Super-efficiency and stability intervals in additive DEA

Abstract

This study addresses the problem of finding the range of efficiency for each Decision Making Unit (DMU) considering uncertain data. Uncertainty in the DMU coefficients in each factor (input or output) is captured through interval coefficients (ie, these are uncertain but bounded). A two-phase additive Data Envelopment Analysis model for performance evaluation is used, which is adapted to include the concept of super-efficiency to provide a robustness analysis of the DMUs in face of uncertain information, assessing whether each DMU is surely efficient, potentially efficient, or surely inefficient for the uncertainty intervals specified. Another contribution is to present how a maximal stability hyper-rectangle can be computed for each DMU such that its efficiency status does not change when the coefficients vary within that interval.

Keywords:

• data envelopment analysis
• multi-criteria analysis
• super-efficiency
• robustness analysis
• uncertainty
• stability intervals

Acknowledgements

The authors are grateful for the comments and suggestions made by the anonymous referees. This work is partially supported by FCT FEDER COMPETE grants MIT/MCA/0066/2009, MIT/SET/0014/2009, PEst-C/EEI/UI0308/2011 and MIT/SET/018/2009.