In this paper, a solution approach based on the column generation technique is pre- sented for solving a time-indexed formulation of the total weighted tardiness problem. An acceleration strategy based on a decomposition of the time horizon into subperi- ods, where each subperiod is associated with a subproblem of the column generation approach, is used to solve the linear relaxation. Branching strategies and dominance rules are also applied in order to find the optimal integer solution. Using this new approach, it has been possible to solve to optimality 89 out of 125 open problems of the OR-Library.