New Learning Framework Optimizes Inventory Allocation

Managing inventory in a one-warehouse multi-store (OWMS) system, where a central warehouse allocates a non-replenishable stock across multiple retail locations over time, is a complex challenge. Existing learning policies for these systems typically rely on a fixed target for resource allocation, which becomes inefficient as actual sales deplete the available stock and change the resource rate per future period. This research proposes a novel framework called Resource-Adaptive Primal-Dual Learning. This new approach dynamically tracks the primal-dual resolving path, adapting to censored demand and the evolving state of remaining resources. In each period, the system uses the current resource rate to index target store allocations and dual variables, while censored sales data provides gradient estimates for continuous updates. The analytical results demonstrate that this framework achieves logarithmic expected regret, a significant improvement over the state-of-the-art square-root-order guarantees of previous OWMS learning policies. The underlying design principles and analytical methods could also be applied to other online learning problems involving shared, depleting resources. Numerical experiments further validate the practical performance of a variant of this method across various horizon lengths and inventory conditions.