Stochastic network DEA models for two-stage systems under the centralized control organization mechanism

•The stochastic centralized two-stage network DEA model is proposed.•The stochastic model is converted to linear models under some assumptions.•Efficiency relationships of the whole system and two stages are discussed.•The model is used for performance evaluate of 16 commercial banks in China.

This paper deals with an extension of the conventional DEA formulations by taking into account the serial relationship of two-stage processes with stochastic data. The stochastic two-stage network DEA model is proposed based on centralized control organization mechanism. The stochastic two-stage network DEA model is converted into a deterministic linear programming model under the assumption that components of inputs, outputs and intermediate products are related with some basic stochastic factors. Stochastic efficiency analysis including the relationships of the whole process and the two sub-processes are then discussed. In addition, an example of 16 commercial banks in China is used to calculate the efficiencies under different levels by applying the proposed model.