Abstract: The Integer-valued Data Envelopment Analysis (IDEA) is a common method to evaluate the relative efficiencyamong different Decision Making Units (DMUs) by using integer-valued inputs and outputs. By identifying such deficiencies of two classical IDEA models (e.g. Lozano & Villa's model (LV), Kuosmanen&Kazemi Martin's model (KKM)) as the overestimation of efficiencies and the lack of ability to obtain optimal projection points, this paper constructed a rectified KKM model (RKKM) and a radial-based distance integer-valued DEA model (RDI) to address the deficiencies mentioned above. Further, a “three-step method” based on both RDI model and RKKM model was suggested to solve IDEA problems. In the first and second steps, RKKM and RDI were adopted separately to get their respective optimal values, and this was followed by the optimal value comparison to determine the final projection values of each DMU in the third step. To verify the effectiveness of our proposed approach, the famous example of 42 university departments of IAUK was used as study samples. Empirical results show that our “three-step method” outperforms the classical IDEA models and overcomes the two shortcomings mentioned above.Owning a solid theoretical foundation, the easily implemented “three-step method” could be used as a new powerful tool to address IDEA problems.

Key words: integer-valued data envelopment analysis, efficiency evaluation, mixed-integer linear programming, “Three-step Method”