On the complexity of the single machine scheduling problem minimizing total weighted delay penalty

We consider a single machine scheduling problem for a fixed penalty function f. For this problem every job j has a priority wj, and a processing time pj and the goal is to find an order on the given jobs that minimizes ∑wjf(Cj), where Cj is the completion time of job j. This paper studies the complexity of this problem for various classes of penalty functions.