Optimizing Replenishment Intervals for Two-Echelon Distribution Systems with Fixed Order Costs

We consider a periodic-review inventory system with one warehouse and N non-identical retailers. Each location has a positive lead time and orders according to a base-stock policy in 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 propose a complete enumeration on feasible solutions. The feasible region is determined based on two analytical results: (1) We decouple the total system cost into each stage and construct a lower bound on the decoupled stage cost; (2) we construct a lower bound on the total system cost by converting the distribution system into a single-location model with the original problem data. These stage and system lower bounds together generate bounds for the optimal reorder intervals. Since the computation of the optimal reorder intervals is quite extensive, we further suggest a simple heuristic by solving a set of serial systems. The heuristic appears to be near-optimal in the tested problems. The primary findings from a numerical study are that the optimal reorder intervals tend to follow integer-ratio relations and that the optimal reorder interval of the warehouse is no less than the minimum of the optimal reorder intervals of the retailers.