Two-stage network-structured production process in the presence of undesirable intermediate measures

Document Type : Research Paper


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

2 Islamic Azad University of Rasht branch


The importance of the issue of environmental pollution is so great that the attention of many researchers has drawn attention to the recycling issue in recent decades. Since a proper evaluation can improve the performance of a system in various situations, the presentation of an appropriate method that can evaluate a production system correctly is necessary. Therefore, first, we introduce a two-stage network structure consists of undesirable intermediate measures. Then, by considering the weak disposability assumption to handle desirable and undesirable outputs, and also links between the subsections of the process, a non-radial model to evaluate the performance of the proposed structure is introduced. The proposed model is developed from the perspective of the centralized approach. Also, it is defined based on the Russell-based model. The introduced model can calculate the efficiency of the whole system without the need to evaluate the efficiency of its subsections. A real case on an industrial production system of 30 regions in China is used to illustrate the proposed model.


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