Optimal control of production with improvement

This article considers a process that produces items and in which the process mean is observed periodically. We use a state-space model to describe the relationship between the process mean and the quality characteristic of the items. At each observation, one of the following actions can be taken: production, repair, replacement, or improvement. When production is chosen, some number of items are produced. The quality characteristic of the items has a target value, and the quality loss is expressed by an asymmetric function of the deviation of the quality characteristic from the target value. Replacement resets the process mean to an initial value. When improvement is selected, the process mean is returned to the same initial value as in replacement. When improvement is repeated, it becomes less likely that the process mean will increase. There are several kinds of repairs, and each repair returns the process mean to some value greater than the initial value. For this model, we obtain a total expected discount cost for an unbounded horizon, and we show that under several reasonable assumptions, a control-limit policy is optimal. Furthermore, we derive the sufficient conditions to ensure that the optimal control policy has monotonic structures.