Summary: Asolution approach based on the column-generation technique is presented for solving a time-indexed formulation of the total weighted tardiness problem. An acceleration strategy based on a decomposition of the time horizon into subperiods, 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 to find the optimal integer solution. Using this new approach, it is possible to solve to optimality 117 out of 125 open problems of the OR-Library.