Base-stock Policies for Lost Sales Models: State Space Aggregation and Limiting Transition Probabilities
This technical note considers the optimization of the base-stock level for the classical periodic review lost sales inventory system. The optimal policy for this system is not fully understood and computationally expensive to obtain. Base-stock policies for this system are asymptotically optimal as lost sales costs approach infinity, easy to implement and prevalent in practice. This note provides an efficient algorithm to find near optimal base-stock levels and accurate cost estimates based on state space aggregation and asymptotic results for the transition probabilities in this aggregated state space. We also show that the limiting results have good convergence properties. The full, unaggregated, state space needed to evaluate the performance of base stock policies grows exponentially in both the lead time and the base stock level. Our aggregations lead to a state-space that grows linearly in the base-stock level only. In a numerical study, we demonstrate that this approach leads to near optimal base stock levels with very little computational cost. We also demonstrate that this approach leads to better base-stock levels than other heuristics. Across a large test bed, the cost difference with the best base-stock policy never exceeds 1.30% and averages at 0.01%.