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We introduce an algorithmic framework for investigating the robustness of efficiency analysis results in the presence of imprecise information about data and preferences. We employ an additive value efficiency model accepting ordinal and interval information about the performances of Decision Making Units and imprecision in the specification of input and output weights and the shapes of marginal value functions. We verify the stability of efficiency measures using a combination of mathematical programming and Monte Carlo simulations. The results capture various certainty levels, emphasizing the necessary, possible, extreme, and expected outcomes and the distribution of outcomes in the space of feasible weights, performances, and marginal functions. The practical usefulness of the proposed framework is demonstrated in a real-world problem concerning the functioning of Special Economic Zones in Poland …