Non-Stationary Inventory Control with Lead Times

2026-02-05

AI Summary

This work addresses the non-stationary single-item inventory control problem under unknown and time-varying demand distributions. The authors propose an adaptive online algorithm that unifies handling of scenarios with or without replenishment lead times, as well as backlogged shortages and lost sales. Leveraging the convexity of inventory costs and a one-sided feedback structure, the method achieves adaptivity to abrupt demand shifts without requiring prior knowledge of the demand process. Notably, it is the first approach to simultaneously attain adaptivity in non-stationary environments and optimality in stationary settings for certain model variants. Theoretical analysis establishes dynamic regret upper bounds across different configurations, and a counterfactual policy evaluation technique is introduced for truncated feedback. Numerical experiments demonstrate that the proposed algorithm significantly outperforms existing benchmarks.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• non-stationary demand
• inventory control
• lead times
• lost-sales
• backlogging

Innovation

• non-stationary demand
• online inventory control
• dynamic regret
• censored feedback
• base-stock policy