On static stochastic order crossover

We borrow the term 'static stochastic' from the classification of order crossover by Riezebos [2006, Inventory Order Crossovers. International Journal of Production Economics, 104(2), p. 668]. The term 'static stochastic' refers to iid lead times, with its consequence of order crossovers. Here, we concern ourselves with iid continuous lead times with an infinite right tail, such as can be modeled by the normal and gamma distributions, where order crossover would be certain. We find that order crossover transforms the original lead times into a time series of receipts, whose mean is the same as that of the original lead time but whose variance is less than the original variance. The implication is that supply chain managers could exploit order crossover (say by frequent ordering) to reduce safety stocks. The reward is lower cost, albeit some administrative inconvenience. So our contribution attempts to shed more light on this type of order crossover and that order crossover is not necessarily baneful but actually helpful in reducing risk in inventory operations. A similar conclusion is provided by Riezebos and Gaalman [forthcoming. A single-item inventory model for expected inventory order crossovers. International Journal of Production Economics] for the case of deterministic order crossovers.