Improvement Methods For Data Envelopment Analysis Cross-efficiency Evaluation

Data envelopment analysis(DEA)is a non-parametric method which has been widely applied for performance evaluation and benchmarking of a group of homogeneous decision-making units(DMUs).However,this method usually identifies many efficient DMUs and fails in fully ranking all the DMUs.To address this problem,scholars proposed to use the DEA cross-efficiency evaluation which is with a very strong power in discriminating and ranking the DMUs.However,this method still has the shortcomings including non-uniqueness optimal weights and non-Pareto optimality of the evaluation results.These shortcomings have made the evaluation results not acceptable to all the DMUs and have futherly reduced the usefulness of this powerful method.This thesis aims at proposing methods to optimize the DEA cross-efficiency evaluation.We mainly focus on addressing the non-uniqueness optimal weights and non-Pareto optimality of the evaluation results in DEA cross-efficiency evaluation.Additionally,we also consider to give improvement methods considering to improving the DMUs acceptance on the evaluation result.The proposed approaches are used for R&D project selection,technology selection,green supplier selection,etc.The main works are concluded as follows.First,we point out that the traditional cross-efficiency targets that used in the secondary goal models are not always feasible for all the DMUs.We then give a cross-efficiency targets identifying model which can provide reachable desirable and undesirable cross-efficiency targets for all the DMUs.Further,several new benevolent and aggressive secondary goal models and a neutral model are proposed for weight selection for cross-efficiency evaluation of the DMUs.Second,we present a DEA cross-efficiency evaluation approach based on Pareto improvement.Two principles for weights selection when improving the cross-efficiency scores of the DMUs are defined.A Pareto optimality estimation model is given to estimate whether a given set of cross-efficiency scores is pareto optimal.Further,we give a cross-efficiency Pareto improvement model to make cross-efficiency for the set of cross-efficiency scores which is not Pareto optimal.An algorithm is furtherly provided to ensure to finally generate a set of Pareto optimal cross-efficiency scores for the DMUs.Third,we give a cross-bargaining game DEA cross-efficiency evaluation approach which addresses both the non-uniqueness of optimal weights and non-Pareto-optimality of the evaluation result.A cross-bargaining game model is proposed to simulate the bargaining between each pair of DMUs among the group for the set of weights which is used for cross-efficiency evaluation between them.Fourth,we propose the DEA cross-efficiency evaluation based on satisfaction degree.Firstly,we introduce the concept of satisfaction degree of each DMU on the optimal weights selected by the other DMUs.Then,a model is given to select the set of optimal weights for each DMU which maximizes all the DMUs' satisfaction degrees.Two algorithms are given furtherly which guarantee to solve the model linearly and the uniqueness of the optimal weights for each DMU respectively.The main innovative aspects of this thesis can be concluded as follows:(?)More reasonable and feasible cross-efficiency targets are incorporated and used in the secondary goal models in DEA cross-efficiency evaluation;(?)The Pareto improvement DEA cross-efficiency evaluation approach always guarantees the Pareto optimality of the evaluation result.Further,the evaluation result unifies DEA self-evaluation,peer-evaluation,and common-weight evaluation;(?)The cross-bargaining game DEA cross-efficiency evaluation approach introduces a new evaluation mode,i.e.,each pair of DMUs are allowed to make a bargaining equilibrium on the set of weights for cross-efficiency calculation of their corresponding cross efficiencies.The evaluation result is unique and always Pareto optimal;(?)The cross-efficiency evaluation approach based on satisfaction degree maximizes the DMUs' satisfaction degrees on the evaluation result.It also guarantees the uniqueness of the optimal weights of each DMU in the evaluation result.All the above have enhanced the DMUs' acceptability on the evaluation result.