We consider a two-level dynamic lot-sizing problem where the first level consists of N finished products competing for a single type of purchased raw material in the second level. While the procurement and production capacities are unlimited, the storage capacity of the raw material is limited and must be carefully managed. The goal is to simultaneously determine a replenishment plan for the raw material and optimal production plans for the finished products on a horizon of T periods while minimizing production, purchasing, setup and inventory holding costs. The problem is modeled using mixed-integer linear programs and solved using both a Lagrangian relaxation-based heuristic and a commercial mixed-integer linear programming solver. 123 N. Brahimi et al. Learning capabilities are integrated in the Lagrangian relaxation to update step size in the subgradient algorithm. The computational results show that the Lagrangian heuris-tic outperforms the solver on different formulations, in particular for large problems with long time horizons.