Non-Stationary Inventory Control with Lead Times

We study non-stationary single-item, periodic-review inventory control problems in which the demand distribution is unknown and may change over time. We analyze how demand non-stationarity affects learning performance across inventory models, including systems with demand backlogging or lost-sales, both with and without lead times. For each setting, we propose an adaptive online algorithm that optimizes over the class of base-stock policies and establish performance guarantees in terms of dynamic regret relative to the optimal base-stock policy at each time step. Our results reveal a sharp separation across inventory models. In backlogging systems and lost-sales models with zero lead time, we show that it is possible to adapt to demand changes without incurring additional performance loss in stationary environments, even without prior knowledge of the demand distributions or the number of demand shifts. In contrast, for lost-sales systems with positive lead times, we establish weaker guarantees that reflect fundamental limitations imposed by delayed replenishment in combination with censored feedback. Our algorithms leverage the convexity and one-sided feedback structure of inventory costs to enable counterfactual policy evaluation despite demand censoring. We complement the theoretical analysis with simulation results showing that our methods significantly outperform existing benchmarks.

💡 Research Summary

The paper tackles a realistic and challenging setting in inventory management: a single‑item, periodic‑review system where demand is non‑stationary (its distribution may change over time) and the decision maker has no prior knowledge of the number, timing, or magnitude of these changes. Moreover, the study explicitly incorporates deterministic lead times, which couple inventory decisions across periods, and considers both backlogging (unsatisfied demand is backordered) and lost‑sales (unsatisfied demand is lost) loss functions.

The authors model non‑stationarity as a piecewise‑stationary process with an unknown number of stationary segments S over a horizon T. They focus on the class of base‑stock policies, which are known to be optimal for the static versions of these problems. By restricting attention to this one‑dimensional policy space