The problem considered is the scheduling of a job shop with job due dates, intermittent job arrivals, and statistical processing times. Centralized scheduling uses a sequence of static problems for generating priorities at review times. The proposed priority generation procedure is an iterative machine procedure that uses a multi-pass heuristic program. Two implementation procedures are described for applying the priorities on the shop floor between review times. A simulation model is used to evaluate the scheduling procedure with priority implementation options. In the experiments used for evaluation, the centralized priority generation and an implementation procedure designed for dynamic problems proved to be an extremely effective combination with respect to tardiness statistics.