Including uncertainty in data envelopment analysis (DEA) is vital to achieving stable and reliable performance evaluations for the field of operational research as business environments are becoming increasingly volatile and unpredictable. Robust DEA models with budgeted uncertainty have been drawing particular attention in the DEA literature for modelling uncertainties, aiming to obtain robust efficiency scores in a way that guarantees the feasibility of solutions. A concern with such robust DEA models – which has been largely ignored in the literature – is that incorporating high uncertainty levels might result in too conservative efficiency measures, possibly reducing the decision support value of such information. To address this concern, this paper tackles uncertainties by employing variable budgeted uncertainty, which is a generalisation of the budgeted uncertainty. We introduce a novel robust DEA model with variable budgeted uncertainty that is less conservative than extant robust DEA models. Furthermore, we suggest a solution for specifying the probabilistic bounds for constraint violations of the uncertain parameters in robust DEA models. A comparison of the introduced robust DEA model with existing robust DEA models based on a numerical example shows an average reduction in the price of robustness by approximately 20%. Finally, the usefulness and applicability of the suggested model are demonstrated by using a large-scale data set in the context of grocery retailing.