Inventory Systems with Record Inaccuracy : Transaction Errors vs Unobservable Loss

Problem definition. We present a continuous-time Bayesian model for managing inventory in a retail setting when inventory records are inaccurate. In our formulation, the inventory level and its record have separate dynamics. The former is driven by the demand and unobservable loss process while the latter is driven by the demand and transaction error process. Methodology/results. We analytically characterize the dynamics of the retailer's belief on the shelf inventory level and prove that the optimal restocking policy is a threshold policy. In contrast to prior conjectures, we show that transaction errors play a prominent role in increasing the uncertainty in the shelf inventory distribution. In addition to this confounding effect, presence of transaction errors breaks the retailer's ability to calculate this distribution by tracking a small set of sufficient statistics: it remains a function of the entire observed history. Hence, computing the optimal restocking policy, even though we obtain its exact analytical form, remains numerically intractable. We tackle this "curse of dimensionality'' by dynamically adjusting the problem's underlying information filtration. This effectively projects the dynamics of the inventory level onto a manifold that is adaptively adjusting to the information revealed by the inventory record process. Managerial implications. Adding this extra layer of adaptation, implemented by dynamic filtration, enables us to reduce the dimensionally of the problem by an arbitrary degree. We show that the resulting implementable policy, which is optimal for the chosen dynamic filtration, also exhibits significant robustness to model misspecification