We study the Capacity Constrained Lot Size Problem with Setup Times (CLST). Based on two strong reformulations of the problem, we present a transformed reformulation and valid inequalities that speed up column generation and Lagrange relaxation. We demonstrate computationally how both ideas enhance the performance of our algorithm and show theoretically how they are related to dual space reduction techniques. We compare several solution methods, and propose a new efficient hybrid scheme that combines column generation and Lagrange relaxation in a novel way. Computational experiments show that the proposed solution method for finding lower bounds is competitive with other state-of-the-art approaches found in the literature. Finally, a branch-and-price based heuristic is designed and computational results are reported. The heuristic scheme compares favorably or outperforms similar approaches.