Goal Programming Method for Solving Tri-Level Data Envelopment Analysis

Data Envelopment Analysis (DEA) is a methodical approach utilizing linear programming to assess the effectiveness and efficiency of Decision-Making Units (DMUs). It particularly focuses on scenarios where these DMUs possess multiple inputs and outputs. However, when dealing with practical situations, we often come across intricate and interconnected circumstances that operate within a hierarchical framework, with decisions being made in a decentralized manner. The traditional DEA models are not suitable for these hierarchical issues because they assume a single decision-making center with all decision-making power and do not consider the decentralized nature of the decision-making process. Recently, a group of scholars proposed an innovative bi-level programming data envelopment analysis approach to assess the entities within a hierarchical framework, wherein decentralized decision-making involves two tiers of decision-making centers. The bi-level programming DEA takes into account the two levels of decision-making centers and their interactions. It considers the decision-making process as a bi-level optimization problem, where the upper-level decision-making center aims to maximize the overall efficiency of the system, while the lower-level decision-making centers aim to optimize their own efficiencies. In this chapter, the DEA model is extended for units with tri-level structures and then to solve the model, a goal programming approach is applied. Finally, an illustrative example is presented to demonstrate the efficacy of this method.