整数数据包络分析（IDEA）是一种用于当投入产出指标为整数时，分析决策单元（DMU）相对效率的评价方法。我们针对传统LV模型和KKM模型存在无法得到最优改进点和高估效率值的不足，提出RKKM模型和RDI模型。基于RKKM模型和RDI模型我们进一步提出“三步法”来解决IDEA问题。“三步法”的第一步和第二步分别求解RKKM模型和RDI模型来得到各自的最优值，第三步通过对比这两个模型的最优值来得到每个DMU最终的最优投影点。为了验证“三步法”的先进性，以伊朗42所高校效率评价的经典算例测算、对比上述各模型的数值效果，发现“三步法”有效解决了传统IDEA模型的不足。“三步法”不仅拥有坚实的理论基础，而且计算上容易实现，因此它可以作为解决IDEA问题的一个重要的工具。
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.
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