Two-agent single-machine scheduling with assignable due dates

We consider several two-agent scheduling problems with assignable due dates on a single machine, where each of the agents wants to minimize a measure depending on the completion times of its own jobs and the due dates are treated as given variables and must be assigned to individual jobs. The goal is to assign a due date from a given set of due dates and a position in the sequence to each job so that the weighted sum of the objectives of both agents is minimized. For different combinations of the objectives, which include the maximum lateness, total (weighted) tardiness, and total (weighted) number of tardy jobs, we provide the complexity results and solve the corresponding problems, if possible.