Merging Decision-Making Units with Stochastic Data

The first problem in merging units is an estimation of the inherited inputs/outputs of the merged unit from merging units and the identification of the least and most achievable efficiency targets from the merged unit is the second one. there are some models to attain a response to these problems. 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 deal with this problem, this paper presents a novel method according to inverse data envelopment analysis for estimating the inherited input/output levels of the merged unit to reach the pre-determined efficiency score in the level of significance α ∈ (0, 1). this paper also suggests a stochastic programming model for estimating the least possible efficiency score via the given merging. the practical applicability of these proposed methodologies is further validated through a comprehensive example within the banking sector.