Efficient branch-and-bound algorithm for minimizing the weighted sum of completion times on a single machine with one availability constraint

In this article, we consider the single-machine scheduling problem with one availability constraint. We aim to minimize the weighted sum of completion times. We propose a branch-and-bound algorithm based on a set of improved lower bounds and heuristics. The numerical experiments show the effectiveness of the proposed method. The improved algorithm is able to solve instances of 6000 jobs in a reasonable amount of computation time.