Data envelopment analysis models with ratio data: A revisit

The performance evaluation of for-profit and not-for-profit organisations is a unique tool to support the continuous improvement of processes. Data envelopment analysis (DEA) is literally known as an impeccable technique for efficiency measurement. However, the lack of the ability to attend to ratio measures is an ongoing challenge in DEA. The convexity axiom embedded in standard DEA models cannot be fully satisfied where the dataset includes ratio measures and the results obtained from such models may not be correct and reliable. There is a typical approach to deal with the problem of ratio measures in DEA, in particular when numerators and denominators of ratio data are available. In this paper, we show that the current solutions may also fail to preserve the principal properties of DEA as well as to instigate some other flaws. We also make modifications to explicitly overcome the flaws and measure the performance of a set of operating units for the input- and output orientations regardless of assumed technology. Finally, a case study in the education sector is presented to illustrate the strengths and limitations of the proposed approach.