Ranking general two-stage feedback systems in the presence of undesirable exogenous inputs

Data Envelopment Analysis (DEA) is a widely used method for evaluating the efficiency of decision-making units in real-world applications. Network Data Envelopment Analysis (NDEA) extends this approach by assessing the efficiency of network systems, taking into account internal processes within departments. A key challenge in evaluating such systems is ranking efficient units, particularly when undesirable data and feedback mechanisms are present. While previous research has explored ranking methods for network systems, no study has addressed the ranking of systems that simultaneously involve undesirable data and feedback loops. This study proposes a novel model for ranking general two-stage feedback systems with undesirable exogenous inputs. A structural numerical example is provided to demonstrate the model's applicability and effectiveness. The results show that the proposed model successfully evaluates and ranks two-stage systems, offering valuable insights for decision-makers. By addressing this gap in the literature, the research provides a practical tool for analyzing complex network systems with undesirable data and feedback, advancing the field of DEA.