DEA Cobb–Douglas frontier and cross-efficiency

W D Cook and J Zhu
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W D Cook: Schulich School of Business, York University, Toronto, Canada
J Zhu: School of Business, Worcester Polytechnic Institute, Worcester, USA

Journal of the Operational Research Society, 2014, vol. 65, issue 2, 265-268

Abstract: The current paper examines the cross-efficiency concept in data envelopment analysis (DEA). While cross-efficiency has appeal as a peer evaluation approach, it is often the subject of criticism, due mainly to the use of DEA weights that are often non-unique. As a result, cross-efficiency scores are routinely viewed as arbitrary in that they depend on a particular set of optimal DEA weights generated by the computer code in use at the time. While imposing secondary goals can reduce the variability of cross-efficiency scores, such approaches do not completely solve the problem of non-uniqueness, and meaningful secondary goals can lead to computationally intractable non-linear programs. The current paper proposes to use the units-invariant multiplicative DEA model to calculate the cross-efficiency scores. This allows one to calculate the maximum cross-efficiency score for each DMU in a converted linear model, and eliminates the need for imposing secondary goals.

Date: 2014
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