Scaling down multi-echelon inventory problems

A two-echelon distribution inventory system with stochastic demand is considered. Existing methods for evaluation and optimization of continuous review (R,Q)-policies are usually very efficient in case of relatively low demand. For systems with high demand an evaluation may be very time consuming. We suggest and evaluate a technique where a high-demand system is approximated by a low-demand system. The real customer demand is scaled down such that the ratio between standard deviation and mean is preserved. Then the low-demand system is optimized. Finally, the solution is scaled up to fit the original high-demand system.