New Policies Exploiting Randomness of Lead Times In Inventory Systems : Extended Version

Stolyar and Wang (2021) provide a proof-of-concept that randomness of lead times in inventory systems can be exploited to achieve large - potentially unlimited - performance improvements, compared to the case of constant lead time. In this paper we explore what improvements are actually achievable under practical system constraints, and which policies both allow significant improvements and are attractive for practical use. In addition to the discrete-time version of the Generalized Base Stock (GBS), introduced and studied in Stolyar and Wang (2021), we introduce two new policies, labeled ADAPTIVE and PIPELINE. We prove the stochastic stability of GBS and PIPELINE policies, in the important special case of bounded lead time. We use simulations to evaluate the performance of the three policies, and its dependence on lead time distributions. We observe that the performance improvements, provided by our policies under practical constraints can indeed be very significant, and they are larger when the lead time ``randomness'' (say, variance) is larger. It also appears that PIPELINE policy typically has the best performance and is robust from the practical use point of view