Cross-efficiency is a ranking technique based on the peer-evaluation that can increase the discriminating power between efficient decision-making units. This paper intends to assess the two-stage processes consisting of undesirable outputs by applying the cross-efficiency evaluation. Given undesirable outputs, the directional distance function under the weak disposability assumption is utilized. The proposed model under variable returns to scale is designed, which makes it different from the previous models. Furthermore, it can reduce the zero optimal coefficients. By measuring the inputs and outputs inefficiency, the whole system and each of its two stages rank, simultaneously. To analyze the suggested method, an application on the industrial productions of 30 regions of China is used. پرونده مقاله

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. پرونده مقاله