Probabilistic solution and bounds for serial inventory systems with discounted and average costs

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 distributions of leadtime demands. This analysis yields a novel approach for developing bounds and heuristics for optimal inventory control policies. In addition to deriving the known bounds in literature, we develop several new upper bounds for both average cost and discounted cost models. Numerical studies show that the bounds and heuristic are very close to optimal.