Determining the Exact Stability Region and Radius Through Efficient Hyperplanes

The main goal of this study was to address the sensitivity analysis fora specific efficient decision-making unit (DMU), which is under evaluation, by the variable returns to scale (VRS) technology to extend the efficiency stability region. Variations in inputs or outputs of any DMU can change the efficiency classification of that DMU as well as other DMUs, i.e., an efficient DMU can become inefficient and vice versa. This study considered the largest performance stability region for an extreme efficient DMU whose data could be changed in all directions of input/output space, including both directions of improving the situation and worsening the situation such that under these changes, the efficiency classification of all extreme DMUs would be preserved. We found the largest symmetric cell to the center of the extreme efficient DMU under evaluation, leading to an efficiency stability radius. In addition, data changes were only applied for the extreme efficient DMU, and the data for the other DMUs were assumed fixed. This stability region was determined by the defining hyperplanes of production possibility set (PPS) of VRS technology and the corresponding half-spaces. The suggested method is illustrated using real-world data.