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

Abstract

We consider a periodic-review inventory system in which N non-identical retailers replenish from a warehouse, which further replenishes from an outside vendor with ample supply. Each facility faces Poisson demand and replenishes according to a base-stock policy in a fixed time interval. Fixed costs are incurred for placing an order. The warehouse fills the retailers’ orders in the same sequence as the occurrence of the demand at the retailers. 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, with fixed reorder intervals, we show that the optimal base-stock levels can be obtained by generalizing the result in the literature. To find the optimal reorder intervals, we first allocate the total system cost to each facility and then construct a lower bound to the allocated facility cost. These lower bound functions, which are separable functions of reorder intervals, can be used to derive bounds for the optimal reorder intervals. The key to tightening the bounds is to obtain a near-optimal total cost. Thus, we propose a simple heuristic that modifies the algorithm that solves the deterministic counterpart. The results of numerical studies suggest that the optimal reorder intervals tend to satisfy integer-ratio relationships and that the suggested heuristic can generate effective integer-ratio policies for large systems.