In practical contexts, decision-making units (DMUs) are frequently organized hierarchically, encompassing various levels of functionality, multiple subunits across different tiers, or multiple stages of production. Traditional data envelopment analysis (DEA) models often neglect these hierarchical arrangements, potentially leading to assessments that do not accurately reflect actual unit performance. This study proposes a novel DEA model specifically designed to assess the efficiency of bi-level DMUs, consisting of a leader at the upper level and a follower at the lower level. By using a directional distance function, the proposed model simultaneously minimizes inputs and maximizes outputs, offering a more flexible and accurate evaluation compared to conventional methods. The model's effectiveness is demonstrated through its application in two case studies within the banking sector, showcasing its ability to provide deeper managerial insights and improve decision-making.
Habibpoor et al. (Sun,) studied this question.