A novel algorithm for complete ranking of DMUs dealing with negative data using Data Envelopment Analysis and Principal Component Analysis: Pharmaceutical companies and another practical example

When there is an extensive number of inputs and outputs compared to the number of DMUs, one of the drawbacks of Data Envelopment Analysis appears, which incorrectly classifies inefficient DMUs, as efficient ones. Accordingly, the DEA ranking power becomes further moderated. To improve the ranking power, this paper renders the details of an algorithm that presents a model combining the Principal Component Analysis and the Slacks-Based Measure (PCA-SBM) which reduces the number of the incorrectly determined efficient DMUs. Also to complete ranking of DMUs, the algorithm presents a Super-Efficiency model integrated with PCA (PCA-Super SBM) which can rank the efficient DMUs (extreme and non-extreme). Whereas the most important previous models for ranking efficient units cannot rank non-extreme ones. Additionally, in most previous studies, DEA models combined with PCA fail to handle negative data, while, the presented models can cover this data. Two case studies (pharmaceutical companies listed on the Iranian stock market and bank branches) are manipulated to demonstrate the applicability and performance of the algorithm. To show the superiority of the presented models, the SBM model without PCA and the Super SBM model without PCA have been implemented on the data of both cases. In comparing the two methods (PCA-SBM and SBM), the PCA-SBM model has higher ranking power (five efficient DMUs versus nineteen in the case of pharmaceutical companies and four efficient DMUs versus twenty-nine in the case of bank branches). Also in comparing the PCA-Super SBM and Super SBM, the PCA-Super SBM model works more powerfully in complete ranking. As the Super SBM model cannot rank non-extreme units unlike the PCA-Super SBM. Consequently, the presented algorithm works successfully in ranking the DMUs completely (inefficient, extreme, and non-extreme efficient) with low complexity.