Research On The Efficiency Evaluation Method Based On Non-radial Distance Function In DEA

Data envelopment analysis(DEA)is a nonparametric linear programming method that measures the relative efficiencies of a set of comparable entities called decision making units with multiple inputs and multiple outputs.The advantages of DEA are that it does not require any predetermined assumptions about the production function and it does not require any information regarding input and output weights.As one of the most useful performance and productivity evaluation tools,it has been adopted for performance evaluation in the areas of economics,finance,traffic,education,healthcare,agriculture,and among others.As the extended DEA approachs,some non-radial distance function models,such as directional distance function(DDF),slacks-based measure(SBM),and the least distance DEA model,have also received substantial attention and research because of their respective advantages in efficiency evaluation.In the non-radial DEA-based modelling and applications,it is very important with respect to the theoretical and practical perspectives that solving how to select the appropriate direction along which to measure the performance of DMUs and obtain an acceptable and convincible evaluation result for all DMUs,and ranking all DMUs in the presence of negative inputs and/or outputs.The main work and the contributions of the dissertation are as follows.First,we propose a cross-bargaining game approach that combines DDF,least distance DEA model and bargaining game.In the least distance DEA models,the inefficient DMU can improve to the efficient frontier with less effort along its own direction determined by the least distance.However,the least distance approach has two limitations.One is that it uses a self-evaluated mode which gives the DMUs total flexibility in selecting the projection direction,which may result in the use of projection direction which contains many zaros.This would lead to a comparably unbalanced development of the DMU.The other limitation is that each DMU is evaluated using its own most favorable projection and the assessed DMUs do not use one consistent projection direction.To address the two limiations of the least distance DEA model,we propose a cross-bargaining game approach based on peer evaluatjon and bargaining.In the cross-bargaining game,each pair of inefficient DMUs will obtain a common projection direction by bargaining with each other.Each inefficient DMU will get a self-evaluated efficiency score by applying its own optimal direction and peer-evaluated efficiency scores calculated by using negotiated directions,and then averaging these scores as the average cross-bargaining-directional efficiency value for each inefficient DMU.The use of cross-bargaining negotiated projection directions and the Pareto-optimality of the DMUs' final average cross-bargaining-directional efficiencies make the evaluation results more acceptable and convincing to all inefficient DMUs.Second,we propose an expected efficiency model based on DDF which incorporates the concept of mean value in the DDF model.In the expected efficiency model,the evaluated DMU considers all possible directions to the frontier,and the expected efficiency is defined as the mean value of all relative efficiency scores of the assessed DMU along all directions.The expected efficiency model resolves the sensitivity issue caused by choosing different directions;overcomes a decision maker's subjectivity in the direction selection;and ensures that all DMUs are estimated in a consistent manner,thus obtaining an more equitable and acceptable results for all DMUs.Third,we propose a modified DEA-SBM measurement which can evaluate the performance of DMUs in the presence of negative input and output values and rank them.To further distinguish the efficient DMUs,we propose a slacks-based DEA ranking method to handle negative data.The proposed approach can evaluate the performance of DMUs which contain negative input and out values and provide a fully ranking result.Therefore,the new method enrichs the DEA ranking methods and DEA methods handling negative data,and enlarges the range of DEA application.To summarize,the research on the efficiency evaluation method in this dissertation based on the non-radial distance funtin DEA models,such as DDF,SBM,and least distance DEA approach.A cross-bargaining game approach which considers peer evaluation and bargaing,and an expected efficiency model which considers consistent and equitable evaluation manner are proposed in the dissertation.Moreover,a modified DEA-SBM approach to assess the performance of DMUs in the presence of negative input and output values and ranking them is provided.