Journal of Applied Mathematics
Volume 2013 (2013), Article ID 102163, 21 pages
Research Article

A Distribution-Free Approach to Stochastic Efficiency Measurement with Inclusion of Expert Knowledge

1TD Canada Trust, Toronto, ON, Canada
2School of Information Technology, York University, 4700 Keele Street, Toronto, ON, Canada M3J 1P3
3Centre for Management of Technology and Entrepreneurship, University of Toronto, 200 College Street, Toronto, ON, Canada M5S 3E5

Received 24 October 2012; Accepted 11 May 2013

Academic Editor: Suh-Yuh Yang

Copyright © 2013 Kerry Khoo-Fazari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper proposes a new efficiency benchmarking methodology that is capable of incorporating probability while still preserving the advantages of a distribution-free and nonparametric modeling technique. This new technique developed in this paper will be known as the DEA-Chebyshev model. The foundation of DEA-Chebyshev model is based on the model pioneered by Charnes, Cooper, and Rhodes in 1978 known as Data Envelopment Analysis (DEA). The combination of normal DEA with DEA-Chebyshev frontier (DCF) can successfully provide a good framework for evaluation based on quantitative data and qualitative intellectual management knowledge. The simulated dataset was tested on DEA-Chebyshev model. It has been statistically shown that this model is effective in predicting a new frontier, whereby DEA efficient units can be further differentiated and ranked. It is an improvement over other methods, as it is easily applied, practical, not computationally intensive, and easy to implement.