A generalized Johnson's rule for stochastic assembly systems

Johnson's rule gives the optimal order to schedule a set of jobs through a two-machine flow shop with deterministic processing times. We extend Johnson's rule to fork-join systems with random processing times. Most of the system may be an arbitrary network. We give conditions under which Johnson's rule is optimal in the stochastic sense, in the increasing convex sense, and in expected value. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 211–220, 1997