Performance Ranking Method Based on Superefficiency with Directional Distance Function in DEA

In data envelopment analysis (DEA) methodology, superefficiency models eliminate the DMU to be evaluated from the production possibility set (PPS) to investigate whether its performance is superefficient. However, the infeasibility has been found in the superefficiency models when variable return-to-scale (VRS) technology is assumed. In recent developments, directional distance functions (DDF) are introduced into VRS superefficiency models to address the infeasibility, and the obtained efficiency scores from the DDF-based VRS superefficiency measure are used to rank all DMUs. In this study, we discuss conditions on selecting some proper reference bundles for feasible DDF and suggest a new DDF-based VRS superefficiency measure, which is unit-invariant and does not need to specify additional parameters. Two example illustrations are evaluated to demonstrate the feasibility and usefulness of our proposed DDF-based VRS superefficiency ranking method.