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.