Determining the Exact Stability Region and Radius through Efficient Hyperplanes

The main goal of this study is to address the sensitivity analysis for a specific efficient decision-making unit (DMU), which is under evaluation, by 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 considers the largest performance stability region for an extreme efficient DMU whose data can 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 will be preserved. Moreover, we find the largest symmetric cell to the center of the extreme efficient DMU under evaluation, leading to an efficiency stability radius. Also, data changes are only applied for the extreme efficient DMU and the data for the other DMUs are assumed fixed. This stability region is determined by the concept of defining hyperplanes of production possibility set (PPS) of VRS technology and the corresponding half-spaces. The suggested method is illustrated using real-world data.