The Enhanced Russell Graph Measure (ERG=SBM): Economic Inefficiency Decompositions

The enhanced Russell graph measure, ERG, (Pastor et al., 1999) was designed as a new global efficiency measure to overcome the computational difficulties of the Russell graph measure of technical efficiency, RG (Färe et al., 1985). Historically, Farrell (1957) implemented the first measure of technical efficiency, while Färe and Lovell (1978), after suggesting some desirable properties that an ideal technical efficiency measure should satisfy, proposed the so-called Russell input measure of technical efficiency. An output version and a graph version were presented in the first book by Färe et al. (1985). These three initial Russell measures have been already presented in Chap. 5 . The difficulty for solving the graph version motivated, in the last 1990s, the search for a new formulation easier to handle and to solve, and the proposed solution was the ERG measure. In the literature, two papers can be found, the first one by Pastor et al. (1999) and the second one by Tone (2001). Both proposed exactly the same linear fractional programming model for solving the Russell graph measure through the same reformulation. Hence, the ERG model was consecutively published twice with a gap of 2 years, which is something that occurs quite seldom in research. Pastor et al. (1999) published it first in the European Journal of Operational Research, and Tone (2001) published exactly the same models in the same journal under a different name, SBM, and related them also to the RG measure. It shows that two groups of researchers, without any interaction, may developed the same idea in a quasi-contemporary way without being aware of it. This is the reason why we refer to both measures, which are the same, as ERG=SBM and call it the “enhanced Russell graph slack-based measure.”