In response to the limitation of classical Data Envelopment Analysis (DEA) models, the super efficiency DEA models, including Andersen and Petersen (Manag Sci 39(10): 1261–1264, 1993)’s model (hereafter called AP model) and Li et al. (Eur J Oper Res 255(3): 884–892, 2016)’s cooperative-game-based model (hereafter called L–L model), have been proposed to rank efficient decision-making units (DMUs). Although both models have been widely applied in practice, there is a paucity of research examining the performance of the two models in ranking efficient DMUs. Consequently, it is unclear how close the rankings obtained by the two models are to the “true” ones. Among the very few studies, Banker et al. (Ann Oper Res 250(1): 21–35, 2017) pointed out that the ranking performance of the AP model is unsatisfactory; Li et al. (Eur J Oper Res 255(3): 884–892, 2016) and Hinojosa et al. (Exp Syst Appl 80(9): 273–283, 2017) demonstrated the L–L model’s capability of ranking efficient DMUs without addressing the ranking performance. In this study, we, thus, examine the ranking performance of the two super-efficiency models. In evaluating their performance, we carry out Monte Carlo simulations based on the well-known Cobb–Douglas production function and adopt Kendall rank correlation coefficient. Unlike Banker et al. (Ann Oper Res 250(1): 21–35, 2017), we use the rankings obtained based on the two models and the “true” ones as the basis of performance evaluation in our simulations. Moreover, we consider several types of returns to scale (RS) and study the impact of changes of some parameters on the ranking performance. In view of the importance, we also carry out additional simulations to examine the influence of technical inefficiency on the two models’ ranking performance. Based on the simulation results, we conclude: (1) Under different RS, the ranking performance of the two models remains the same when changing parameters, e.g., the distribution of input variables; (2) Under different RS, when technical inefficiency (in comparison with random noise) is more important, the two models have satisfactory performance by providing rankings that are close to, or the same as, the “true” ones; (3) The L–L model has better performance than the AP model and is more robust. This is especially true when technical inefficiency is less important; (4) Under different RS, when technical inefficiency is less important, both models have unsatisfactory ranking performance; and (5) The relative importance of technical inefficiency plays an prominent role in ranking efficient DMUs.

针对经典数据包络分析 (DEA) 模型的局限性，超高效 DEA 模型，包括 Andersen 和 Petersen (Manag Sci 39(10): 1261–1264, 1993) 的模型（以下称为 AP 模型）和 Li等。(Eur J Oper Res 255(3): 884–892, 2016) 的基于合作博弈的模型（以下称为 L–L 模型）已被提议用于对高效决策单元 (DMU) 进行排名。尽管这两种模型都在实践中得到了广泛应用，但很少有研究检查这两种模型在对高效 DMU 进行排名方面的性能。因此，不清楚这两个模型获得的排名与“真实”排名有多接近。在极少数研究中，Banker 等人。（Ann Oper Res 250(1): 21–35, 2017）指出AP模型的排名表现不尽如人意；李等人。(Eur J Oper Res 255(3): 884–892, 2016) 和 Hinojosa 等人。(Exp Syst Appl 80(9): 273–283, 2017) 展示了 L–L 模型在不考虑排序性能的情况下对高效 DMU 进行排序的能力。因此，在本研究中，我们检查了两个超效率模型的排名性能。在评估它们的性能时，我们基于著名的 Cobb-Douglas 生产函数进行蒙特卡罗模拟，并采用 Kendall 等级相关系数。与银行家等人不同。（Ann Oper Res 250(1): 21–35, 2017），我们使用基于两个模型和“真实”模型获得的排名作为我们模拟中性能评估的基础。此外，我们考虑了几种类型的规模回报（RS）并研究了一些参数的变化对排名性能的影响。鉴于重要性，我们还进行了额外的模拟，以检查技术效率低下对两个模型排名性能的影响。基于仿真结果，我们得出结论： (1) 在不同的 RS 下，当改变参数，例如输入变量的分布时，两个模型的排序性能保持不变；(2) 在不同的 RS 下，当技术低效率（与随机噪声相比）更重要时，两个模型通过提供与“真实”接近或相同的排名来获得令人满意的性能；(3) L-L模型比AP模型性能更好，鲁棒性更强。当技术效率低下不那么重要时尤其如此；(4) 在不同的 RS 下，当技术效率不那么重要时，两种模型的排名表现都不令人满意；