Interval Cross Efficiency Measurement for General Two-Stage Systems

The data envelopment analysis (DEA), which is based on mathematical programming, is employed to measure the relative efficiency of several homogeneous decision-making units (DMUs) with multiple inputs and outputs. There has been extensive research on developing the classical DEA models for various forms and conditions. For example, ranking models such as cross efficiency have been proposed to address the shortcomings of the initial basic models. The data envelopment analysis for network systems has been developed as the network data envelopment analysis (NDEA), and models such as interval data envelopment analysis (IDEA) have been provided to take into account data uncertainty. But using this technique for issues that have all these conditions requires a single model, in which all the conditions are included. In the case study of this paper, the branches in the banking industry are ranked, and several models are presented according to different approaches to the NDEA in order to calculate the interval cross efficiency of a general two-stage network system. Finally, the results of the models are compared.