A multi-pass heuristic scheduling procedure developed for job shop scheduling problems with deterministic processing times is tested with processing times that are random variables. The heuristic procedure, which uses expected processing times, typically generates a delay schedule (i.e., a schedule in which some operations are delayed while the machine to process these operations is kept idle awaiting the arrival of another operation). Simulation is employed to compare the performance of the schedule generated by the heuristic procedure, a non-delay transformation of that schedule, and the non-delay schedules obtained with four single-pass dispatching rules, The criteria employed are fraction of jobs tardy, mean tardiness variance of tardiness, and maximum tardiness. The delay schedule produced by the heuristic procedure was found to be markedly superior under certain conditions. Under other conditions, the relative performance of the scheduling rules appears highly problem dependent. Implications of these results are discussed in relationship to dynamic scheduling situations and man-machine interaction.