AbstractThis paper deals with schedulingnjobs on a single machine in order to minimize the weighted sum of squared waiting times of the jobs. We present a powerful decomposition mechanism, based on a precedence relation concept, that easily handles problems of the sizen= 50 and 100 where the processing times and penalties are independently drawn from a uniform distribution. This mechanism is incorporated along with new branching rules in a branch-and-bound scheme that efficiently handles tough problems of the size 20 and 50.