In recent years, wireless sensor networks have the advantages in a variety of applications. However, due to the limitations of hardware and the environment, the sensors are highly energy-constrained. By adopting data aggregation, we can effectively reduce the amount of data and thereby save energy consumption. In this thesis, we adopt data aggregation trees to efficiently arrange routing assignments in order to maximize the system lifetime of data-centric WSNs. We model the problem a mathematical formulation, where the objective function is to maximize the system lifetime, and use Lagrangean Relaxation method to derive an optimal solution.