Robust Multiplier Data Envelopment Analysis Under Data Uncertainty: Correlated Budgeted and Order Statistics Models

In engineering and management, multiplier Data Envelopment Analysis (DEA) models provide decision-makers with a foundational and interpretable framework by defining efficiency as the ratio of weighted outputs to weighted inputs. However, the pervasive presence of data uncertainty across applications is often overlooked, compromising the robustness of the results. This paper builds on the widely adopted budgeted uncertainty model in robust optimisation to develop two novel robust multiplier-based DEA models: one that incorporates correlated budgeted uncertainty to account for dependencies among uncertain variables, and another that employs order statistics to capture distribution-based risk scenarios. The proposed models are examined through both theoretical analysis and computational experiments using real and simulated datasets. The results demonstrate that the correlated model strikes an effective balance between robustness and computational efficiency, whereas the order statistics model enhances reliability by explicitly capturing distributional characteristics of the uncertain data. Together, these models are complementary, with the correlated budgeted model suited to large-scale or routine evaluations, and the order statistics model preferable when resilience under extreme uncertainty is the priority. This study provides decision-makers with practical guidance for selecting the most suitable robust DEA framework in environments where data uncertainty is a critical concern.