This paper deals with the parallel-machine scheduling problem with the aim of minimizingthe total (weighted) tardiness under the assumption of different release dates. Thisproblem has been proven to be NP-hard. We introduce some new lower and upper bounds basedon different approaches. We propose a branch-and-bound algorithm to solve the weighted andunweighted total tardiness. Computational experiments were performed on a large set ofinstances and the obtained results showed that our algorithms are efficient.
