A single-item inventory model for a nonstationary demand process

In this paper, we consider an adaptive base-stock policy for a single-item inventory system, where the demand process is nonstationary. In particular, the demand process is an integrated moving average process of order (0, 1, 1), for which an exponential-weighted moving average provides the optimal forecast. For the assumed control policy we characterize the inventory random variable and use this to find the safety stock requirements for the system. From this characterization, we see that the required inventory, both in absolute terms and as it depends on the replenishment lead-time, behaves much differently for this case of nonstationary demand compared with stationary demand. We then show how the single-item model extends to a multi-stage, or supply-chain context; in particular we see that the demand process for the upstream stage is not only nonstationary but also more variable than that for the downstream stage. We also show that for this model there is no value from letting the upstream stages see the exogenous demand. The paper concludes with some observations about the practical implications of this work.