A New Branch-and-Bound for the Problem of Mean Completion Time for the Single Machine with Release Time

Preemptively scheduling a set of independent jobs with release time on one processor is a historical problem. In this paper, the same problem has been considered in which objective is to minimize the mean flow time. To prepare a perfect branch-and-bound, some optimality conditions have been represented and they have been compared with the optimality conditions which have been proposed before. Our branch-and-bound has been coded with C++, and the results indicate efficiency of our algorithm and our new optimality conditions.