This paper examines two special cases of the n-job, m-machine permutat
ion scheduling flowshop problem. The first case assumes an increasing
series of dominating machines; while the second case assumes a decreas
ing series of dominating machines. Efficient solution procedures for f
inding the optimal permutation schedules for various performance measu
res, including maximum flowtime, mean flowtime, mean completion time o
f machines, the number of tardy jobs, maximum lateness, and maximum ta
rdiness, are developed.