develops a general framework for modeling and treating qualitative data in DEA, and provides a unified structure for embedding rank order data into the DEA framework. We show that the approach developed earlier in Cook et al (1993, 1996) is equivalent to the IDEA methodology given in Chapter 3. It is shown that, like IDEA, the approach given her for dealing with qualitative data lends itself to treatment by conventional DEA methodology. [ABSTRACT FROM AUTHOR]

Over the recent years, we have seen a notable increase in interest in data envelopment analysis (DEA) techniques and applications. Basic and advanced DEA models and techniques have been well documented in the DEA literature. This edited volume addresses how to deal with DEA implementation difficulties involving data irregularities and DMU structural complexities. Chapters in this volumes address issues including the treatment of ordinal data, interval data, negative data and undesirable data, data mining and dimensionality reduction, network and supply chain structures, modeling non-discretionary variables and flexible measures, context-dependent performance, and graphical representation of DEA. [ABSTRACT FROM AUTHOR]

Validated age and growth estimates are important for constructing age-structured population dynamic models of chondrichthyan fishes, especially those which are exploited. We review age and growth studies of chondrichthyan fishes, using 28 recent studies to identify areas where improvements can be made in describing the characteristics of ageing structures (both traditional and novel) utilized to estimate ages of sharks, rays, and chimaeras. The topics identified that need consistency include the: (1) terminology used to describe growth features; (2) methods used to both verify and validate age estimates from chondrichthyan calcified structures, especially edge and marginal increment analyses; and (3) the functions used to produce and describe growth parameters, stressing the incorporation of size at birth (L0) and multiple functions to characterize growth characteristics, age at maturity and longevity. [ABSTRACT FROM AUTHOR]