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.