A ranking model according to grey analysis theory based on cross-evaluation strategy

Data envelopment analysis (DEA) is a useful method for evaluating the relative efficiency of Decision Making Units (DMUs), and the cross-efficiency evaluation method has been proposed for ranking. To solve the non-uniqueness of the value of cross-efficiency evaluation, this paper uses the idea of grey relational analysis and defines the ideal DMU, then calculates the grey relational degree of each DMU with the ideal DMU. The new DEA model determines input and output weights depending on the maximum value of the grey relational degree between each DMU and the IDMU, then the cross-efficiency value of all DMUs can be determined and used for ranking. Finally, a numerical example is used to illustrate the efficiency of the new model.