Stability analysis and enhancement of super-efficiency model based on space distance

The traditional super-efficiency data Enveloping analysis (DEA) model can further distinguish the efficiency of efficient DMU. However, this distinction is unstable when there are perturbations in the efficient DMU inputs and outputs. The spatial distance can reflect the spatial variation of DMU on the envelope surface. We investigate the stability of the modified VRS super-efficiency model in the presence of data perturbations in efficiency DMUs and calculate its stability with spatial distances, providing a necessary and sufficient condition for such perturbations to affect the results of calculations of other efficient DMU super-efficiencies. A new super-efficiency model is proposed, which combines spatial distance to increase the constraint on projection point. Numerical examples are used to illustrate the model. On this basis, a spatial distance model for calculating inefficient DMU efficiency is further developed.