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

Kazuyuki Sekitani and Yu Zhao

Journal of the Operational Research Society, 2025, vol. 76, issue 10, 2150-2168

Abstract: 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.

Date: 2025
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DOI: 10.1080/01605682.2025.2460617

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