Combination of DEA and PCA for Full Ranking of Decision Making Units

This paper presents a combination of Data Envelopment Analysis (DEA) and Principal Component Analysis (PCA) to reduce the dimensionality of data set. DEA is known as effective tool for assessment and benchmarking. The weak point of DEA, it is that the number of efficient DMUs relies on the number of variables (inputs and outputs). For solving this, first, we do principal component analysis (PCA) on the ratios of a single 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. One of the main differences of this model versus previous models is that this one's multi objective model. We used this approach to rank the bank branches of Tehran.