The Joint Effect of Leadtime Variance and Lot Size in a Parallel Processing Environment

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 base-stock 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.