Dynamic control of a multiclass queue with setups and lost sales

We consider scheduling a shared machine in a two-class make-to-stock system subject to switching costs and lost sales costs for lost jobs. If the switching costs are negligible, the optimal policy has a monotonic threshold type of switching curve provided that the service times are identical. For completely symmetric systems without set-ups, it is optimal to serve the longer queue. Using simple analytical models as approximations, we derive a heuristic scheduling policy. Numerical results demonstrate the effectiveness of our heuristic, which is typically within 10% of optimal