A Note on Stochastic Shop Models in Which Jobs have the Same Processing Requirements on Each Machine - Pinedo, Michael (Management Science, 1985)
We consider stochastic models for flow shops, job shops and open shops in which the work required by job j is the same at each machine, being a random variable W j . Because machines operate at different speeds, S i , the processing time of job j at machine i is W j /S i ,. It is the main result of this note that in a flow shop where the machine speeds increase (decrease) from the first to last machine and the workload distributions are ordered by a likelihood ratio criterion, then the makespan of the jobs is stochastically minimized by processing the jobs in the order of least to greatest (greatest to least) workload.