Optimal control of failure-prone manufacturing systems with constant repair times

This paper considers a failure-prone manufacturing system with exponentially distributed operational times and constant repair times. Under the hedging-point policy, the steady-state probability density function of the buffer level is determined. The optimality of the hedging-point policy for this problem is proven, and analytical expressions for the computation of the optimal hedging point are determined. It is also shown that the optimal hedging point for the system with constant repair times provides a lower bound for the optimal hedging point for any other independent, identically distributed (iid) repair time sequence having the same mean. Using a queueing equivalence, an expression is derived for determining the optimal hedging point for any iid repair time sequence.