An exact approach for single machine scheduling with quadratic earliness and tardiness penalties

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose two different lower bounds, as well as a lower bounding procedure that combines these two bounds. Optimal branch-and-bound algorithms are then presented. These algorithms incorporate the proposed lower bound, as well as an insertion-based dominance test. The lower bounding procedure and the branch-and-bound algorithms are tested on a wide set of randomly generated problems. The computational results show that the branch-and-bound algorithms are capable of optimally solving, within reasonable computation times, instances with up to 20 jobs.