Two-stage Stochastic DEA Model With Undesirable Outputs And Its Application Research

Efficiency evaluation is an important aspect of system research.In the actual production process,due to the influence of the external environment,the input and output of the system are often random,but in the past studies,most of the models used for efficiency evaluation are determined,and random factors are rarely considered.Since the existing random DEA model is mainly applied to the efficiency evaluation of a single-stage system,the system is regarded as a black box,and the information of internal activities is not explicitly utilized.In addition,most of the research on the internal activities of the decision-making unit is based on minimizing the maximum output of the input,and that the input and output of the system are expected.Unrealistic output is very common in reality,especially in a two-stage system where undesired outputs need to be handled in a suitable way.Therefore,based on the classical theory of DEA model,this paper extends the stochastic DEA model to a two-stage form and discusses the processing of undesired outputs under random conditions to make up for the shortcomings of existing research.In this thesis,we combine theoretical modeling and empirical research to comprehensively expound the feasibility and practicability of the model.Firstly,the paper summarizes the random DEA model research and the efficiency evaluation method of the two-stage system in the literature.Then,based on the basic theory of DEA and the existing model,the types of output indicators in the two-stage system are discussed.By introducing weak free disposition,a random DEA production set with undesired output is constructed,and according to the production possible set.The form of the construction of a random DEA model.Next,the model is transformed into a linear form by the opportunity constraint method,which makes the model easy to solve,and time series regression analysis is used to estimate the parameter information such as the mean and standard deviation of the random variables.Finally,an empirical study on the efficiency of China's commercial banks.17 commercial banks were selected as the research object.Assuming that the input is controllable,the output is randomized by the random factor-economic conditions.The single-stage random DEA model is used(the system is regarded as a black box,ignoring the intermediate process).The two-stage stochastic network DEA model and the two-stage stochastic DEA model with undesired output evaluate commercial bank efficiency.Empirical studies show that:(1)Under the assumption of randomness,different risk levels are selected,and the results of commercial bank efficiency evaluation are significantly different.Compared with city banks,the fluctuations in the efficiency of state-owned banks and joint-stock banks are more obvious.These two types of banks are more sensitive to changes in the external environment such as economic policies;(2)Overall,the evaluation results of the three models are consistent.However,compared with the single-stage random DEA model,the two-stage stochastic DEA model proposed in this paper considers the intermediate process,and the evaluation results are more differentiated,especially for the decision-making units whose efficiency values are very close.(3)The stochastic DEA model can evaluate the system efficiency of undesired output.The results show that the rankings of state-owned banks such as Bank of China and Industrial and Commercial Bank of China have dropped significantly,and the rankings of several joint-stock banks have risen.It can be seen that non-performing loans have a significant impact on system efficiency.The model can consider risk factors such as non-performing loans in the efficiency evaluation of commercial banks.