A note on DEA vs principal component analysis: An improvement to Joe Zhu's approach
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TL;DR
Numerical results reveal that both approaches show a consistency inranking with DEA when the data set has a small number of efficient units, but, when a majority of the DMUs in the sample are efficient, only the modified approach produces consistent ranking with DEA.
Abstract
This paper considers a previous article published by Zhu in the European Journal of Operational Research which describes a joint use of data envelopment analysis (DEA) and principal component analysis (PCA) in ranking of decision making units (DMUs). In Zhu's empirical study, DEA and PCA yield a consistent ranking. However, this paper finds that in certain instances, DEA and PCA may yield inconsistent rankings. The PCA procedure adopted by Zhu is slightly modified in this article by incorporating other important features of ranking that Zhu has not considered. Numerical results reveal that both approaches show a consistency in ranking with DEA when the data set has a small number of efficient units. But, when a majority of the DMUs in the sample are efficient, only the modified approach produces consistent ranking with DEA.