<p>Sea-rail intermodal transportation is an essential infrastructure in global supply chains nowadays. However, the efficiency of this system is often hindered by bottlenecks in the storage and retrieval of containers in the yard. Recent studies on container-to-stack assignment treat all stacks as a whole, resulting in a large solution space that makes these approaches unsuitable for large-scale problems. Additionally, widely adopted heuristic methods often lead to suboptimal solutions. The challenge of achieving real-time, optimal yard storage allocation in large yards remains unresolved. In this work, we address this critical issue and make the following contributions. By exploiting the independence among stacks, we formulate the yard storage allocation problem as a restless multi-armed bandit (RMAB) problem and leverage the Whittle index policy to address it. We empirically establish the indexability of this RMAB problem for the general case and provide theoretical verification for a specific scenario. Recognizing the challenges of analytically deriving the Whittle index for this practical application, we propose a novel algorithm, SWIRL, which leverages reinforcement learning to estimate the Whittle index both accurately and efficiently. Unlike existing methods for Whittle index estimation, SWIRL is capable of handling complex RMAB problems with large arm state spaces. Numerical experiments demonstrate the effectiveness and scalability of the proposed method. Furthermore, the model trained by SWIRL can be directly applied to different scenarios without requiring retraining, even when the container distribution or the number of stacks changes, showing the potential of the proposed method to be applied in practice.</p>