Single machine with Wiener increment yield: optimal offline control

In many manufacturing systems prone to random interference, such as machine breakdowns and fluctuating yield, information about the interference as well as other system states, e.g., inventory levels, may not be available in a timely manner. Therefore an online feedback control will be difficult to implement, and a good offline control strategy may be the only alternative. In this note we develop such a strategy for a production system with random yield, which is characterized by a Wiener process. Assuming the initial inventory level is known, we derive closed form expressions of the optimal production control to minimize the expected inventory and backlog costs over a production horizon.