Scheduling problems with a weight-modifying-activity

We study single machine scheduling problems with an additional option of performing a weight-modifying-activity. If such an activity is performed, the cost of subsequent jobs is reduced, as reflected by smaller job-weights. We focus first on minimizing total weighted completion time. A pseudo-polynomial dynamic programming algorithm is introduced for this problem. Several special cases of unit processing time jobs are solved in polynomial time. We also solve in polynomial time (an extension of) the minmax version of the problem, by adapting the well-known Lawler's Algorithm for minimizing maximum cost on a single machine.