Note—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 [Bradley, J. R., L. W. Robinson. 2005. Improved base-stock approximations for independent stochastic lead times with order crossover. Manufacturing Service Oper. Management7 319–329.] 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.