We consider the non-preemptive flexible flowshop scheduling problem with a fixed number of stages, li identical uniform machines at the stage i, a set of n jobs, each job consisting of s operations, each one of which can only be processed on a machine at the corresponding stage, the same routing of all jobs on stage 1 through stage s. The aim is to determine a feasible order of the jobs that minimizes the sum of the weighted completion time of all jobs on the machines at final stage. By grouping this machine setting, we have proved that when the bounded processing time of each job is a statistically exchangeable random variable across stages and independent across jobs, the heuristic based on weighted shortest processing time is asymptotically optimal, as the number of jobs goes to infinity.
