Robust data envelopment analysis based MCDM with the consideration of uncertain data

The application of data envelopment analysis (DEA) as a multiple criteria decision making (MCDM) technique has been gaining more and more attention in recent research. In the practice of applying DEA approach, the appearance of uncertainties on input and output data of decision making unit (DMU) might make the nominal solution infeasible and lead to the efficiency scores meaningless from practical view. In this paper, we analyze the impact of data uncertainty on the evaluation results of DEA, and propose several robust DEA models based on the adaptation of recently developed robust optimization approaches, which would be immune against input and output data uncertainties. The robust DEA models we developed are based on input-oriented and output-oriented CCR model, respectively, when the uncertainties appear in output data and input data separately. Furthermore, our robust DEA models could deal with random symmetric uncertainty and unknown-but-bounded uncertainty, in both of which the distributions of the random data entries are permitted to be unknown. We implement the robust DEA models in a numerical example and the efficiency scores and rankings of these models are compared. The results indicate that the robust DEA approach could be a more reliable method for efficiency evaluation and ranking in MCDM problems.