In this paper, we propose a two-tier mixed integer linear programming (MILP) model, composed of aggregate production planning (APP) and family disaggregation planning (FDP), to solve the hierarchical production planning (HPP) problem with nontrivial setup times. In addition to disaggregating the aggregate plan in the first period into detailed lot sizing plans as traditional models do, the proposed FDP model optimally adjusts the aggregate plan and eliminates infeasibility arising from the positive setup times. The performance of the proposed model is validated with a case study. Results of the validation show that the proposed model leads to significant cost savings and efficiencies in the supply chain compared to traditional HPP models.