Permutation flow shop scheduling with dominant machines to minimize discounted total weighted completion time

This paper deals with some special cases of general, no-wait and no-idle permutation flow shop scheduling problems, respectively. Special cases means that the machines form an increasing series of dominant machines, a decreasing series of dominant machines, an increasing–decreasing series of dominant machines and a decreasing–increasing series of dominant machines. Efficient polynomial time algorithms for finding the optimal schedules to minimize discounted total weighted completion time are developed.