On three-machine flow shops with random job processing times

The paper deals with scheduling n jobs on three machines in Johnson’s flow shops. The job processing times are assumed to be independent random variables, and the problem is to minimize stochastically the makespan. Using a convenient makespan representation, we present sufficient conditions on the job processing time distributions which imply that the makespan becomes stochastically smaller when two adjacent jobs in a given job sequence are interchanged. They lead, in particular, to an extension of Talwar’s rule known for two-machine stochastic flow shops with exponential job processing times. Extensions of other results are also included.