具有重量限制的规模收益测量：如何处理多个支撑超平面的出现？
Measurement of returns to scale with weight restrictions: How to deal with the occurrence of multiple supporting hyperplanes?
摘要：
在数据包络分析（DEA）中，多个支撑超平面的出现是衡量规模收益的一个关键问题。为了有效地处理这一问题，在加权限制（WR）框架，我们首先精确地确定其起源的两个潜在的来源，在非径向DEA设置。如果被评估的公司P是WR-有效的，其相应的P-面的非全维性-包含P的最小维度的面-是唯一的来源（问题类型I）。否则，多个WR-投影的出现，或者相应地，多个P-面成为另一个额外的起源源（问题类型II）。据我们所知，虽然在文献中已经正确地解决了第一类问题，但同时发生的第一类和第二类问题还没有得到有效的处理。出于这一动机，我们首先表明，II型问题可以绕过使用一个P-面包含所有的P-面。基于这一发现，我们设计了一个两阶段的线性规划为基础的程序，通过扩展最近开发的方法[Mehdiloozad，M.，Mirdehghan，S. M.，萨胡湾K.，& Roshdi，I.（2015年）。数据处理分析中全局参考集的识别。欧洲运筹学杂志，245，779-788]。我们提出的方法继承了最近开发的方法的所有优点，是计算效率高。我们所提出的方法的实际适用性证明，通过一个真实世界的数据集80所伊朗中学。
英文摘要：
While measuring returns to scale in data envelopment analysis (DEA), the occurrence of multiple supporting hyperplanes has been perceived as a crucial issue. To deal effectively with this in weigh restrictions (WR) framework, we first precisely identify the two potential sources of its origin in the non-radial DEA setting. If the firm under evaluation P is WR-efficient, the non-full-dimensionality of its corresponding P-face-a face of minimum dimension that contains P-is the unique source of origin (problem Type I). Otherwise, the occurrence of multiple WR-projections or, correspondingly, multiple P-faces becomes the other additional source of origin (problem Type II). To the best of our knowledge, while problem Type I has been correctly addressed in the literature, the simultaneous occurrences of problems Types I and II have not effectively been coped with. Motivated by this, we first show that problem Type II can be circumvented by using a P-face containing all the P-faces. Based on this finding, we then devise a two-stage linear programming based procedure by extending a recently developed methodology by [Mehdiloozad, M., Mirdehghan, S. M., Sahoo, B. K., & Roshdi, I. (2015). On the identification of the global reference set in data envelopment analysis. European Journal of Operational Research, 245, 779-788]. Our proposed method inherits all the advantages of the recently developed method and is computationally efficient. The practical applicability of our proposed method is demonstrated through a real-world data set of 80 Iranian secondary schools.
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