Single-machine preemptive scheduling with assignable due dates or assignable weights to minimize total weighted late work

In this paper we study single-machine preemptive scheduling to minimize the total weighted late work with assignable due dates or assignable weights. For the problem with assignable due dates, we show that it is binary NP-hard, solvable in pseudo-polynomial time, and solvable in polynomial time when all the jobs have agreeable processing times and weights. For the problem with assignable weights, we show that it is solvable in polynomial time. For the problem with assignable due dates and assignable weights, we show that it is binary NP-hard, solvable in pseudo-polynomial time, and solvable in polynomial time when all the jobs have the same processing times.