We develop a dispatching policy for stochastic scheduling simulation especially for a continuous manufacturing system with machine breakdowns. The proposed dispatching policy computes an urgency index with consideration of reheating, setup cost and remaining due date. Prioritized by the index, we execute swapping or reassigning material sequences in order to minimize the total penalty cost. To evaluate the performance of the proposed policy, a discrete event simulation model is developed. With 200 data sets and 20 iterations, we compare the performance of the urgency policy with those of SPT (Shortest Processing Time) and FCFS (First Come First Served), which are the most common policies. The results show that the proposed policy consistently provides the lowest total costs by reducing the penalty costs for lateness.