Solvable cases of permutation flowshop scheduling with dominating machines

In this paper we study the permutation flowshop scheduling problem with an increasing and decreasing series of dominating machines. The objective is to minimize one of the five regular performance criteria, namely, total weighted completion time, maximum lateness, maximum tardiness, number of tardy jobs and makespan. We establish that these five cases are solvable by presenting a polymonial-time solution algorithm for each case.