DEA中决策单元的分类：一个基于优势的统一模型
On classifying decision making units in DEA: A unified dominance-based model
摘要：
在数据包络分析（DEA）中，效率的概念是在法雷尔（DEA）或帕累托意义上进行检验的。在这两种意义上，决策单元（DMU）的效率状态分为弱或强。强DEA有效是实现帕累托有效的充分必要条件。然而，对于弱Pareto有效性，弱DEA有效性只是充分的，而不是必要的。因此，DEA无效的DMU可以是弱帕累托有效或帕累托无效。出于这一事实，我们提出了一个新的分类的决策单元的DEA和帕累托效率。为了进行这种分类，我们首先证明了法雷尔效率是基于FGL优势的概念。基于优势的概念，我们提出并证实了一种替代的单阶段方法。我们的方法是计算效率高，因为（i）它涉及解决一个独特的单阶段模型为每个DMU，（ii）它完成了分类的DMU在输入和输出方向同时进行。最后，我们提出了一个数值例子来说明我们提出的方法。
英文摘要：
In data envelopment analysis (DEA), the concept of efficiency is examined in either Farrell (DEA) or Pareto senses. In either of these senses, the efficiency status of a decision making unit (DMU) is classified as either weak or strong. It is well established that the strong DEA efficiency is both necessary and sufficient for achieving the Pareto efficiency. For the weak Pareto efficiency, however, the weak DEA efficiency is only sufficient, but not necessary in general. Therefore, a DEA-inefficient DMU can be either weakly Pareto efficient or Pareto inefficient. Motivated by this fact, we propose a new classification of DMUs in terms of both DEA and Pareto efficiencies. To make this classification, we first demonstrate that the Farrell efficiency is based on the notion of FGL dominance. Based on the concept of dominance, we then propose and substantiate an alternative single-stage method. Our method is computationally efficient since (i) it involves solving a unique single-stage model for each DMU, and (ii) it accomplishes the classification of DMUs in both input and output orientations simultaneously. Finally, we present a numerical example to illustrate our proposed method.
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