Common set of weights (CSWs) method is one of the popular ranking methods in DEA which can rank efficient and inefficient units. Based on an identical criterion, the method selects the most favorable weight set for all units. An important issue is that in most common DEA models, the internal structure of the production units is ignored and the units are often considered as black boxes. In this paper, in order to evaluate the units and subunits in the two-stage NDEA based on an identical criterion, it is suggested to use CSWs method on the basis of separation vector. Our research contribution in this paper includes: (1) CSWs method is formulated in two-stage NDEA as a multiple objective fractional programming (MOFP) problem. (2) A method is suggested based on separation vector to change MOFP problem into single objective linear programming (SOLP) problem in two-stage NDEA. In the theorem, it is shown that the obtained solutions from MOFP and SOLP in two-stage NDEA are identical. (3) In the framework of the new models of two-stage NDEA, a process is introduced to improve efficiency evaluation by CSWs on the basis of separation vector which is based on the radial improvement of inputs and final outputs. Finally, an enlightening application is presented.

中文翻译：

---

两阶段网络数据包络分析中基于分离向量的通用权重集和效率提高

通用权重集（CSW）方法是DEA中流行的排名方法之一，可以对有效和无效的单位进行排名。基于相同的标准，该方法为所有单位选择最有利的权重集。一个重要的问题是，在大多数常见的DEA模型中，生产单元的内部结构被忽略，并且通常将这些单元视为黑匣子。在本文中，为了根据相同的标准评估两级NDEA中的单位和亚单位，建议在分离向量的基础上使用CSWs方法。本文的研究成果包括：（1）在两阶段NDEA中将CSWs方法描述为多目标分数规划（MOFP）问题。（2）提出了一种基于分离向量的方法，将两阶段NDEA中的MOFP问题转化为单目标线性规划（SOLP）问题。定理表明，在两阶段NDEA中从MOFP和SOLP获得的解是相同的。（3）在两阶段NDEA新模型的框架内，引入了一个过程，以基于分离向量的方式改进CSW的效率评估，该向量基于输入和最终输出的径向改进。最后，提出了一个启发性的应用程序。引入了一种基于分离向量改进CSW效率评估的过程，该向量基于输入和最终输出的径向改进。最后，提出了一个启发性的应用程序。引入了一种基于分离向量改进CSW效率评估的过程，该向量基于输入和最终输出的径向改进。最后，提出了一个启发性的应用程序。