Scheduling problems arise in many real-world applications, e.g., in the elds of economy, industry, or transport logistics. For many such problems, fast algorithms have been developed with the condition that all input parameters are known in advance. However, in practical applications, problems become more complex when considering uncertainty in the input data, which may result from the limited access to information, estimated data or simple measuring errors. One successful approach to tackle uncertainty in problem data is robust optimization [4], which deals with the deterministic set-based representation of the uncertainty without any probabilistic description, in order to produce decisions that will have a reasonable objective value under any possible realization of parameters (called scenario). In this paper, we apply the robustness approach to examine the fundamental single machine sequencing problem de ned in section 2. In section 3, we describe our structuring of data uncertainty. In section 4, we discuss the choice of the robustness criterion. Literature review in section 5 and our results in section 6.