Stochastic state space in supply chains under AR(1) demand profiles

This work aims to present a stochastic state-space model for a three-node series supply chain under first-order Autoregressive (AR) customer demand profiles. It is assumed that inventory replenishment in each node follows continuous (proportional) base stock policies via specific control parameters. Dynamic properties of the supply chain model are encapsulated in closed-form covariance matrix, i.e., as an explicit function of the control parameters and autoregression coefficient. The model is analysed under stationary conditions, allowing to analyse the effect of inventory-replenishment policies and correlated demand profiles on the 'bullwhip effect' (demand amplification) and related instability phenomena in supply chains.