Document Type : Original Article


1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.


Most organizations and companies have hierarchical structures, and appropriate models are required to measure the efficiency of this kind of network systems. Data envelopment analysis (DEA) is a well-known method introduced for measuring the relative efficiency of a set of decision-making units (DMUs) that use multiple inputs to produce multiple outputs. Conventional DEA models usually generate misleading results while evaluating the performance of network systems. The present study aims at developing suitable models for measuring the efficiency of hierarchical structures using the centralized and non-cooperative leader-follower game models. In the proposed method, the divisional efficiencies (within an organization) and the overall efficiency of the organization are calculated. The proposed models are applied to assess the performance of 20 schools in Iran. The results of the two proposed models show that none of the schools are efficient, suggesting that these schools do not optimally utilize their resources. The application of the results of the proposed models enables managers to identify inefficient sub-units and develop strategies to improve their performance.