Further Improvements on Base-Stock Approximations for Independent Stochastic Lead Times with Order Crossover

When inventory replenishments can arrive in a different sequence than the one in which they were placed, it is important to use the shortfall distribution to set the base–stock level. Because the exact shortfall distribution is quite difficult to compute, heuristics are commonly used in its stead. Bradley and Robinson (2005) developed an upper bound on the variance of the number of outstanding orders that they used within a normal approximation of the shortfall distribution. In this short note, we tighten their upper bound and use it within a beta approximation of the shortfall distribution to derive a policy whose costs average only 0.05% above that of the optimal.