Optimizing Replenishment Intervals for Two-echelon Distribution Systems with Stochastic Demand

We consider a periodic-review inventory system with one warehouse and N non-identical retailers. Each location replenishes inventory according to a base-stock policy in a fixed time interval. A fixed cost is incurred for each inventory reorder. The warehouse fills the retailers’ orders in the same sequence as the original demand. The objective is to minimize the long-run average system cost per period. This paper provides an approach to obtain the optimal base-stock levels and reorder intervals. Specifically, for fixed reorder intervals, we show that the optimal base-stock levels can be obtained by generalizing a result in the literature. To find the optimal reorder intervals, we derive solution bounds by constructing bounds for the cost of each stage. The optimal reorder intervals can therefore be found by a complete enumeration. To reduce the computation, we prove a useful property: If the optimal policy is an integer-ratio policy, the optimal reorder interval of the warehouse is no shorter than the minimum of those of the retailers. A numerical study suggests that the optimal policy tends to be an integer-ratio policy and that the power-of-two solution generated from the corresponding deterministic model may perform poorly under some conditions.