Whittle Index with Multiple Actions and State Constraint for Inventory Management

Whittle index is a heuristic tool that leads to good performance for the restless bandits problem. In this paper, we extend Whittle index to a new multi-agent reinforcement learning (MARL) setting with multiple discrete actions and a possibly changing constraint on the state space, resulting in WIMS (Whittle Index with Multiple actions and State constraint). This setting is common for inventory management problems, where each agent chooses a replenishing quantity level for the corresponding stock-keeping-unit (SKU) such that the total profit is maximized while the total inventory does not exceed a certain limit. Accordingly, we propose a deep MARL algorithm based on WIMS for inventory management, and evaluate our algorithm empirically on real large-scale inventory management problems with up to 2307 SKUs. The results show that our algorithm outperforms operation-research-based methods and baseline MARL algorithms.