Due to the nonlinear and discrete nature of BCC (Banker, Charnes, and Cooper, [11]) models for determining the most efficient decision-making unit, it is practically impossible to evaluate the models' dual and, consequently, optimistic case. Thus, in this paper, the linear model with linear constraints proposed by Akhlaghi et al. [2] is used to investigate the dual equality of the model's robust problem and the optimistic case of the new model's dual under VRS uncertainty. The model proposed in this paper is novel in comparison to previous models because it solves the most efficient decision-making unit only once, without relying on uncertain data to determine its rank. The paper demonstrates how the proposed robust model can also ascertain the most efficient decision-making unit when uncertainty exists. Furthermore, the dual issues raised by robust counterparts in the new linear programming (LP) model are addressed to identify the most efficient decision-making unit. The robust counterpart is demonstrated to be equivalent to a linear program under interval uncertainty, and the dual of the robust counterpart is shown to be equal to the optimistic counterpart of the dual problem. Consequently, this study aims to demonstrate that the dual problem is equivalent to a decision-maker operating under optimal data, whereas the primal robust problem is equivalent to a decision-maker operating through the worst-case possible data scenario. Manuscript profile

In this article, we investigate a new continuous linear model with constraints for the direct selection of the most efficient unit in the analysis of data coverage presented by Akhlaghi et al. (2021) on uncertainty robust optimization. Considering the importance of incorporating uncertainty into performance evaluation models in the real world and its increasing application in various problems, we propose a robust optimization approach. Given the discrete and non-convex nature of the introduced models for selecting the most efficient decision-making unit, examining the dual and finding an optimistic scenario is practically impossible. Therefore, by utilizing the linear model presented by Akhlaghi et al. (2021) with constraints for identifying the most efficient unit, we can investigate the robustness of the desired model using(BS )Bertsimas and Sim's (2004) robust estimation method while also considering uncertainty. We aim to demonstrate that employing a robust formulation leads to reliable performance in uncertain conditions Manuscript profile