This paper extends the conventional DEA models to a robust DEA (RDEA) framework by proposing new models for evaluating the efficiency of a set of homogeneous decision-making units (DMUs) under ellipsoidal uncertainty sets. Four main contributions are made: (1) we propose new RDEA models based on two uncertainty sets: an ellipsoidal set that models unbounded and correlated uncertainties and an interval-based ellipsoidal uncertainty set that models bounded and correlated uncertainties, and study the relationship between the RDEA models of these two sets, (2) we provide a robust classification scheme where DMUs can be classified into fully robust efficient, partially robust efficient and robust inefficient, (3) the proposed models are extended to the additive DEA model and its efficacy is analyzed with two imprecise additive DEA models in the literature, and finally, (4) we apply the proposed models to study the performance of banks in the Italian banking industry. We show that few banks which were resilient in their performance can be robustly classified as partially efficient or fully efficient in an uncertain environment.

中文翻译：

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通过椭球不确定性集进行稳健的数据包络分析，并应用于意大利银行业

本文通过提出用于评估椭球不确定性集下的同类决策单元（DMU）效率的新模型，将常规DEA模型扩展到鲁棒DEA（RDEA）框架。主要有四个方面的贡献：（1）我们基于两个不确定性集合提出了新的RDEA模型：一个对无界和相关不确定性进行建模的椭圆集和一个对有界和相关性不确定性进行建模的基于区间的椭圆形不确定性集，并研究了两者之间的关系。这两个集合的RDEA模型（2）提供了一种鲁棒的分类方案，其中DMU可以分为完全鲁棒的有效，部分鲁棒的有效和鲁棒的低效率，（3）将提出的模型扩展到加性DEA模型，并通过文献中两个不精确的加性DEA模型分析其有效性，最后，（4）我们将提出的模型用于研究意大利银行业的银行绩效。我们表明，在不确定的环境中，很少有表现出色的银行可以可靠地分类为部分有效或完全有效。