Large deviations-based asymptotics for inventory control in supply chains

We consider a model of a capacitated single-class supply chain consisting of a tandem of production facilities and propose production policies in two cases: (a) when each facility has access to its local inventory only, and (b) when it has knowledge of the total downstream inventory. In case (a) the proposed policy guarantees stock-out probabilities at each stage to stay bounded below given constants (service level constraints). In case (b) we minimize total expected inventory cost subject to service level constraints. In both cases we rely upon large deviations asymptotics to analytically obtain the policy parameters; this leads to huge computational savings compared to simulation. Our model can accommodate autocorrelated demand and service processes, both critical features of modern failure-prone manufacturing systems. We demonstrate that detailed distributional information on demand and service processes, which is incorporated into large deviations asymptotics, is critical in inventory control decisions. Some extensions to a multiclass setting are discussed.