A data-driven constraint learning approach for multi-echelon supply chains

Simulation is widely used in supply chain management because it can represent uncertainty and complex network dynamics. Inventory management plays a central role in maintaining high service levels while reducing total supply chain cost. However, optimizing inventory policies is computationally intensive because it typically requires a large number of simulation runs. This paper addresses the problem of identifying satisfactory inventory policies that minimize total supply chain cost in a multi-echelon distribution network subject to target service level and target order frequency constraints. To address this problem, this study proposes a scalable multi-echelon inventory optimization framework that integrates learned constraints into the optimization model, enabling simultaneous consideration of multiple operational requirements without substantially increasing computational effort. First, simulation is used to generate sample points for the multi-echelon distribution network. Next, a machine learning model trained on the generated data is embedded within a mathematical optimization framework. Finally, the ( s , S ) inventory policy parameters for each location are determined by solving a mixed-integer programming (MIP) model. Computational experiments on three synthetic divergent distribution networks demonstrate the effectiveness of the proposed framework. Among the evaluated machine learning models, gradient boosting achieves the best performance. Compared with an evolutionary optimization approach, the proposed method reduces computational time by approximately 29%, 81%, and 77% for the two-, three-, and four-echelon networks, respectively. Furthermore, sensitivity analysis provides insights into the impact of order-frequency and service-level targets on total costs.