Overcoming the infeasibility of the super-efficiency DEA model: A model with generalized orientation

The super-efficiency (SE) model is identical to the standard model, except that the unit under evaluation is excluded from the reference set. This model has been used in ranking efficient units, identifying outliers, sensitivity and stability analysis, measuring productivity changes, and solving two-player games. Under the assumption of variable, non-increasing and non-decreasing returns to scale (VRS, NIRS, NDRS), the SE model may be infeasible for some efficient DMUs. Based on the necessary and sufficient conditions for the infeasibility of SE, in the current paper, we develop a DEA model with generalized orientation to overcome infeasibility problems in the VRS models. Among the special cases of the generalized model, two cases, named as the modified input-oriented model and the modified output-oriented model, overcome the infeasibility problem in SE-VRS models, while keeping the complete consistency with the traditional input-oriented model and the traditional output-oriented model, respectively. This approach can be extended from VRS to NIRS and NDRS. The newly developed model is illustrated with a real world dataset.