Abstract
Data Envelopment Analysis (DEA) cross-efficiency has been used to replace the self-evaluation system, which requires decision-makers to rank a series of decision-making units (DMUs) according to cross-efficiency scores, and finally determine the order of each DMU, so as to provide decision-making basis for decision-makers. However, this method has certain deficiencies: one is that the cross-efficiency value is not unique; the other one is that the cross-efficiency evaluation uses the same weight to aggregate cross-efficiency. In this paper, Technique for order performance by similarity to ideal solution (TOPSIS) and The Best Worst Method (BWM) methods are used to aggregate the aggressive cross-efficiency values and benevolent cross-efficiency values. Besides, the high consistency of the BWM method improves the shortcomings of the TOPSIS method. The result of TOPSIS method is not necessarily close to the ideal solution, and far away from the negative ideal solution. At the same time, the distance measured by the TOPSIS method replaces the preference of the BWM method, which makes BWM method more objective. Finally, a numerical example is given to verify the feasibility and effectiveness of the method.
Highlights
Data Envelopment Analysis (DEA) is a nonparametric mathematical programming method for evaluating the relative efficiency of decision-making units (DMUs) in the same type which Originated from the study of productivity by Farrell [1]
Banker [4] extended the work of Charnes and Cooper, proposed DEA-BCC model based on the variable return to scale (VRS)
The weight obtained by DEA model which relates to the other DMUs is the most efficient weight of the evaluated DMU, which makes the result cannot be accepted
Summary
DEA is a nonparametric mathematical programming method for evaluating the relative efficiency of DMU in the same type which Originated from the study of productivity by Farrell [1]. Doyle and Green [6] proposed the classic aggressive and benevolent models which selected a group of optimal weights for self-evaluated efficiency and peer-evaluated efficiency. In order to improve the original cross-efficiency method, the paper applies the TOPSIS and BWM methods to integrate the cross-efficiency values based on the aggressive and benevolent cross-efficiency model. Variables vid and urd represent the weights given to the ith input and the rth output for DMUd for the above fractional program (1), the following equivalent forms of linear programming problems can be obtained through the classical Charnes et al [2] transformation:.
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