Learning to replenish: A hybrid deep reinforcement learning for dynamic inventory management in the pharmaceutical supply chains

Modern supply chain operations can require coordinating replenishment across thousands of heterogeneous items under correlated stochastic demand, heterogeneous lead times, and shared fixed ordering costs, yielding observation spaces exceeding $10^4$ dimensions. At this scale, rolling-horizon stochastic mixed-integer linear programs (MILPs) become prohibitively slow, while standard reinforcement learning (RL) methods face increasingly challenging credit assignment in high-dimensional action spaces. We introduce OR-Transformer, a deep reinforcement learning framework for joint replenishment under stochastic demand, with an item-permutation-equivariant Transformer architecture and pathwise-gradient training through the inventory dynamics. Across problem sizes up to 1,024 inventory items, OR-Transformer increasingly outperforms learning-based and rolling-horizon MILP baselines as scale grows. It also reduces online decision-making time by over 4 million times relative to MILP solvers, enabling real-time, large-scale deep RL in supply chain operations.

Modern supply chains span diverse operational environments, ranging from e-commerce distribution networks to customized production-to-order manufacturing lines. Across these settings, operational efficiency depends on coordinating two highly interdependent stages: order preparation and downstream delivery. Although these stages are traditionally managed in isolation, real-world fulfillment systems must satisfy stringent delivery expectations under dynamic stochastic order arrivals. To bridge this gap, we introduce the Dynamic Order Fulfillment Problem (DOFP), a new problem class unifying logistical challenges previously studied separately. We model DOFP as a Markov decision process whose state and decision spaces are partitioned into preparation and delivery sub-spaces, linked by synchronization constraints. While recent approaches attempt to optimize both fulfillment stages simultaneously over myopic rolling horizons, our framework isolates and optimizes the downstream delivery policy, treating preparation strictly as a state-level constraint filter. To solve this, we develop the Decomposition-Driven Framework with Value Function Approximation (DDF-VFA), which utilizes a novel policy-level decomposition. This design partitions the search into a delivery-stage master problem and a preparation-stage compatibility subproblem, iteratively refined via feedback loops. DDF-VFA executes this strategy by combining a large-neighborhood search over partial delivery decisions with a neural-network value function approximation for the cost-to-go. Numerical illustrations on two example variants using real-world datasets show that DDF-VFA consistently outperforms benchmarks that optimize the two stages independently or jointly without decomposition. Finally, the framework naturally scales to accommodate additional real-world complexities such as batched or multi-stage preparation.

Supply chain resilience and efficiency are vital in industries characterized by volatile demand and uncertain supply, such as textiles and personal protective equipment (PPE). Traditional forecasting and optimization approaches often operate in isolation, limiting their real-world effectiveness. This paper proposes a Hybrid AI Framework for Demand-Supply Forecasting and Optimization (HAF-DS), which integrates a Long Short-Term Memory (LSTM)-based demand forecasting module with a mixed integer linear programming (MILP) optimization layer. The LSTM captures temporal and contextual demand dependencies, while the optimization layer prescribes cost-efficient replenishment and allocation decisions. The framework jointly minimizes forecasting error and operational cost through embedding-based feature representation and recurrent neural architectures. Experiments on textile sales and supply chain datasets show significant performance gains over statistical and deep learning baselines. On the combined dataset, HAF-DS reduced Mean Absolute Error (MAE) from 15.04 to 12.83 (14.7%), Root Mean Squared Error (RMSE) from 19.53 to 17.11 (12.4%), and Mean Absolute Percentage Error (MAPE) from 9.5% to 8.1%. Inventory cost decreased by 5.4%, stockouts by 27.5%, and service level rose from 95.5% to 97.8%. These results confirm that coupling predictive forecasting with prescriptive optimization enhances both accuracy and efficiency, providing a scalable and adaptable solution for modern textile and PPE supply chains.