基于虚拟包络面和TOPSIS的DEA排序方法

传统的DEA模型将决策单元简单地分为DEA有效或DEA无效两大类, 无法实现决策单元的完全排序. 为实现决策单元完全、合理的排序, 文献中出现多种DEA排序方法. 文章在文献总结的基础上, 对现有DEA排序方法的局限性进行了详细的探讨; 基于实际评价的决策单元, 提出了一种虚拟前沿面的DEA方法, 并给出了基于最优虚拟前沿面和最劣虚拟前沿面的效率评价模型; 然后基于TOPSIS排序思想, 构造了基于最优虚拟前沿面理想决策单元和基于最劣虚拟前沿面的负理想决策单元, 提出了一种集成的DEA排序方法. 该方法同时考虑决策单元的最优和最劣权重体系, 兼顾所有决策单元的效率信息, 能够获得较为合理的排序结果. 算例分析验证了所提出的方法的合理性和优越性.

DEA ranking method based upon virtual envelopment frontier and TOPSIS

Traditional DEA can classify DMUs into two groups: efficient or inefficient, while it cannot rank efficient DMUs effectively. To overcome this weakness, many researches have developed several DEA approaches to rank DMUs. This paper firstly reviews the existing DEA ranking methods, and discusses their limitations in detail. Secondly, the current paper proposes a virtual frontier DEA approach, and develops two corresponding DEA models, one based on the best virtual frontier and the other based on the worst frontier. Finally, based upon TOPSIS, the paper constructs an ideal DMU and an anti-ideal DMU, and gives a full-ranking DEA method based on virtual frontier DEA models and TOPSIS. Since the proposed approach can simultaneously consider the overall efficiency information of all DMUs, it can rank all DMUs effectively. An example is employed to illustrate the rationality of the proposed approach.