| Data envelopment analysis(DEA)is an important analytical tool and research means in the fields of efficiency measurement,decision analysis,management science and system engineering.The evaluation reference set of the traditional DEA method is composed of all decision making units(DMUs),and the decision maker can only get the information compared with excellent decision making units.However,in reality,there are some evaluation problems,the comparison object needed by the decision maker may not be excellent decision making units,but the special decision making units or non decision making units.At this time,the traditional DEA method cannot solve this problem.The generalized DEA method can evaluate the decision making units according to any reference set,extend the traditional DEA theory,and has more application advantages than the traditional DEA method.However,the existing generalized DEA models are all radial models,and the decision making unit is regarded as a whole,and the internal structure of decision making unit is rarely considered.In view of this,this paper studies non-radial generalized DEA method,including generalized SBM method and generalized network SBM method.The research is to further perfect the generalized DEA method and theoretical system,and expand the application scope of generalized DEA method.The main research contents are as follows:(1)Research on generalized SBM(slacks-based measure)method by using sample units.The existing generalized DEA models require all inputs to decrease in the same proportion or output to increase in the same proportion,which has certain limitations in practical application.In view of this,the sample production possibility set with moving factor is defined and the generalized SBM model is proposed based on the sample production possibility set.According to whether the decision making unit belongs to the sample production possibility set,the efficiency of generalized SBM and the projection property of decision making units in the sample production possibility set are studied.The rationality and feasibility of this method are illustrated by comparing the method with other methods.Compared with traditional SBM,the generalized SBM method can arbitrarily select the evaluation reference set to evaluate decision making units according to needs.The generalized SBM model contains the output oriented moving factor,and the change of the moving factor can be used to further predict the change of the efficiency when the overall technical level of the sample production possibility set is improved or decreased.(2)Research on generalized SBM method considering the projection efficiency of decision making units.In view of the possibility that the efficiency may be overestimated when the generalized SBM measures the efficiency of some decision making units,the generalized SBM method considering the projection efficiency of decision making units is proposed in this paper.In this method,a unified efficiency measurement model is proposed,and the generalized SBM efficiency measurement method is improved to ensures that the projections of the decision making units on the sample production possibility set is generalized SBM efficient,which makes the efficiency measurement more reasonable.In this paper,the rationality and feasibility of this method are illustrated by example in the literature.Then,taking the data from 2011 as the evaluation reference set and the data from 2012 to 2016 as the decision making unit set,this paper analyzes and studies the change trend of scientific research efficiency of universities in 27 regions of China in the past five years.The research results help managers to find out the advantages and disadvantages of decision making units compared with sample units,the reasons for the decline of efficiency and the problems existing in the management system,and further allocate resources to achieve effective output.(3)Research on efficiency decomposition in generalized network SBM method by using sample units.The existing generalized DEA methods rarely study the internal structure of decision making units,and the inefficiency problems caused by the organizational activities in decision making units cannot be found and solved,which leads to the problem that the information that helps to improve the efficiency of decision making units is not easy to obtain.In this paper,two-stage and multi-stage extended sample production possibility sets are defined,and the generalized network SBM model based on extended sample production possibility set is proposed for two-stage system and general multi-stage system respectively.The decomposition method of generalized overall efficiency of decision making unit and the relationship between generalized overall efficiency and generalized stage efficiency are studied.In this paper,an example is given to illustrate that the method can select the same sample unit set to evaluate the efficiency of different decision making units according to the needs,and divide the decision making unit into multi-stage system,which is conducive to find out the reasons for the low efficiency of the decision making unit in stages and improve it.The rationality and feasibility of this method are verified by example.Then,the university scientific research system is divided into two stages:R&D stage and achievement transformation stage.Taking the data from 2011 to 2013 as the sample unit set and the data from 2011 to 2017 as the decision making unit sets,this paper analyzes and studies the change trend of scientific research efficiency of universities and the status quo of scientific research in 27 regions of China.The results show that the generalized efficiency of R&D stage is significantly higher than that of achievement transformation stage,and the achievement transformation stage has a greater impact on the whole scientific research system.Managers should promote the coordinated development of the two stages,pay more attention to the value realization of scientific research achievements while paying attention to R&D innovation,and strengthen the management awareness of further promotion and application of scientific research achievements.(4)Research on efficiency aggregation in generalized network SBM method based on internal evaluation.The generalized network SBM method based on extended sample production possibility set measures the efficiency of decision making units from the viewpoint of outside peers.The endogenous inputs and outputs of decision making units is not considered in the measurement of generalized overall efficiency,and different decision making units have different extended sample production possibility sets.In view of this,this paper defines two-stage and multi-stage sample production possibility sets.From the viewpoint of internal managers,this paper proposes a generalized network SBM method based on internal evaluation for two-stage system and general multi-stage system respectively.The generalized stage efficiency and stage weight of decision making unit are defined.The generalized overall efficiency is the weighted average of the generalized stage efficiency,and all the inputs and outputs,including exogenous and endogenous,are considered.The evaluation reference set of the generalized network SBM method based on internal evaluation is the same when measuring the efficiency of decision making units.In this paper,the rationality and feasibility of this method are verified by example,and then the change trend of scientific research efficiency of universities and the status quo of scientific research in 27 regions of China is analyzed and studied.Compared with the generalized network SBM method based on extended sample production possibility set,although the evaluation viewpoint,method and the calculated efficiency value are different,the analysis results are basically the same in the empirical analysis. |
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