Optimal dynamic scheduling policy for a make-to-stock production system

This paper considers the dynamic scheduling problem of a single-server, make-to-stock queue with two products. For the case of Poisson demands and exponential production times, we show that it is optimal to produce the product with the larger mu index when it is backordered. If the production times are identically distributed, the optimal policy can further be characterized by monotone switching curves. We also prove that a base stock policy coupled with a switching curve is optimal for some initial inventory levels. A simple linear switching rule for determining production priority is proposed and compared with other heuristic policies in a computational experiment.