Super-efficiency measurement under variable return to scale: an approach based on a new directional distance function

Abstract

A modified super-efficiency model based on the directional distance function (DDF) has recently been developed in order to tackle the infeasibility issue in the two exceptions of the Nerlove–Luenberger (N–L) super-efficiency model under variable return to scale (VRS). However, we find that model does not fully eliminate the infeasibility issue. This paper chooses an appropriate reference bundle in the DDF so that the resulting DDF-based VRS super-efficiency model is always feasible. The proposed new model successfully addresses the infeasibility issue of conventional VRS super-efficiency models and fully eliminates the infeasibility issue in the two exceptions of the VRS N–L super-efficiency model. Additional advantages of the new model include: it is unit-invariant and does not need to predetermine any parameter. Theoretical analyses and numerical examples support the practicality and superiority of our model when compared with other super-efficiency models.

Keywords:

• data envelopment analysis
• directional distance function
• super-efficiency
• variable returns to scale
• infeasibility

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11301395, 11201344, 71371152 and 70971109).