Optimal Control of Production Rate in a Manufacturing System Prone to Failure With General Distribution for Repair Time

The hedging-point policy is shown to be the optimal production rate control policy minimizing the expected total inventory cost over an infinite time horizon for a single-product production-inventory system prone to failure with exponentially distributed time to failure and generally distributed repair time. Then, using Laplace transform techniques, general expressions of the steady state probabilities and the optimal policy parameter, minimizing the expected inventory cost per unit of time, are developed for the general case of repair time. These general expressions are in turn used to deal with the special cases of exponentially, deterministically, and discretely distributed repair time.