Using the inventory-theoretic framework to determine cost-minimizing supply strategies in a stochastic setting

In a stochastic supply link between a supplier and a receiver, a crucial component of the total logistics costs is formed by the costs of safety stock held by the receiver to protect against stockouts. The level of safety stock depends on, among other things, the statistical distribution of demand during lead time (DDLT). For practical reasons, DDLT is often assumed to be normally distributed. However, previous research has indicated that this assumption is often invalid in real-life situations and that it can have a significant impact on safety stocks or service levels. This paper first presents an extensive review of previous research on stochastic inventory models, with specific emphasis on the distributions used to model period demand, lead time and/or DDLT. The paper also discusses a real-life case study in which the total logistics costs are calculated for a number of different transport modes for a gamma demand-gamma lead time setting.