Inverse Data Envelopment Analysis Models for Inputs/Outputs Estimation in Two-Stage Processes

Considering the interior of decision-making units (DMUs) is essential when evaluating a system's performance in the practical and real-world circumstances. Knowing what happens inside a DMU allows a more accurate study of relevant process. It identifies the efficiency, and inefficiency of the sub-units in the system being evaluated. This study focuses on two-stage inverse data envelopment analysis (DEA) problems. In these problems, a portion of the outputs from the first period is used as inputs in the second stage. For this purpose, several models are offered to address the input/output estimation problem, in which decision makers should deal with intermediate products and shared and non-shared inputs in a two-stage system. Furthermore, the proposed models are examined using a window DEA because of the importance of assessing repetitive processes in some two-stage systems. Next, an Iranian bank is considered as a case study to further elucidate using the presented models. Finally, we present a conclusion and suggestions for further research.