Handbook on Data Envelopment Analysis

In about 30 years, Data Envelopment Analysis (DEA) has grown into a powerful quantitative, analytical tool for measuring and evaluating the performance. DEA has been successfully applied to a host of many different types of entities engaged in a wide variety of activities in many contexts worldwide. This chapter discusses the basic DEA models and some of their extensions.

This chapter discusses returns to scale (RTS) in data envelopment analysis (DEA). The BCC and CCR models described in Chap. 1 of this handbook are treated in input-oriented forms, while the multiplicative model is treated in output-oriented form. (This distinction is not pertinent for the additive model, which simultaneously maximizes outputs and minimizes inputs in the sense of a vector optimization.) Quantitative estimates in the form of scale elasticities are treated in the context of multiplicative models, but the bulk of the discussion is confined to qualitative characterizations such as whether RTS is identified as increasing, decreasing, or constant. This is discussed for each type of model, and relations between the results for the different models are established. The opening section describes and delimits approaches to be examined. The concluding section outlines further opportunities for research and an Appendix discusses other approaches in DEA treatment of RTS.

This chapter presents some of the recently developed analytical methods for studying the sensitivity of DEA results to variations in the data. The focus is on the stability of classification of DMUs (decision making units) into efficient and inefficient performers. Early work on this topic concentrated on developing algorithms for conducting such analyses after it was noted that standard approaches for conducting sensitivity analyses in linear programming could not be used in DEA. However, recent work has bypassed the need for such algorithms. It has also evolved from the early work that was confined to studying data variations in one input or output for one DMU. The newer methods described in this chapter make it possible to analyze the sensitivity of results when all data are varied simultaneously for all DMUs.

We review the literature of extensions and enhancements of the DEA basic methodology from the perspective of the problems that can be addressed by dealing with the dual multiplier formulation of the DEA models. We describe different approaches that allow incorporating into the analysis price information, reflecting meaningful trade-offs, incorporating value information and managerial goals, making a choice among alternate optima for the weights, avoiding non-zero weights, avoiding large differences in the values of multipliers, improving discrimination and ranking units. We confine attention to the methodological aspects of these approaches and show in many instances how others have used these approaches in applications in practise.

In this chapter, we provide an overview of our recent work on data envelopment analysis (DEA) and Malmquist productivity indexes. First, we review the construction of static and dynamic DEA technologies. Based on these technologies we show how DEA can be used to estimate the Malmquist productivity index introduced by Caves et al. (Econometrica 50(6):1393–14, 1982) in the static case as well as its extension into the dynamic case.

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.

Congestion is a term that is applicable in a variety of disciplines which range from medical science to traffic engineering. It has also many uses in practical everyday life. This brings with it a certain looseness in usage. We therefore expand (and refine) our discussion of congestion with reference to its use in economics where we have access to a precise meaning which we can develop in this chapter. This chapter covers the standard approaches used for treating congestion in data envelopment analysis.

There are two types of models in DEA: radial and nonradial. Radial models are represented by the CCR (Charnes–Cooper–Rhodes) model. Basically, they deal with proportional changes of inputs or outputs. On the other hand, nonradial models, e.g., the slacks-based measure of efficiency (SBM) model, handle input or output slacks directly, and do not assume proportional changes of inputs or outputs. In this chapter, we introduce the SBM model and its extensions.

Incorporation of random variations into DEA analysis has received significant attention in recent years. This chapter describes some of these developments and offers examples of possible uses in the area of chance-constrained programming models in DEA.

This chapter further examines the bootstrap method proposed by Simar and Wilson (Manag Sci 44(11):49–61, 1998) for DEA efficiency estimators. Some simplifications as well as Monte Carlo evidence on the coverage probabilities of confidence intervals estimated by the method are offered. In addition, we present similar evidence for confidence intervals estimated with the so-called naive bootstrap to illustrate the fact that the naive bootstrap is inconsistent in the DEA setting. Finally, we propose an iterated version of the bootstrap which may be used to improve bootstrap estimates of confidence intervals.

This chapter is written for analysts and researchers who may use data envelopment analysis (DEA) to statistically evaluate hypotheses about characteristics of production correspondences and factors affecting productivity. Contrary to some characterizations, it is shown that DEA is a full-fledged statistical methodology, based on the characterization of DMU efficiency as a stochastic variable. The DEA estimator of the production frontier has desirable statistical properties, and provides a basis for the construction of a wide range of formal statistical tests (Banker RD Mgmt Sci. 1993;39(10):1265–73). Specific tests described here address issues such as comparisons of efficiency of groups of DMUs, existence of scale economies, existence of allocative inefficiency, separability and substitutability of inputs in production systems, analysis of technical change and productivity change, impact of contextual variables on productivity, and the adequacy of parametric functional forms in estimating monotone and concave production functions.

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.

The banking industry has been the object of DEA analyses by a significant number of researchers and probably is the most heavily studied of all business sectors. Various DEA models have been applied in performance assessing problems, and the banks’ complex production processes have further motivated the development and improvement of DEA techniques. The main application areas for DEA in bank and branch performance analysis include the following: efficiency ranking; resource allocation, efficiency trends investigation; environmental impacts compensation; examining the impacts of new technology, ownership, deregulation, corporate, economic, and political events, etc.

Engineering is concerned with the design of products, services, processes, or in general with the design of systems. These design activities are managed and improved by the organization’s decision-makers. Therefore, the performance evaluation of the production function where engineering plays a fundamental role is an integral part of managerial decision-making. In the last 20 years, there has been limited research that uses data envelopment analysis (DEA) in engineering. One can attribute this to a number of issues that include but are not limited to the lack of understanding of the role of DEA in assessing and improving design decisions, the inability to open the input/output process transformation box, and the unavailability of production and engineering data. Nevertheless, the existing DEA applications in engineering have focused on the evaluation of alternative design configurations, have proposed performance improvement interventions for production processes at the disaggregated level, assessed the performance of hierarchical manufacturing organizations, studied the dynamical behavior of production systems, and have dealt with data imprecision issues. This chapter discusses the issues that the researcher faces when applying DEA to engineering problems, proposes an approach for the design of an integrated DEA-based performance measurement system, summarizes studies that have focused on engineering applications of DEA, and suggests some systems thinking concepts that are appropriate for future DEA research in engineering.

The service sector holds substantial challenges for productivity analysis because most service delivery is often heterogeneous, simultaneous, intangible, and perishable. Nevertheless, the prospects for future studies are promising as we gently push the data envelopment analysis research envelope by using more innovative research designs that may include synergistic partnerships with other methods and disciplines, as well as delve deeper into the sub-DMU network of organizations. This chapter is dedicated to providing a selection of applications in the service sector with a focus on building a conceptual framework, research design, and interpreting results. Given the expanding share of the service sector in gross domestic products of many countries, the twenty-first century will continue to provide fertile grounds for research in the service sector.

This chapter focuses on health-care applications of DEA. The paper begins with a brief history of health applications and discusses some of the models and the motivation behind the applications. Using DEA to develop quality frontiers in health services is offered as a new and promising direction. The paper concludes with an eight-step application procedure and list of do’s and don’ts when applying DEA to health services.