Developing a Two-stage Data Envelopment Analysis Model Handling Rough Variables

The case in many real- life applications deals with complex, vague, imprecise, and uncertain data. Traditional Data Envelopment Analysis (DEA) requires accurate and exact inputs and outputs; hence it cannot deal with many practical problems. As well, traditional DEA assumes the dependent relations among decision- making units (DMUs) are not exist. DMUs are treated as black boxes where the initial inputs enter the first stage and the final outputs from the second stage are only considered. The intermediate stage is neglected to measure their efficiency. Therefore, the “black box” theory reflects inaccurate efficiency indicators about systems consisting of complex structures. This paper integrates classical DEA, two- stage DEA, and rough theory to obtain a comprehensive evaluation. The proposed two- stage RDEA model is a constant return to scale (CRS) that measures relative efficiencies of DMUs containing two subprocesses while handling some uncertain rough variables in inputs and outputs. The model is applied in the supply chain (Sc) to measure the efficiency of two stages of the supply chain, including suppliers and manufacturers. The numerical example shows the applicability of the model we proposed to deal with the intermediate stage and uncertainty data. Moreover, we compare the proposed model with the rough DEA (RDEA) model and explain how to improve the relative efficiency. We also introduce a sensitivity analysis for helping the decision- maker in improving the comprehensive efficiency by changing trust- level ($\alpha$).