Production control of manufacturing systems: a multiple time scale approach

In this note, a stochastic production model containing processes with different time scales is developed. It is shown that if the time scales of the processes are very different, some hierarchical algorithms that are much more efficient than the standard policy iteration method can be developed to find the optimal production control. Moreover, if the time scales fall far apart, the optimal control of a deterministic limiting problem depending only on the mean characteristics of the processes can be used to approximate the optimal control of the original problem. The limiting problem has much lower dimension than its original counterpart and thus is much easier to solve. A numerical example is used to illustrate the potential of the proposed approach