Testing and selecting mixed data type DEA scenarios with PCA post-processing

Abstract

Data Envelopment Analysis (DEA) with a large amount of variables and little DMUs is problematic. Such a configuration with high variable dimensionality yields too much 100 % efficient DMUs, hence making results invaluable. In this paper a new method is provided, which applies Principal Component Analysis (PCA) as a post-processing tool, to test and select valuable DEA scenarios. DEA efficiencies are calculated for all possible scenarios, which then are analyzed with PCA. Additionally, this method is applied on a dataset with both quantitative and qualitative data and an input- and output-oriented approach. It is apparent that scenarios with high loadings on particular Principal Components yield valuable results with both efficient and inefficient DMUs with different model configurations. Therefore, the new PCA-DEA method has the advantage to work with both DEA orientations and a mixed dataset, with both quantitative and qualitative data. Also it is shown that the method's results can be incorporated in a cash cow diagram, in order to interpret a benchmarking case.