The hyperbolic-oriented efficiency measure as a remedy to infeasibility of super efficiency models

Abstract

The infeasibility problem in traditional super efficiency models has been well established. A generalization of traditional input- or output-oriented super efficiency models, the directional distance function also suffers from infeasibility and related problems. The hyperbolic-oriented efficiency measure provides an alternative to the input-oriented, output-oriented, and directional efficiency measures in super efficiency models and it has the distinct advantage of eliminating the infeasibility problem for positive input/output data. We also show that using a hyperbolic orientation in a super efficiency model allows us to find feasible solutions for certain cases when the requirement for all data to be positive is relaxed. Further we demonstrate the hyperbolic orientated super efficiency method in an outlier detection application. Together, these results establish the use of the hyperbolic orientation in super efficiency analysis as a realistic alternative in practice.

Keywords:

• data envelopment analysis
• hyperbolic distance function
• super efficiency
• outlier

Acknowledgements

The authors acknowledge the support for this work by the National Science Foundation under grant 0400187, and the Book Industry Study Group (BISG), and the contributions of the anonymous referees in improving the paper.