Slack-based models for inverse data envelopment analysis in merging units with interval data

The paper proposes non-radial slack-based measure (SBM) models for the inverse data envelopment analysis (InvDEA) when dealing with data involving uncertainty represented by interval values. The models are specifically developed to ascertain the optimal inputs or outputs for the merged decision-making unit (DMU) to attain its desired efficiency level. To achieve the predefined optimistic efficiency, we estimate the input interval for the newly merged DMU while keeping its outputs equal to the sum of the outputs from the merging DMUs. Conversely, to achieve the predefined pessimistic efficiency, we estimate the output interval for the new DMU while maintaining its inputs as the sum of the inputs from the merging DMUs. In addition, we also calculate the minimum and maximum possible values for optimistic and pessimistic efficiency. The advantages of the SBM InvDEA models are highlighted in comparison to the radial BCC model. We apply the proposed models to a real-world scenario involving the 2017 merger of a few public sector banks with one of India’s largest banks.