Stochastic machine dominance in flowshops

We consider a two-machine flowshop scheduling problem where machines are subject to random breakdowns. We consider the cases where uptimes and downtimes of the machines follow uniform and exponential distributions. We define the stochastic machine dominance problem and suggest five rules for finding the makespan. We use simulation to find the performance of these five rules. Out of these five rules, one rule (LPT) seems to perform well when machine 1 stochastically dominates machine 2, whereas when machine 2 stochastically dominates machine 1 another rule (SPT) is found to be good. The results of the experimentation reveal that when uptimes and downtimes follow exponential distributions, the Talwar rule performs well. The results of the experimentation also reveal that the performance of Johnsonʹs rule is acceptable when machines break down.