Feature-Based Nonparametric Inventory Control with Censored Demand

Problem definition: We study stochastic periodic-review inventory systems with lost sales, where the decision maker has no access to the true demand distribution a priori and can only observe historical sales data (referred to as censored demand) and feature information about the demand. Academic/practical relevance: In an inventory system, excess demand is unobservable due to inventory constraints, and sales data alone cannot fully recover the true demand. Meanwhile, feature information about the demand is abundant to assist inventory decisions. We incorporate features for inventory systems with censored demand. Methodology: We propose two feature-based nonparametric inventory algorithms called the feature-based adaptive inventory algorithm and the dynamic shrinkage algorithm. Both algorithms are based on the stochastic gradient descent method. We measure the performance of the proposed algorithms through the average expected regret in finite periods: that is, the difference between the cost of our algorithms and that of a clairvoyant optimal policy with access to information, which is acting optimally. Results: We show that the average expected cost incurred under both algorithms converges to the clairvoyant optimal cost at the rate of $O(1/\sqrt{T})$. The feature-based adaptive inventory algorithm results in high volatility in the stochastic gradients, which hampers the initial performance of regret. The dynamic shrinkage algorithm uses a shrinkage parameter to adjust the gradients, which significantly improves the initial performance. Managerial implications: This paper considers feature information. The idea of dynamic shrinkage for the stochastic gradient descent method builds on a fundamental insight known as the bias-variance trade-off. Our research shows the importance of incorporating the bias-variance in a dynamic environment for inventory systems with feature information.