Infeasibility of super-efficiency data envelopment analysis models

The paper investigates the infeasibility of super-efficiency data envelopment analysis (DEA) models in which the unit under evaluation is excluded from the reference set. Necessary and sufficient conditions are provided for infeasibility of the super-efficiency DEA measures. By the returns to scale (RTS) classifications obtained from the standard DEA model, we can further locate the position of the unit under evaluation when infeasibility occurs. It is shown that the ranking of the total set of efficient decision making units is impossible because of the infeasibility of super-efficiency DEA models. Also we are able to identify the endpoint positions of the extreme efficient units. The results are useful for sensitivity analysis of efficiency classifications.