A branch-and-bound algorithm for the single-machine weighted earliness-tardiness scheduling problem with job independent weights

In this paper we propose a branch-and-bound algorithm for the single-machine earliness-tardiness scheduling problem where weights for earliness and tardiness are independent of jobs. Here, machine idle times are allowed. In our branch-and-bound algorithm, the search tree is generated by fixing the processing order of jobs from the first to the last, or, from the last to the first. To improve the efficiency of the algorithm, we propose new lower bounds. We also show dominance properties that are utilized both for reducing branches in the search tree and for improving the lower bounds. Then, we show the effectiveness of our algorithm by numerical experiments.