Online Inventory Control with Censored Demand : A Neural Network-Based Approach

Inventory management for a new product is challenging due to the lack of historical data, and sales data cannot fully capture the actual demand as excess demand is usually unobservable. Meanwhile, demand-related features are available in the era of big data. We study how to determine the order-up-to level in a periodic-review inventory system with feature information and limited historical sales data to minimize the long-term average overage and underage costs. We allow the mean demand to be any function of the features. To solve the problem, we develop a neural network-based non-parametric online learning method, NeuroVendor. We prove through regret analysis that the cost of NeuroVendor converges at a rate of O(logT/T) and O(1/√T) for perishable and nonperishable inventory respectively, to the clairvoyant optimal cost with an approximation error. Additionally, we show that the approximation error is bounded and diminishes when the neural network size increases. We also note that the smaller the network, the faster the algorithm converges, but the larger the approximation error, indicating a bias-variance trade-off. In numerical experiments, NeuroVendor exhibits faster convergence rates and smaller regrets compared to existing methods. The advantage is more significant with more complex demand functions