Stochastically minimizing the makespan in two-machine flow shops without blocking

This paper deals with a two-machine stochastic flow shop with an infinite storage between the machines. We present a new sufficient condition on the job processing time distributions that implies that the makespan becomes stochastically smaller when two jobs in a given job sequence are interchanged. This condition is weaker than that given by Ku and Niu, and is not restricted to adjacent jobs. It is claimed that all optimal scheduling rules for minimizing the makespan, that have been identified so far in the literature, can be derived from the new condition. Examples and generalizations of known results are presented.