Target coverage problem in wireless sensor networks remains a challenge. Due to nonlinear nature, previous work has mainly focused on heuristic algorithms, which remain difficult to characterize and have no performance guarantee. To solve the problem, this paper offers two important contributions. The first contribution is to have two lifetime upper bounds, which could be used to justify performance of previously proposed heuristic algorithms. One upper bound is based on the relaxation and reformulation technique while the other is derived by relaxing coverage constraints. We study the interesting connection between those two bounds and thus endow them with physical meanings. The second contribution is proposing a column generation based (CG) approach. The objective is to find an optimal schedule, defined as a time table specifying from what time up to what time which sensor watches which targets while the maximum lifetime has been obtained. We also offer an in-depth theoretic analysis as well as several novel techniques to further optimize the approach. Numerical results not only demonstrate that the lifetime upper bounds are very tight, but also verify that the proposed CG based approach constantly yields the optimal or near optimal solution.