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.

3 Department of Mathematics, Shahr.e Qods Branch, Islamic Azad University, Tehran, Iran.


Data Envelopment Analysis (DEA) is one of the methods most widely used for measuring the relative efficiency of DMUs in the world today.  The efficiency evaluation of the network structure opens the “black box” and considers the internal structure of systems. In this paper, a three-stage network model is considered with additional inputs and undesirable outputs and obtains the efficiency of the network, as interval efficiency in presence of the imprecise datum. The proposed model of this paper simulates a factory in the factual world with a production area, three warehouses and two delivery points. This factory is taken into consideration as a dynamic network and a multiplicative DEA approach is utilized to measure efficiency. Given the non-linearity of the models, a heuristic method is used to linearize the models. Ultimately, this paper concentrates on the interval efficiency to rank the units. The results of this ranking demonstrated that the time periods namely, (24) and (1) were the best and the poorest periods, respectively, in context to the interval efficiency within 24 phases of time.


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