Closest target setting for two-stage network system: An application to the commercial banks in China

Traditional data envelopment analysis (DEA) models mainly set the furthest targets as the frontier projection for inefficient decision-making units (DMUs). To achieve the efficient status with less effort, the closest target models are introduced which projected the least input/output improvement for inefficient DMUs. However, these works typically consider each DMU as a "black box" in the closest target setting, and thus these models cannot be directly extended to a system with network structure because there may be no efficient DMU for reference. This paper fills the gap by developing a closest target model for a two-stage system. Instead of constructing the efficient frontier only by the system efficient DMUs in the "black box" system, all the extreme efficient stages of the DMUs are considered to form the closest target for an inefficient DMU. Using our network closest target (NCT) model, a case of the 16 leading commercial banks in China is analyzed. The results show that these commercial banks performed steadily in both efficiency and input/output required improvement during the study period. Moreover, compared with the network furthest target (NFT) model, NCT requires each DMU less improvement on inputs/outputs, and usually obtain the higher efficiency. That is, NCT is more feasible, economical and optimistic. Lastly, we discuss the proportion of each dominating peer referred by the inefficient banks and the importance of these peers is ranked accordingly.