The study deals with scheduling a set of independent jobs with unequal release dates to minimize total weighted tardiness on a single machine. We propose new dominance properties that are incorporated in a branch and bound algorithm. The proposed algorithm is tested on a set of randomly generated problems with 10, 15 and 20 jobs. To the best of our knowledge, this is the first exact approach that attempts to solve the l|rj|ΣwjTjproblem.