Ranking decision making units with large set of highly correlated performance indicators: A method based on Gram–Schmidt process

The current paper presents an approach based upon Gram–Schmidt process to deal with a kind of typical ranking problem, which has the following two characteristics: (1) each decision making unit (DMU) has a large set of performance indicators; (2) there exist multiple correlations among these indicators. In the proposed approach, we firstly use the maximum variance method based on Gram–Schmidt process to transform the original indicators into the corresponding orthogonal variables (Schmidt variables). And at the same time, a measure of investigating the cumulative variation information for selecting Schmidt variables is described. Secondly, a method for setting weights attached to the chosen Schmidt variables is provided; and then a ranking approach through weighted sum of the chosen Schmidt variables is presented. Finally, two Chinese cases are used to illustrate the rationality and advantage of the proposed ranking approach.