Flexibility in selecting the weights of inputs and outputs in data envelopment analysis models and uncertainty associated with the data might lead to unreliable efficiency scores. In this paper, to avoid these problems, first, we discuss robust Charnes, Cooper, Rhodes (CCR) model under Bertsimas and Sim approach. Then, the robust CCR solutions are used to find robust common set of weights under norm-1 and Bertsimas and Sim approach. Finally, on two numerical real-world examples, the performance of the proposed approach is compared by a similar recent approach from the literature to show the advantages of the new method and its applicability.

Data Envelopment Analysis (DEA) is a method for evaluating the performance of a set of homogeneous Decision Making Units (DMUs). When there are uncertainties in problem data, original DEA models might lead to incorrect results. In this study, we present two stochastic p-robust two-stage Network Data Envelopment Analysis (NDEA) models for DMUs efficiency estimation under uncertainty based on Stackelberg (leader-follower) and centralized game theory models. This allows a deleterious effect to the objective function to better hedge against the uncertain cases those are commonly ignored in classical NDEA models. In the sequel, we obtained an ideal robustness level and the maximum possible overall efficiency score of each DMU over all permissible uncertainties, and also the minimal amount of uncertainty level for each DMU under proposed models. The applicability of the proposed models is shown in the context of the analysis of bank branches performance.

The slacks-based measure (SBM) and additive SBM (ASBM) models are two widely used DEA models acting based on inputs and outputs slacks and giving efficiency scores between zero and unity. In this paper, we use both models with the application of the weak disposability axiom for outputs to evaluate efficiency in a two-stage structure in the presence of undesirable outputs. In the external evaluation, the SBM model is reformulated as a linear program and the ASBM model is reformulated as a second-order cone program (SOCP) that is a convex programming problem. In the internal evaluation, the SBM model for a specific choice of weights is linearized while the ASBM model is presented as an SOCP for arbitrary choice of weights. Finally, the proposed models are applied on a real dataset for which efficiency comparison and Pearson correlation coefficients analysis show advantages of the ASBM model to the SBM model.