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Data envelopment analysis (DEA), as originally proposed is a methodology for evaluating the relative efficiencies of a set of homogeneous decision making units (DMUs) in the sense that each uses the same input and output measures (in varying amounts from one DMU to another). In some situations, however, the assumption of homogeneity among DMUs may not apply. As an example, consider the case where the DMUs are plants in the same industry which may not all produce the same products. Evaluating efficiencies in the absence of homogeneity gives rise to the issue of how to fairly compare a DMU to other units, some of which may not be exactly in the same ‘business’. A related problem, and one that has been examined extensively in the literature, is the missing data problem; a DMU produces a certain output, but its value is not known. One approach taken to address this problem is to ‘create’ a value for the missing output (e.g. substituting zero, or by taking the average of known values), and use it to fill in the gaps. In the present setting, however, the issue isn’t that the data for the output is missing for certain DMUs, but rather that the output isn’t produced. We argue herein that if a DMU has chosen not to produce a certain output, or for any reason cannot produce that output, and therefore does not put the resources in place to do so, then it would be inappropriate to artificially assign that DMU a zero value or some ‘average’ value for the nonexistent factor. Specifically, the desire is to fairly evaluate a DMU for what it does, rather than penalize or credit it for what it doesn’t do. In the current chapter we present DEA-based models for evaluating the relative efficiencies of a set of DMUs where the requirement of homogeneity is relaxed. We then use these models to examine the efficiencies of a set of manufacturing plants.

Data envelopment analysis (DEA) is a methodology for evaluating the relative efficiencies of peer decision-making units (DMUs), in a multiple input/output setting. While it is generally assumed that all outputs are impacted by all inputs, there are many situations where this may not be the case. For example, in a food manufacturing setting, certain foods are exempt from nutrition labeling and as a result are not influenced by labeling resources. This chapter extends the conventional DEA methodology to allow for the measurement of technical efficiency in situations where only partial input-to-output impacts exist. The new methodology involves viewing the DMU as a business unit, consisting of a set of mutually exclusive subunits, each of which can be treated in the conventional DEA sense.

Recently network DEA models have been developed to examine the efficiency of DMUs with internal structures. The internal network structures range from a simple two-stage process to a complex system where multiple divisions are linked together with intermediate measures. In general, there are two types of network DEA models. One is developed under the standard multiplier DEA models based upon the DEA ratio efficiency, and the other under the envelopment DEA models based upon production possibility sets. While the multiplier and envelopment DEA models are dual models and equivalent under the standard DEA, such is not necessarily true for the two types of network DEA models. Pitfalls in network DEA are discussed with respect to the determination of divisional efficiency, frontier type, and projections. We point out that the envelopment-based network DEA model should be used for determining the frontier projection for inefficient DMUs while the multiplier-based network DEA model should be used for determining the divisional efficiency. Finally, we demonstrate that under general network structures, the multiplier and envelopment network DEA models are two different approaches. The divisional efficiency obtained from the multiplier network DEA model can be infeasible in the envelopment network DEA model. This indicates that these two types of network DEA models use different concepts of efficiency. We further demonstrate that the envelopment model’s divisional efficiency may actually be the overall efficiency.

In conventional data envelopment analysis (DEA), decision making units (DMUs) are generally treated as a black-box in the sense that internal structures are ignored, and the performance of a DMU is assumed to be a function of a set of chosen inputs and outputs. A significant body of work has been directed at problem settings where the DMU is characterized by a multistage process; supply chains and many manufacturing processes take this form. The current chapter presents DEA modeling approaches for network DEA where additive efficiency decompositions are assumed for sub-units/processes/stages. In the additive efficiency decomposition approach, the overall efficiency is expressed as a (weighted) sum of the efficiencies of the individual stages. This approach can be applied under both constant returns to scale (CRS) and variable returns to scale (VRS) assumptions.

As discussed in the previous chapters, the DMU may perform different types of functions. In that case it is desirable to derive a measure of performance not only at the DMU level but as well at the level of the particular functions within the DMU. In the current chapter we examine a set of manufacturing plants operating under a single umbrella, with the objective being to use the component or function measures to decide what might be considered as each plant’s core business. It is proposed that this information can aid the company in any reorganization initiatives designed to capitalize on the strengths of each location (DMU).

There is a growing need to view performance in organizations in a more disaggregated sense, paying specific attention to different components of the operation. In this chapter we present models for deriving aggregate measures of bank-branch performance, with accompanying component measures that make up that aggregate value. The technical difficulty surrounding the development of an appropriate model is the presence of shared resources on the input side and mechanisms for allocating such resources to the individual components. The chapter presents both a conventional radial model as well as an additive model for handling multiple components in an organization. The models are applied to data for a set of bank branches.

This chapter presents a Nash bargaining game model to measure the performance of two-stage decision making units (DMUs) in data envelopment analysis (DEA). The two stages are viewed as players to bargain for a better payoff, which is represented by DEA ratio efficiency score. The efficiency model is developed as a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, the newly-developed bargaining approach yields the same results as applying the standard DEA approach to each stage separately.

The current chapter focuses on how to identify DEA frontier when decision making units (DMUs) are in forms of two-stage network processes. In these two stage network processes, all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. Due to the existence of intermediate measures, the usual procedure of adjusting the inputs or outputs by the efficiency scores, as in the standard DEA approach, does not necessarily yield a frontier projection. The current chapter presents an approach for determining the frontier points for inefficient DMUs within the framework of two-stage network processes.

Data envelopment analysis (DEA) is a method for identifying best practices among peer decision making units (DMUs). An important area of development in recent years has been that devoted to applications wherein DMUs represent network processes. One particular subset of such processes is those in which all the outputs from the first stage become inputs to the second stage. We call these types of DMU structures “two-stage networks”. Existing approaches in modeling efficiency of two-stage networks can be categorized as using either Stackelberg (leader-follower), or cooperative game concepts. There are two types of efficiency decomposition; multiplicative and additive. In multiplicative efficiency decomposition, the overall efficiency is defined as a product of the two individual stages’ efficiency scores, whereas in additive efficiency decomposition, the overall efficiency is defined as a weighted average of the two individual stages’ efficiency scores. We discuss modeling techniques used for solving two-stage network DEA models in linear programs.

In many real world applications involving performance measurement, it is necessary to deal with qualitative data factors. This chapter discusses the modeling of such factors within the DEA structure.

An important area of development in recent years in data envelopment analysis has been the applications wherein internal structures of DMUs are considered. For example, DMUs may consist of subunits or represent two-stage processes. One particular subset of such processes is those in which all the outputs from the first stage are the only inputs to the second stage. This chapter first reviews these models and discusses relations among various approaches. Our focus here is the approaches based upon either Stackelberg (leader–follower) or cooperative game concepts. We then examine the more general problem of an open multistage process where some outputs from a given stage may leave the system while others become inputs to the next stage. As well, new inputs can enter at any stage. We then discuss the modeling of this more general network structure.

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.

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.

Data Irregularities And Structural Complexities In Dea.- Rank Order Data In Dea.- Interval And Ordinal Data.- Variables With Negative Values In Dea.- Non-Discretionary Inputs.- DEA with Undesirable Factors.- European Nitrate Pollution Regulation and French Pig Farms' Performance.- PCA-DEA.- Mining Nonparametric Frontiers.- DEA Presented Graphically Using Multi-Dimensional Scaling.- DEA Models For Supply Chain or Multi-Stage Structure.- Network DEA.- Context-Dependent Data Envelopment Analysis and its Use.- Flexible Measures-Classifying Inputs and Outputs.- Integer Dea Models.- Data Envelopment Analysis With Missing Data.- Preparing Your Data for DEA.