Two-stage production scheduling with separated set-up times and stochastic breakdowns

The problem of scheduling a two-machine flowshop, where set-up times are considered as separate from processing times and machines suffer random breakdowns, is addressed with respect to the makespan objective. A dominance relation for minimizing makespan with probability 1 is established. Furthermore, it is shown that Yoshida and Hitomi’s algorithm for the deterministic problem stochastically minimizes makespan when random breakdowns are present.