Optimal policies for the "yield learning" problem in manufacturing systems

The yield learning problem encountered in many manufacturing systems involves controlling the production rate of a process so as to maximize cumulative rewards over some time interval. Because yield improvement occurs as a result of discrete events coinciding with lot processing completions, a basic tradeoff arises as high production rates increase rewards for a given yield but also cause longer average lot lead times which delay the events that trigger yield improvement. We show that in some cases simple bang-bang solutions can be obtained for this problem through standard optimal control techniques.