Optimal policies for serial inventory systems under fill rate constraints

A continuous review serial production/distribution system with discrete compound Poisson demand for the end product is considered. Unmet demand is back-ordered. Production/transportation times are constant. All deliveries from one stage to the next must be multiples of given batch sizes. We consider the problem of minimizing the holding costs under a fill rate constraint. Using recent results by Chen, we show that under a set of restricted but plausible assumptions, the optimal policy is an echelon stock multistage (R,nQ) policy with one of the reorder points varying over time. We provide a simple procedure for the determination of the optimal policy.