Abstract The measurement of technical efficiency is a topic of great interest. Since the beginning, many researchers have developed new approaches to gauge technical efficiency, mainly in the non-parametric area of Data Envelopment Analysis (DEA). However, the first measures in DEA, the well-known radial models, only accounted for radial inefficiency, which motivated the introduction in the literature of the so-called Global Efficiency Measures (GEMs); non-oriented and non-radial in nature. Two famous GEMs are the Russell Graph Measure and the Enhanced Russell Graph Measure, also known as the Slacks-Based Measure. These approaches aggregate input and output specific efficiencies through the arithmetic mean, which may not be the most appropriate aggregator function when input and output efficiency ratios are considered, as will be shown. In this paper, in contrast, we propose aggregating input and output specific inefficiencies by applying the geometric average, which will allow us to define new multiplicative versions of the Russell Graph Measures. We also prove some theoretical results and introduce an iterative algorithm, based upon Second Order Cone Programming, to solve the new models. Finally, the implementation of the introduced approaches is empirically illustrated through a data set taken from the literature.

中文翻译：

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数据包络分析中的罗素图效率度量：乘法方法

摘要 技术效率的衡量是一个非常有趣的话题。从一开始，许多研究人员就开发了衡量技术效率的新方法，主要是在数据包络分析 (DEA) 的非参数领域。然而，DEA 中的第一个度量，即众所周知的径向模型，只考虑了径向低效率，这促使文献中引入了所谓的全球效率度量（GEM）；本质上是非定向和非径向的。两个著名的 GEM 是 Russell Graph Measure 和 Enhanced Russell Graph Measure，也称为 Slacks-Based Measure。这些方法通过算术平均值聚合输入和输出特定效率，当考虑输入和输出效率比时，这可能不是最合适的聚合函数，如下所示。相比之下，在本文中，我们建议通过应用几何平均来聚合输入和输出特定的低效率，这将使我们能够定义罗素图度量的新乘法版本。我们还证明了一些理论结果，并介绍了一种基于二阶锥规划的迭代算法来求解新模型。最后，通过从文献中提取的数据集，经验性地说明了所介绍方法的实施。