Whittle Index with Multiple Actions and State Constraint for Inventory Management

Chuheng Zhang, Xiangsen Wang, Wei Jiang, Xianliang Yang, Siwei Wang, Lei Song, Jiang Bian

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Keywords: MARL, Inventory Management, Whittle Index

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TL;DR: We propose a novel form of Whittle index that extend to a MARL setting suitable for practical inventory management.

Abstract: 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 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. Empirically, our algorithm is evaluated on real large-scale inventory management problems with up to 2307 SKUs and outperforms operation-research-based methods and baseline MARL algorithms.

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Primary Area: reinforcement learning

Submission Number: 7012