Increasing the discriminatory power of DEA in the presence of the undesirable outputs and large dimensionality of data sets with PCA

This paper proposes an effective approach to deal with undesirable outputs and simultaneously reduces the dimensionality of data set. First, we change the undesirable outputs to be desirable ones by reversing, then we do principal component analysis (PCA) on the ratios of a single desirable output to a single input. In order to reduce the dimensionality of data set, the required principal components have been selected from the generated ones according to the given choice principle. Then a linear monotone increasing data transformation is made to the chosen principal components to avoid being negative. Finally, the transformed principal components are treated as outputs into data envelopment analysis (DEA) models with a natural assurance region (AR). The proposed approach is then applied to real-world data set that characterizes the ecology performance of 17 Chinese cities in Anhui province.