Exploiting random lead times in inventory systems

First, we discuss a proof-of-concept theoretical result, showing that a policy exploiting randomness of a lead time can provide a potentially infinite inventory cost reduction compared to the standard Constant Base Stock (CBS) policy. Specifically, we consider the classical single-item inventory system with backlogs, random replenishment lead times and order crossovers, operating in continuous time. We propose a new policy that, instead of focusing on the inventory position, uses the net inventory level to set a dynamic target for inventory in-transit, and places orders to follow that target. We prove that in the case of exponentially distributed lead times, as the demand rate becomes large, the expected (absolute) inventory level under our policy vanishes relatively to that under CBS policy.

In addition to this proof-of-concept, we introduce and study new policies exploiting lead time randomness in a more realistic — discrete-time — setting. For these policies we obtain stochastic stability and average inventory finiteness results. Simulations show that, under a variety of lead time distributions, new policies do provide very substantial inventory cost reduction over CBS.

Based on joint works with Q.Wang (UIUC) and A. Taneja (UIUC)