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A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio

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Abstract

Cross-efficiency evaluation is a useful approach to ranking decision making units (DMUs) in data envelopment analysis (DEA). The possible existence of multiple optimal weights for the DEA may reduce the usefulness of the cross-efficiency evaluation since the ranking is according to the choice of weights that different DMUs make. Most of existing approaches for cross-efficiency evaluation employ the average cross-efficiency to further discriminate among the DEA efficient units or focus on how to determine input and output weights uniquely, but lay little emphasis on the consideration of the ranges and variances of cross-efficiencies as alternative ranking factors. In this paper we consider cross-efficiency intervals and their variances for ranking DMUs. The aggressive and benevolent formulations are taken into account at the same time. Consequently, a number of cross-efficiency intervals is obtained for each DMU. The signal-to-noise (SN) ratio, originally designed for optimizing the robustness of a process, is constructed as a numerical index for ranking DMUs. A nonlinear fractional program with bound constraints is formulated to find the optimal value of the SN ratio. By model reduction and variable substitution, this nonlinear fractional program is transformed into a quadratic one for deriving the global optimum solution. With the derived SN ratios, we are able to fully rank all DMUs accordingly. Two examples are given to illustrate the effectiveness of the methodology proposed in this paper.

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Notes

  1. As a nonparametric method, DEA models require much more observations than parametric methods to get a good estimation. A rule of thumb is the number of DMUs should be at least three times than the total numbers of input and output variables (Cooper et al. 2007). Without an appropriate statistical test to check the change in the technology (or production set), it is dangerous to pool the data from two time periods, since the technology could be changed. Therefore, we only use the observations, the 22 commercial banks in 2013, as the dataset to demonstrate the new approach.

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Acknowledgements

Research was supported by the Ministry of Science and Technology of Taiwan under Contract No. MOST104-2410-H-238-002-MY2. The author is indebted to the editor and the reviewers that significantly improve the quality of the paper.

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  1. Graduate School of Business and Management, Vanung University, Chung-Li, Taiwan, ROC

    Shiang-Tai Liu

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Liu, ST. A DEA ranking method based on cross-efficiency intervals and signal-to-noise ratio. Ann Oper Res 261, 207–232 (2018). https://doi.org/10.1007/s10479-017-2562-8

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