Cross-efficiency evaluation capable of dealing with negative data: A directional distance function based approach

Abstract

Cross-efficiency evaluation is a commonly used technique for ranking decision making units (DMUs) in data envelopment analysis while it is just applicable to the non-negative data set. Based on the range directional measure (RDM), we explore the duality relation regarding the maximum slacks formulation of RDM and define cross-efficiencies on the basis of the equivalences with some fractional programming problems. The newly defined cross-efficiency evaluation is under the variable returns to scale condition. It can handle negative values in inputs and outputs well and the resulting cross-efficiencies as well as cross-efficiency scores are between 0 and 1 for all DMUs. It provides self- and peer-evaluations of DMUs by measuring the inefficiency in both inputs and outputs simultaneously. In addition, we propose a corresponding model that implements the benevolent criterion to select weights. A numerical example demonstrates the validity and effectiveness of the proposed cross-efficiency evaluation in dealing with negative data.

Keywords:

• Data envelopment analysis
• cross-efficiency evaluation
• directional distance function
• negative data
• range directional measure

Acknowledgements

The authors appreciate the important comments made by Prof. Jie Wu, and are grateful to anonymous referees and the editor for their constructive comments, which have helped us to improve the paper significantly in both content and style.

Disclosure statement

No potential conflict of interest was reported by the author.

Funding

The work was supported by the National Natural Science Foundation of Zhejiang Province, China (Grant Nos. LY17G010004); the National Natural Science Foundation of China (Grant Nos. 11301395); Science and Technology Planning Projects of Wenzhou (Grant Nos. R20160004).