New Policies Exploiting Randomness of Lead Times In Inventory Systems

Abstract

Recent research provided 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. Specifically, the Generalized Base Stock (GBS) policy serves as such proof-of-concept -- it can deliver unlimited improvements

within a certain class of models, when the ratio of the minimum lead time to the mean lead time can be arbitrarily small. In this paper we explore what improvements are actually achievable under practical system constraints, most importantly -- in discrete-time systems, where the minimum-to-mean lead time ratio is lower bounded by a positive constant;

and also, which policies both allow significant improvements and are attractive for practical use. We consider a discrete-time version of GBS, and introduce two new discrete-time policies, labeled ADAPTIVE and PIPELINE. We prove the stochastic stability and finiteness of average inventory level under GBS, ADAPTIVE 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, in the sense that it applies to a wide range of practical scenarios and does not require a careful parameter tuning.

Keywords: Inventory control policy, random lead time, constant base stock, generalized base stock, pipeline, stochastic stability

JEL Classification: C02