The Effect of Leadtime Uncertainty in a Simple Stochastic Inventory Model

We study a basic continuous-time single-item inventory model where demands form a compound Poisson process and leadtimes are stochastic. The performance measure of interest is the long-run average cost. Order costs are linear, so a base-stock policy is optimal. We focus on the behavior of the optimal base-stock level in response to stochastically larger or more variable leadtimes. We also investigate the behavior of the corresponding long-run average costs. We show that a stochastically larger leadtime requires a higher optimal base-stock level. However, a stochastically larger leadtime may not necessarily result in a higher optimal average cost, because sometimes the variability effects may dominate. On the other hand, a more variable leadtime always leads to a higher optimal average cost. The effect of leadtime variability on optimal policies depends on the inventory cost structure: A more variable leadtime requires a higher optimal base-stock level if and only if the unit penalty (holding) cost rate is high (low). Similar results regarding the effect of leadtime demand are also discussed. In this latter case, the compound Poisson assumption is not necessary.