We propose an inventory control model for an uncapacitated warehouse in a manufacturing facility under demand and lead time uncertainty. The objective is to make ordering decisions to minimize the total system cost. We introduce a two-stage tri-level optimization model with a rolling horizon to address the uncertain demand and lead time regardless of their underlying distributions. In addition, an exact algorithm is designed to solve the model. We compare this model in a case study with three decision-making strategies: optimistic, moderate, and pessimistic. Our computational results suggest that the performances of these models are either consistently inferior or highly sensitive to cost parameters (such as holding cost and shortage cost), whereas the new tri-level optimization model almost always results in the lowest total cost in all parameter settings.