A set of n jobs is to be processed on either two machines or m machines, and the objective is to find a job sequence which stochastically minimizes a total penalty cost function. For the two-machine flow shop, two sufficient optimality conditions are derived when all the job processing time distributions are nonoverlapping and a particular job has the same processing time distribution on both machines. For the m-machine flow shop, two sufficient optimality conditions are derived when the processing time of a particular job on each one of the m machines is the same random variable.
