New Robust Single Machine Scheduling to Hedge against Processing Time Uncertainty

This paper focuses on the single machine scheduling problem with uncertain processing times described via a set of scenarios. Rather than the traditional worst-case model, a new robust model is proposed based on two-bad-scenario set and the new problem is proved NP-complete. The proposed solution method is based on a branch-and-bound algorithm, in which a pruning rule and a method to get the upper bound and lower bound values are designed. The extensive computational results demonstrate the effectiveness of the branch-and-bound algorithm and the advantages of the new model.