利用旋转算法构建DEA模型生产前沿面

Rotation algorithm on constructing DEA production frontier

传统数据包络分析模型的生产前沿面构造方法较为复杂,为了解决这一问题,提出了一个新的构建DEA生产前沿面的算法,称为旋转法.阐述了旋转算法的含义.分别从二维和高维角度对传统的四类DEA模型的生产前沿面进行构建,并对算法的理论依据进行了证明.通过实际算例证明,相比起传统的方法,比如极点极方向法、Graham扫描法等,旋转法非常简单而且实用价值很广.最后提供了一个关于该算法在实际中的应用——构建决策单元中含有负值的DEA模型,解决了传统DEA模型无法处理决策单元中含有负值的不足.

Traditional method of constructing production frontier in data envelopment analysis seems to be much more complex, in order to solve this problem, we propose a new DEA production frontier algorithm, which is called the rotation algorithm. We explain the meaning of rotation algorithm. Respectively, from the two-dimensional and high-dimensional perspective, we build the production frontier of traditional four DEA models, and prove the theoretical basis of the algorithm. Through practical examples, we prove that, compared to traditional methods, such as vertex and extreme direction method, Graham scanning method, rotation algorithm is much simpler and has a very wide practical value. Finally, we apply the rotation algorithm to practice -- Construct a new DEA model dealing with negative data in decision making units, which the traditional DEA model cannot handle.