Developing a novel inverse data envelopment analysis (DEA) model for evaluating after-sales units

This paper proposes a novel model of inverse data envelopment analysis (IDEA) based on the slack-based measure (SBM) approach. The developed inverse SBM model can maintain relative efficiency of decision making units (DMUs) with new input and output. This model can also measure the input and output volumes when a decision maker (DM) increases efficiency score. The inverse SBM model is a kind of multi-objective non-linear programming (MONLP) problem, which is not easy to solve. Therefore, we suggest a linear programming model for solving inverse SBM model. In this model efficiency score of DMU under evaluation remains unchanged. Furthermore, we suggest an optimal combination of inputs and outputs in the production possibility set (PPS). A case study is presented to demonstrate the efficacy of our proposed model.