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