本文从银行运营结构入手，建立符合银行结构特征的复杂网络DEA模型，评价银行整体结构效率。该模型刻画了商业银行的营业费用和固定资产投入被同时用于负债业务、表外业务和资产业务这一特征，更加贴近现实。根据对于投入可处置性的不同假定，我们给出处理复杂网络DEA模型的两种方法。前者假定决策单元（DMU）是类似的，存在相同的最优投入比例，为线性模型；后者假定决策单元具有独立性，可根据自身需要对投入进行自由划分，为非线性模型。最后我们将这两个模型与基准网络DEA模型WYP（2011）一起用于中国商业银行结构效率的经验分析。
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.
[1] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units[J]. European Journal of Operational Research, 1978, 12(6): 429-444.
[2] Chen Yao, Liang Liang, Yang Feng, et al. Evaluation of information technology investment: A data envelopment analysis approach[J]. Computers & Operations Research,2006, 33(5): 1368-1379.
[3] Chen Yao, Cook W D, Zhu J. Deriving the DEA frontier for two-stage processes[J]. European Journal of Operational Research,2010, 202(1):138-142.
[4] Cook W D, Liang Liang, Zhu J. Measuring performance of two-stage network structures by DEA: A review and future perspective[J]. Omega, 2010, 38(6): 423-430.
[5] Färe R, Grosskopf S. Productivity and intermediate products: A frontier approach[J]. Economics Letters, 1996, 50(1):65-70.
[6] Färe R, Grosskopf S. Network DEA[J]. Socio-Economic Planning Sciences, 2000, 34(1):35-49.
[7] Kao C, Hwang S N. Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[J]. European Journal of Operational Research, 2008, 185(1): 418-429.
[8] Liang Liang, Cook W D, Zhu J. DEA models for two-stage processes: Game approach and efficiency decomposition[J]. Naval Research Logistics. 2008, 55(7): 643-653.
[9] Liu Wenbin, Zhou Zhongbao, Ma Chaoqun, et al. Two-stage DEA models with undesirable input-intermediate-outputs[J]. Omega, 2015, 56:74-87.
[10] Luo Yan, Bi Gongbing, Liang Liang. Input/output indicator selection for DEA efficiency evaluation: An empirical study of Chinese commercial bank[J]. Expert Systems with Applications, 2012, 39(1): 1118-1123.
[11] Matthews K.Risk management and managerial efficiency in Chinese banks: A network DEA framework[J]. Omega, 2013,41(2): 207-215.
[12] Seiford L M, Zhu J. Profitability and marketability of the top 55U.S. commercial banks[J]. Management Science, 1999, 45(9): 1270-1288.
[13] Sexton T R, Lewis H F. Two-stage DEA: An application to major league baseball [J]. Journal of Productivity Analysis, 2003, 19(2): 227-249.
[14] Wang Ke, Huang Wei, Wu Jie, et al. Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA[J]. Omega, 2014, 44: 5-20.
[15] Wei Quanling, Yan Hong, Pang Liyong. Composite network data envelopment analysis model[J]. International Journal of Information Technology & Decision Making, 2011, 10(4): 613-633.
[16] Zha Yong, Liang Nannan, Wu Maoguo, et al. Efficiency evaluation of banks in China: A dynamic two-stage slacks-based measure approach[J]. Omega, 2016, 60:60-72.
[17] 毕功兵,梁樑,杨锋.两阶段生产系统的DEA效率评价模型[J]. 中国管理科学,2007,15(2):93-97.
[18] 丁曼,马超群,周忠宝,等. 基于三阶段加性DEA模型的我国上市商业银行效率研究[J]. 系统工程,2013, 4: 19-26.
[19] 葛虹,黄祎,徐红英.基于决策者偏好的网络DEA模型-以我国若干家商业银行为例[J]. 运筹与管理,2011,20(1):135-142.
[20] 黄祎,葛虹,冯英俊. 基于链型系统的关联网络DEA模型:以我国14家商业银行为例[J]. 系统工程理论与实践,2009,29(5):106-114.
[21] 胡晓燕,程希骏,马利军.考虑非期望产出的两阶段DEA模型及其在银行效率评价中的应用[J]. 中国科学院大学学报,2013,30(4):462-471.
[22] 芦烽,刘维奇,史金凤. 我国商业银行效率研究-基于储蓄新视角下的网络DEA方法[J]. 中国软科学,2012, (2): 174-184.
[23] 周逢民,张会元,周海,等. 基于两阶段关联DEA模型的我国商业银行效率评价[J]. 金融研究,2010, (11): 169-179.
[24] 周忠宝,喻怀宁,马超群,等.基于自由处置性的网络系统效率评价模型研究[J]. 中国管理科学,2015,23(11):145-152.
