PRODUCTION-RATE CONTROL FOR FAILURE-PRONE PRODUCTION SYSTEMS WITH NO BACKLOG PERMITTED

Previously, the problem of optimal production rate control for failure-prone production systems has beers studied exclusively under the assumption that backlog is permitted. It is well known that when backlog is permitted, the optimal control is usually the hedging point policy. In this note, we consider systems in which backlog is not allowed. we show that the hedging point policy is still optimal. For systems with backlog, it is usually quite straightforward to show that their optimal cost-to-go functions are convex-a key property that is needed for the hedging point policy to be optimal. With no backlog permitted, it becomes much more difficult to establish the convexity property, and the explicit formulas for the optimal hedging point and the optimal cost-to-go functions have to be obtained, based on which the convexity property can then be verified. The method we use in this note to derive these explicit formulas is mainly based on an interesting relationship between the inventory process of the system under the hedging point policy and some stochastic process which is well studied in queueing theory.