Research On Theory And Application Of Generalized Data Envelopment Analysis With Uncertain Factors

Data envelopment analysis(DEA)is a nonparametric method to evaluate the relative efficiency of multi input and multi output decision-making units.After more than 40 years of development,DEA has become one of the important analysis tools in the fields of economics,management and system science.The traditional DEA method can only evaluate the decision-making unit relative to the set of decision making units,but not relative to any specified reference system.Generalized DEA method puts forward the concept of sample unit,which effectively solves this problem and expands the theoretical system of traditional DEA method.This thesis mainly studies two kinds of problems in the category of generalized DEA method.1.The sample unit is the evaluation reference system in the generalized DEA method,and the decision-making unit should be evaluated based on the sample unit.In the actual evaluation,the decision-making unit or sample unit may be affected by uncertain factors,and its input and output indicators can not be characterized by deterministic values,so it is impossible to evaluate the relative efficiency of decision-making unit with deterministic DEA model.To solve this problem,this thesis preliminarily studies the basic generalized DEA method in which the input and output indexes of decision-making unit or sample unit are in the form of grey number.Several kinds of generalized grey DEA models are constructed,the models are further whitened,and the concept of generalized grey DEA efficiency under the corresponding models is given.It mainly includes the following four aspects.(1)The generalized DEA model in the case of grey decision unit and deterministic sample unit is constructed,the drift whitening solution of the model with interval grey number as the input and output index of decision unit is solved,and the corresponding concept of generalized grey DEA efficiency is given.(2)The generalized DEA model in the case of grey decision-making unit and deterministic sample unit is constructed.According to the historical data sequence of input and output grey quantity of decision-making unit,the predictive solution of the model is carried out by using the single variable grey predict-ion model,and the corresponding concept of generalized grey DEA efficiency is given.(3)The generalized DEA model of deterministic decision unit and grey sample unit is constructed,the drift whitening solution of the model whose input and output index of sample unit is in the form of interval grey number is solved,and the corresponding concept of generalized grey DEA efficiency is given.(4)The generalized DEA models of grey decision-making unit and grey sample unit are given,the drift whitening solution of the model whose input and output indexes of the two units are in the form of interval grey number is solved,and the corresponding concept of generalized grey DEA effectiveness is given.2.The traditional DEA method evaluates the relative efficiency of each decision making unit based on decision making unit set.If there is a large difference in quantity among decision making units,the evaluation results may not reflect the influence of quantity scale.Based on the classification of decision-making units according to certain standards by cluster analysis,this thesis makes self-evaluation and other evaluation of decision-making units according to categories by using traditional and generalized DEA methods,and gives the cross efficiency of decision-making units according to the weight of various quantities and scales.Through the comprehensive operation efficiency evaluation of the top three hospitals in Inner Mongolia,it is verified that the crossefficiency can reflect the scale difference between hospitals through empowerment and overcome the problem of insufficient differentiation of DEA effectiveness sometimes existing in the traditional DEA method.