A new modified DEA model for distinguishing efficient decision making units

The efficiency evaluation value which is provided by C²R model of data envelopment analysis (DEA) can be used for ranking decision making units (DMUs), however, this ranking procedure does not yield relative rankings for those units with 100% efficiency. Some researchers have proposed a modified efficiency measure for efficient units which can be used for ranking, but this ranking breaks down in some cases, and can be unstable when one of the DMUs has a relatively small value for some of its inputs. To solve the problems of distinguishing efficient DMUs and unreasonable input and output weights in traditional C²R model of DEA, a modified DEA model (MC²R) for distinguishing DMUs is set up in this paper by introducing two virtual DMUs. The common weights vector is computed and then all DMUs are distinguished and ranked with the modified model. The result of an example proves that our new model can differentiate the efficient DMUs in C²R model and give a more reasonable evaluation.