Robust data envelopment analysis models for efficiency evaluation with new uncertainty sets

The integration of robust optimisation techniques and data envelopment analysis (DEA) models results in a methodology called robust DEA. This methodology aims to tackle uncertain data and ensure robust and reliable efficiency measures. In applying robust optimisation approaches, the selection of the uncertainty set plays a pivotal role since it determines the trade-off between achieving optimal objective and ensuring a high probability of constraint feasibility, a concept well-known as the price of robustness. This trade-off can be adjusted using a robust parameter based on managers’ risk preferences. Similar to robust optimisation, robust DEA aims to protect the deterministic DEA models against data uncertainty within a user-specified uncertainty set, providing a probability bound on constraint feasibility. Despite recent advancements in robust optimisation approaches, robust DEA models are still in their early stages of development, accentuating the need for further research, especially in the application of new types of uncertainty sets. To address the identified research gap, this study aims to develop two novel robust DEA models considering recently introduced uncertainty sets—namely, variable budgeted and order statistic uncertainty sets—to improve the flexibility and generality of the existing robust DEA models. We discuss in depth how the existing robust DEA models under budgeted uncertainty sets represent a special case of the proposed robust DEA models in this paper when the robust parameter is appropriately selected. Finally, we present a case study on EU banks to illustrate the efficacy and applicability of the proposed models, which show a robust evaluation strategy for management in uncertain environments.