Add to ORKGThis work focuses on the interests of interval analysis in scheduling. The analysis of intervals considers the order relation (Allen's algebra) among the execution intervals of the tasks (or their processing time intervals) in order to deduce useful problem properties. For several kinds of scheduling problems, we particularly show how interval analysis allows defining dominance-based optimality conditions or sufficient conditions of feasibility, which characterize remarkable sets of schedules. Using these conditions, taking an interest in some one machine scheduling problems, we establish new and efficient integer-linear-programming formulations. Since the dominance conditions are relatively insensitive to variations of schedule parameters,...