Two novel robust network data envelopment analysis models to obtain the performance score interval of multi-stage series systems

The main goal of this paper is to present a new approach for measuring the performance of n -stage series systems in the presence of uncertain data, which are two challenging issues in evaluating the efficiency of Decision -Making Units (DMUs) using traditional Data Envelopment Analysis (DEA) models. By using a Network DEA model and its dual, as well as using Bertsimas et al.'s robustness technique, two Robust Network DEA have been presented. These models can display a range of DMUs performance with appropriate accuracy. Proposed models were used to determine the efficiency range of Iranian dairy companies' supply chain with three stages. The results show that the proposed models are applicable and effective. Total efficiency bounds are obtained with percentage deviations of 20%, 10% and 5%. The lower bounds have relative errors of 0.39, 0.23 and 0.12 and a correlation coefficient of more than 97%, and the upper bounds have relative error of 1.1, 0.84 and 0.62 and a correlation coefficient of about 90%. Therefore, the proposed model for calculating the lower bound is more accurate. The calculation of the efficiency bounds of the sub -stages also confirms this issue. Finally, the obtained results have been compared with the values obtained through a fuzzy three -stage DEA model, our results have a higher correlation coefficient and more accurate upper bounds.