Summary: We study a basic \((r,q)\) system, in which the demand is a Poisson process and the leadtimes are independent, identically-distributed random variables. The key issue is the joint effect of the leadtime variance and the lot size \(q\) on performance. We know that, under a simple basestock policy (with \(q=1\)), the leadtime variance has no effect at all. We find here that, for larger \(q\), the leadtime variance can have a significant adverse impact on performance.
To explore this effect, we test two simple approximations. The simplest ignores the leadtime variance. The second approach is only a bit more complex; it captures the variance effect through a hybrid of two limiting approximations. Both methods provide useful information, but the second is more robust.