基于Shephard距离函数的DEA TOPSIS方法研究

A Study on Integrating DEA and TOPSIS Based upon Shephard Distance Function

本文通过对Shephard距离函数的引入,正式构建了DEA TOPSIS决策单元排序方法的框架。本文首先定义了正(负)理想决策制定单元(DMU)以及相应的(反)生产可能集,然后在考虑正(负)理想DMU的条件下分别给出DMU的(反)效率评价模型以及对应的Shephard距离函数,然后基于评价对象到理想DMU相对接近度这一综合评价值给出了DMU的一个完全排序。最后,本文通过算例分析说明了该方法的有效性和实用性。

Traditional DEA models measure DMU’s efficiency using a set of specific weights which is most beneficial to that DMU’s efficiency score.Some scholars point out that it can’t guarantee the accuracy of efficiency measure.TOPSIS provides a good idea to solve this problem because it considers both ideal and anti-ideal situations.By introducing Shephard distance function,this paper formally develops a general framework of integrating DEA and TOPSIS for ranking.The paper first defines ideal(anti-ideal)DMUs and corresponding(anti-)production possibility set,then based upon the ideal(anti-ideal)DMUs,elicits the efficiency measurement models and Shephard distance function for each DMU,and shows a complete rank by a comprehensive index called the relative closeness to the ideal DMU.At the end,the numerical experiment has shown that proposed method is relatively valid and practicable.This paper combines advantages of DEA and TOPSIS,considers ideal DMUs and anti-ideal DMUs,generates fairer results,and improves 2 defects of WL’s model.