A distributionally robust optimization approach for data envelopment analysis under uncertainty with an application to Chinese airports

Abstract

Uncertainty is an inherent characteristic of the business environment, making it crucial to address uncertainty in data envelopment analysis (DEA) for reliable performance evaluation. In this paper, we propose a distributionally robust optimization approach to capture the underlying probability distribution of uncertain variables and develop distributionally robust DEA (DRDEA) models to mitigate the overly pessimistic limitations of RDEA. First, two moment‐based ambiguity sets are introduced to describe the mean and covariance characteristics of uncertain outputs. We then construct the DRDEA framework with these sets and reformulate it via duality theory as equivalent tractable linear and semidefinite programs. Specifically, we prove that the DRDEA model with the MAD ambiguity set reduces to the traditional DEA model under specific conditions. Theoretical guarantees for the model solvability are provided. Finally, experimental results demonstrate that the proposed DRDEA models outperform several benchmark methods and deliver robust management strategies under uncertainty.