Optimizing Reorder Intervals for Two-Echelon Distribution Systems with Stochastic Demand

We consider a periodic-review inventory system in which multiple non-identical retailers replenish from a warehouse, which further replenishes from an outside ample source. Each facility faces Poisson customer demand and replenishes according to a base-stock policy in a fixed time interval. There are fixed costs incurred for placing an order. The warehouse fills the retailers’ orders in the same sequence as the original demand. The objective is to minimize the average system cost per period. This paper develops an evaluation scheme and provides a method 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 the result of Axsäter (1990). To find the optimal reorder intervals, we first decompose the total cost into each facility and then construct a lower bound to the allocated facility cost. These lower bound functions, each depending on the facility’s reorder interval, can be used to derive the solution bounds. One enabler to tighten the bounds is an effective heuristic cost. Thus, we propose a simple heuristic that combines a revised algorithm of solving the deterministic counterpart and the lower bound cost functions. The results of numerical studies suggest that the optimal policy tends to be an integer-ratio policy, that the power-of-two solution obtained from the deterministic counterpart may perform poorly, and that the suggested heuristic can generate an effective solution for large systems.