Misspecification Loss in Inventory Systems with Correlated Demand

We study a periodic-review inventory system with positive lead time and correlated demand. While most inventory models assume independent demand for tractability, this simplification may lead to model misspecification in practice. We consider a decision maker who implements a myopic base-stock policy based on a misspecified i.i.d. model, while the true demand follows a stationary Gaussian AR(1) process. We derive closed-form expressions for the optimal policy under the true model and for the cost of the misspecified policy, and quantify misspecification loss via a competitive ratio. Our results show that longer lead times do not necessarily amplify misspecification loss. In particular, when demand exhibits positive correlation, increasing the lead time can attenuate the impact of misspecification. At the same time, this misspecification becomes increasingly consequential when backlog penalties are high. Under positive correlation, underestimation of uncertainty leads to persistent understocking and substantial losses, whereas under negative correlation, misspecification induces overstocking and the resulting loss is less sensitive to stockout penalties. Overall, the cost of using a simplified demand model depends not only on demand variability, but also on whether demand exhibits persistence or reversal over time and the relative costs of backlog versus excess inventory.