A companion paper introduces new lower bounds and heuristics for the problem of minimizing makespan onidentical parallel machines. The objective of this paper is threefold. First, we describe further enhancementsof previously described lower bounds. Second, we propose a new heuristic that requires solving a sequence of0–1 knapsack problems. Finally, we show that embedding these newly derived bounds in a branch-and-boundprocedure yields a very effective exact algorithm. Moreover, this algorithm features a new symmetry-breakingbranching strategy. We present the results of computational experiments that were carried out on a large setof instances and that attest to the efficacy of the proposed algorithm. In particular, we report proven optimalsolutions for some benchmark problems that have been open for some time