Analysis of lead time correlation under a base-stock policy

We analyze the impact of lead time correlation on the inventory distribution, assuming a periodic review base-stock policy. We present an efficient method to compute the shortfall distribution for any Markovian lead time process, and we provide structural results when lead times are characterized by a 2-state Markov-modulated process. The latter reveals how lead time correlation increases the inventory variance and enables a closed form for the asymptotic behavior of the shortfall's variance in case the two possible lead time values are sufficiently different. We also establish upper and lower bounds on the inventory variance, which hold for any general time-homogeneous lead time process. Our results are complemented by a numerical experiment that indicates how commonly used approximations of the shortfall distribution mis-specify base-stock levels in the presence of lead time correlation. Not only does the inventory distribution increase in variance as the lead time correlation increases, it also becomes multi-modal.