Merging decision-making units with stochastic data

The inverse Data Envelopment Analysis (InvDEA) is an exciting and notable issue in the DEA field. Various InvDEA models have been established to estimate the inherited input/output levels of the newly generated unit from merging units to achieve the pre-defined performance index. However, these models could not be employed when a deviation from the frontier is observed due to noise and random error in the data. In order to tackle this problem, the current paper contributes to InvDEA by introducing a novel method for estimating the inherited input/output levels of the merged unit to reach the pre-determined efficiency score in the level of significance $\alpha\in (0, 1)$. This paper also suggests a stochastic programming model for estimating the least possible efficiency score via the given merging. The managers can employ the results of this study to develop useful approaches to improve the efficiency of units. The validity of the proposed models is illustrated through a banking application.