On the dominance of permutation schedules for some ordered and proportionate flow shop problems

•We consider the ordered and the proportionate flow shop with unequal machine speeds.•We consider both the Cmax and the ∑j=1nCj objectives.•We show that permutation schedules are dominant for Cmax with V-shaped speeds.•We show that permutation schedules are dominant for ∑j=1nCj with three stages.