Document Type : Research Paper


1 Department of Applied Mathematics, Islamic Azad University, Rasht Branch, Rasht, Iran

2 Department of Mathematics, Technical and Vocational University (TVU), Rasht branch,



Naturally, managers are interested in analyzing the relative efficiency of the production systems with parametric or non-parametric methods. One of the non-parametric methods utilized in recent three decades is a data envelopment analysis (DEA) that can evaluate the relative efficiency of these structures and determine their strengths and weaknesses. In the real world, most production systems have a network structure. So, network data envelopment analysis (NDEA) is a suitable non-parametric method to evaluate the performance of production processes, which considers the internal processes. In addition to the importance of treating consumed waters and pollutants in environmental protection in today’s world, increasing the profitability of the production unit can be an important motivation to design the proper model to evaluate the performance of these structures in terms of profitability. In this sense, we first introduce a two-stage feedback structure including undesirable factors. Then, by applying the assumption of weak disposability for undesirable factors, a method for analyzing the relative performance of such network structures is given. The focus would be on profitability maximization. Moreover, to illustrate the proposed approach, a real case on the ecological system of 31 regions of China is used.


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