A new approach for fair efficiency decomposition in two-stage structure system

Traditional data envelopment analysis has been applied to many areas to evaluate the relative efficiency of decision making units and it takes the internal structure of system as a "black box". Recently, many two-stage DEA models are built to open up the "black box" of a two-stage system, where the outputs of the first stage are taken as the inputs for the second stage. By applying the two-stage DEA, more inefficiency in the system can be measured. The overall efficiency and divisional efficiencies of DMUs can be simultaneously obtained. Although some works take measures to decompose the overall efficiency into two divisional efficiencies, few works consider the competition between two stages because one stage has larger efficiency value and the other one will have smaller value. More importantly, in previous decomposition works, there are few works considering a DMU's individual performance among its homogenous divisions. Based on the difference between two divisional performance (reference ratio), in this paper, a new model with fairness is proposed to decompose the overall efficiency and further applied to measure Chinese commercial banks' performance from both the individual and overall perspectives.