We consider a two-level lot-sizing problem where the first level consists of N end products competing for a single type of raw material (second level), which is supposed to be critical. In particular, the storage capacity of raw materials is limited and must be carefully managed. The goal is to simultaneously determine an optimal replenishment plan for the raw material and optimal production plans for the end products on a horizon of T periods. The problem is modeled as an integer linear program and solved using both a Lagrangian relaxation-based heuristic and a commercial optimization software. The results obtained using the Lagrangian heuristic are promising and new ideas are generated to further improve the quality of the solution.