Closest targets in Russell graph measure of strongly monotonic efficiency for an extended facet production possibility set

The Russell graph measure is a non-radial efficiency measure for non-oriented Data Envelopment Analysis (DEA) models. It is strongly monotonic, but its projection point is not the closest one. Prior studies attempted to reverse the optimization of DEA models from a minimization problem to a maximization one for finding closer targets; however, this modification fails to satisfy strengthen the monotonicity of he efficiency measure. To resolve the conflict between the closer targets and strong monotonicity of efficiency measures, this study proposes a maximum Russell graph measure DEA model based on an extended facet production possibility set. It provides the closest target with only a single improvement in either an output or input term for the assessed DMU and avoids the free-lunch issue. Moreover, the maximum Russell graph measure satisfies strong monotonicity. Further practical advantages of the proposed efficiency measure are demonstrated numerically in comparison to other existing non-radial efficiency measures.