Large Deviations-Based Asymptotics for Inventory Control in Supply Chains

Abstract

We consider a model of a capacitated single-class supply chain consisting of production facilities (stages) in tandem. External demand is met from the available finished goods inventory maintained in front of the most downstream facility; unsatisfied demand is backlogged. Every stage orders from its upstream facility, thus production is constrained by the local production capacity and the availability of upstream inventory. We propose production policies in two separate cases: (1) when each facility has information about its local inventory only, and (2) when each facility has knowledge of the total downstream inventory. In case (1) the proposed policy guarantees that stockout probabilities at each stage stay bounded below given constants (service level constraints). In case (2) the proposed policy minimizes total expected inventory cost subject to desirable service-level constraints. In both cases the parameters of the proposed policies are obtained analytically based on large deviations asymptotics, which leads to drastic computational savings compared to simulation. An important feature of our model is that it accommodates 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. We discuss extensions to a multiclass setting and to a model where unsatisfied demand is lost instead of backordered.