Most Favorable Russell Measures of Efficiency: Properties and Measurement

Conventional radial efficiency measurement models in data envelopment analysis are unable to produce appropriate efficiency scores for production units lying outside the cone generated by the convex hull of the extreme efficient production units. In addition, in the case of production technologies with variable returns to scale, the efficiency scores measured from the input and output sides are usually different. To solve these problems, the Russell measure of efficiency, which takes both the inputs and outputs into account, has been proposed. However, the conventional Russell efficiency is measured under the least favorable conditions, rather than the general custom of measuring under the most favorable ones. This paper develops a model to measure Russell efficiency under the most favorable conditions in two forms, the average and the product. They can be transformed into a second-order cone program and a mixed integer linear program, respectively, so that the solution can be obtained efficiently. A case of Taiwanese commercial banks demonstrates that they are more reliable and representative than the radial measures. Since the most favorable measures are higher than the least favorable measures, and the targets for making improvements are the easiest to reach, they are more acceptable to the production units to be evaluated.