Improved lower bounds for the early/tardy scheduling problem with no idle time

In this paper, we consider the single machine earliness/tardiness scheduling problem with no idle time. Two of the lower bounds previously developed for this problem are based on Lagrangean relaxation and the multiplier adjustment method, and require an initial sequence. We investigate the sensitivity of the lower bounds to the initial sequence, and experiment with different dispatch rules and some dominance conditions. The computational results show that it is possible to obtain improved lower bounds by using a better initial sequence. The lower bounds are also incorporated in a branch-and-bound algorithm, and the computational tests show that one of the new lower bounds has the best performance for larger instances.