The uncertain two-stage network DEA models

The two-stage network DEA models based on the framework that the efficiency of the whole stage is equal to the product of the efficiencies of two sub-stages can not only turn the 'black box' into the 'glass box' to identify the root causes of the inefficiency of the network system, but also consider the relationship between the two sub-stages within the whole stage. Nowadays, the two-stage network DEA models have been widely applied in the field of economy and management, such as green supply chain and reverse supply chain. Due to the novelty of evaluation indexes, these emerging research objects with network structure, such as green supply chain, involve not only traditional evaluation indexes such as cost and time, but also some novel evaluation indexes such as customer satisfaction and flexibility. However, these new evaluation indexes are difficult to quantify accurately, which will lead to the failure of the traditional two-stage network DEA models. Therefore, this paper attempts to extend the traditional two-stage network DEA models to the uncertain two-stage network DEA models with the application of uncertainty theory. In the new models, inputs, intermediates and outputs are considered to be uncertain variables to deal with the problem of inaccurate data. Finally, a numerical example of the uncertain two-stage network DEA models will be presented for illustration.