Abstract: Traditional DEA applied in analysis of productivity are usually one-stage or basic two-stage models, and these over-simplified settings make numerical calculation and mathematical speculation easy to be solved. However, weakness of these models are also obvious that a complex structure of DMU can not be depicted. In this paper, DEA models with complex networks are developed, which depicts the operating structure of Chinese commercial banks, to evaluate the structural efficiency of these banks. By taking into consideration of not only a basic two-stage but a cross connection structure, knowledge of a DEA structure is deepened. The key feature depicted in this paper is that fixed assets and overheads of banks are not only used in liability business of commercial banks but also in OBS (off-balance-sheet) activities and assets operation. Along with the complication is the increasing difficulty of modeling and calculation.An improved mathematical programming problem is introduced to depict the complex network, then the model is simplified by deduction, and the problem is solved by numerical simulation. Under two types of assumptions on inputs disposability, one of which is that all of the decision making units have a same allocation ratio of inputs to two stages and the other is that the decision making units make the allocation choices respectively since they are separate entities, two DEA models with complex networks are developed. The first assumption makes a linear model, and the second makes a nonlinear one. Instead of 16 listed banks in A-share markets, data in 2008-2011 of 85 Chinese commercial banks from Bankscope is used, banks in China are divided into four categories, which are state-owned bank, joint-stock banks, urban commercial banks and foreign banks. Then empirical analysis is conducted on structural efficiency of these banks. Based on the calculation, it is found out that in terms of structural efficiency, state-owned banks are most efficient among these four categories, and urban commercial banks are most inefficient. This result contradicts most former literature, whose efficiency calculations ussally show that state-owned banks are most inefficent. This contradiction is attributed to that intermediary business and investment activities of banks are taken into consideration. A general method is provided to study on complex DMU structure, which extends the application of DEA models. Also the empirical results of this paper provides a different view of the operation of commercial banks.

Key words: banking structure efficiency, complex network DEA model, network DEA efficiency