On the Imbalance of Inventories in Multi-Echelon Systems

A central depot periodically orders or produces new stock and withdraws inventory in order to allocate it among several demand points, each experiencing random demands over a finite planning horizon. This system gives rise to a dynamic program with a state space of very large dimension. We determine a near-optimal allocation policy and construct a tractable, approximate dynamic program to help determine good orders and withdrawals. This is done by exploring the effects of a measure of the imbalance of inventories at the demand points. Numerical results are included.