The asymptotic optimality of the shortest processing time rule for the flow shop mean completion time problem

In the flow shop mean completion time problem, a set of jobs has to be processed on m-machines. Every machine has to process each one of the jobs, and every job has the same routing through the machines. The objective is to determine a sequence of the jobs on the machines so as to minimize the sum of the completion times of all jobs on the final machine. In this paper, we prove the asymptotic optimality of the Shortest Processing Time algorithm for any continuous, independent, and identically distributed job processing times.