基于数据包络分析松弛变量的排序方法

Slacks-based Ranking Method in Data Envelopment Analysis

为协助管理层更加全面充分地评价所有决策单元(decision making unit,DMU)的绩效表现,提出一种新的基于松弛变量和(有效)DMU影响力的排序方法。根据数据包络分析中关于松弛变量的研究,定义了直接使用投入-产出松弛变量来计算的δ-效率值,将所有DMU分为δ-有效和非δ-有效两类。依据δ-效率值大小来区分和排列非δ-有效DMU;同时对于δ-有效DMU,考虑将其从参考集中剔除后,利用δ-效率值的变化来度量其对其它DMU的影响程度,根据影响程度的大小可以有效区分那些被传统模型定义为有效的DMU,实现所有DMU的排序。通过对算例和实际应用的计算比较,提出的排序方法展现了较高的可操作性,实现了比较好的区分效果和相对合理的排序结果,可以为决策者提供有效的决策支持。

In order to assist the management to fully evaluate all decision making units(DMUs),this paper proposes a new ranking method using a slacks-based measure of influence.Based on data envelopment analysis(DEA),this paper utilizes input and output slacks to defineδ-efficiency,which is further used to differentiate efficient DMUs from inefficient ones,and to rankδ-inefficient DMUs.Forδ-efficient DMUs,their respective slacks-based measure of influence on other DMUs is studied for distinguishing and ranking.In that way,all DMUs,especially for those evaluated as efficient via conventional DEA models,can be fully and effectively differentiated and ranked by performance.Both numerical examples and real world application show that the proposed method is easy to apply,and demonstrates effective distinguishing power and reasonable results.