DEA efficiency assessment using ideal and anti-ideal decision making units

This paper introduces two virtual decision making units (DMUs) called ideal DMU (IDMU) and anti-ideal DMU (ADMU) into the data envelopment analysis (DEA). The resultant DEA models are, respectively, referred to as the data envelopment analysis with ideal and anti-ideal decision making units. One evaluates DMUs from the viewpoint of the best possible relative efficiency, while the other evaluates them from the perspective of the worst possible relative efficiency. The two distinctive efficiencies are combined to form a comprehensive index called the relative closeness (RC) to the IDMU just like the well-known TOPSIS approach in multiple attribute decision making (MADM). The RC index is then used as the evidence of overall assessment of each DMU, based on which an overall ranking for all the DMUs can be obtained. Two numerical examples are provided to illustrate the applications of the proposed DEA models and the RC index.