A note on 'Some new ranking criteria in data envelopment analysis under uncertain environment'

摘要

In a recent paper, Wen et al. (2017) developed three Data Envelopment Analysis ranking models (formulations) proposing new ranking criteria in a framework of uncertainty theory. The three are the expected, the maximal chance and the optimistic ranking model. The purpose of this note is threefold with focus of the latter two models. First, since the original formulation of the maximal chance ranking model includes uncertain variables in the objective function and hence is a non-deterministic non-linear programming (NLP) problem, we convert it into a deterministic NLP problem that alleviates the computational burden substantially. Secondly, we show that the transformed NLP problem can further be written as a deterministic linear programming (LP) problem for the special cases of linear and zigzag uncertain distributions. Lastly, we convert the original formulation of the optimistic ranking model, which is expressed as a fractional programming problem, into a deterministic LP problem as well, under the assumption of the linear or the zigzag uncertain distribution.