A time-series framework for supply-chain inventory management

We consider a supply chain in which the underlying demand process can be described in a linear state space form. Inventory is managed at various points of the chain (members), based on local information that each member observes and continuously updates. The key feature of our model is that it takes into account the ability of the members to observe subsets of the underlying state vector, and adopt their forecasting and replenishment policies accordingly. This enables us to model situations in which the members are privy to certain explanatory variables of the demand, with the latter possibly evolving according to a vector autoregressive time series. For each member, we identify an associated demand evolution model, for which we propose an adaptive inventory replenishment policy that utilizes the Kalman filter technique. We then provide a simple methodology for assessing the benefits of various types of information-sharing agreements between members of the supply chain. We also discuss inventory positioning and cost performance assessment in the supply chain. Our performance metrics and inventory target levels are usually presented in matrix forms, allowing them to accommodate a relatively large spectrum of linear demand models, and making them simple to implement. Several illustrations for possible applications of our models are provided.