The papers comprising this special journal issue contribute to the theory and application of data envelopment analysis (DEA). The original idea of this special issue was discussed at the 48th Annual Conference of the Operational Research Society held in Bath, UK, in September 2006. Although this issue was originally planned to accommodate extended papers presented at the conference, it was solicited as an open invitation to the broader academic community working in the area of efficiency and performance analysis. The 10 papers included in the special issue are a fraction of the total number of submitted manuscripts that ‘survived’ the rigorous refereeing process.

The issue opens with three application-focused papers. Amado and Dyson demonstrate the potential of using DEA as a tool for formative evaluation in health care. The study contributes to the methodology of DEA by considering different perspectives for efficiency evaluation. The authors’ aim is to help decision-makers to understand the performance of primary care practices in providing diabetes services. The authors also overcome the difficulty arising from a relatively small sample of practices in their study by using trade-offs between inputs in the construction of weight restrictions.

Gonzalez, Rubio and Molinero apply DEA to a large database of insurance policies to identify the value of different customer segments to the insurer. After some standardization, each segment is regarded as a decision-making unit and is compared to other segments by the use of a DEA model. The authors identify several customer segments that outperform others on the company's measure of efficiency, and report that their findings were unexpected and surprising for the insurance company.

The paper by Chang, Galantine and Thevaranjan explores the efficiency and types of returns to scale of the top-100 accounting firms in the USA. The authors find that the first-tier of these firms (largest by revenue) operate at the most productive scale size whereas the second-tier firms exhibit increasing, constant or decreasing types of returns to scale.

The next seven papers in the issue deal with various theoretical aspects of DEA. Liu, Lu, Yang and Chuang develop a network-based approach aimed at the improvement of the discrimination of DEA models. The suggested method involves the computation of the efficiency of units in several scenarios based on different combinations of inputs and outputs. The final ranking procedure for efficient units is based on their overall contribution to the reference sets in all of the scenarios considered.

The use of the hyperbolic efficiency measure in DEA models, which improves both inputs and outputs at the same time, is explored in the paper by Johnson and McGinnis. The authors show certain advantages of the hyperbolic measure with respect to the infeasibility issues in the super-efficiency models. The noted infeasibility can arise in applications of standard radial measures and more general directional distance functions.

The paper by Krivonozhko, Utkin, Safin and Lychev offers a yet more general DEA model that includes a previous generalization as a special case. In an interesting academic exercise the authors show that any known DEA model can be approximated by some standard DEA model based on the assumption of variable returns to scale.

A non-traditional computational algorithm for the identification of the types of returns to scale in DEA is introduced in the paper by Soleimani-damaneh. The suggested approach is based on the calculation of certain ratios within the data set and offers obvious computational advantages over the traditional approaches involving the solution of standard DEA models. The latter are still, however, needed if one is interested in the actual efficiency measure of the units, and not only in their returns-to-scale characteristics.

The paper by Førsund, Kittelsen and Krivonozhko revisits the legacy of the work by Farrell whose definitions of efficiency measures and related non-parametric models have been widely acknowledged in the literature on DEA. The authors demonstrate that the models developed by Farrell had certain theoretical drawbacks that have only been overcome in the subsequent, now considered classical, papers of Charnes, Cooper, Rhodes and Banker. A significant part of this paper is devoted to the visualization techniques applicable to production frontiers.

A non-traditional view of DEA and its applications is offered in the paper by Dulá. The author outlines several possible practical areas in which DEA models can be used to identify outliers in a data set. The suggested approach can accommodate the decision maker's preferences in the form of weight restrictions that will shape the geometric characteristics of the feasible set and influence the way the outliers are determined.

The paper by Chen, Larbani and Chang explores the problem of obtaining a common set of weights for all the units in a DEA assessment. The authors’ goal to represent all units in the best light naturally leads to a multi-objective formulation. The authors show how methods of multi-objective programming can be used in this situation.

Overall, the papers included in the special issue give us a snapshot of some of the current avenues of research in the area of DEA. All of these papers contribute either to the theoretical or implementation aspects of DEA and should be of interest to a broad academic and practitioner audience.

In conclusion, the Guest Editors wish to thank a small army of academic referees whose dedication and hard work made this issue a reality. Although it was not possible to accommodate all submitted manuscripts, the Guest Editors hope that all authors found the feedback they received helpful for their future work.

Note from the Joint Editors

In order to reduce the backlog of papers awaiting publication in issues, we have included a further four Theoretical Papers on the topic of DEA in this issue. These are papers submitted in the usual way to the journal.

Southampton University Terry Williams

Loughborough University John Wilson