Probabilistic solution and bounds . . .

We consider the infinite horizon serial inventory system with both average cost and discounted cost criteria. The optimal echelon base-stock levels are obtained in terms of only probability distri-butions of leadtime demands. This analysis yields an approach for developing bounds and heuristics for optimal inventory control polices. In addition to deriving the known bounds in literature, we develop several new upper bounds for both average cost and discounted cost models. Numerical analysis is conducted to illustrate the effectivenss of the bounds and heuristic