Complexity results for single-machine scheduling with positional learning effects

This note presents complexity results for a single-machine scheduling problem of minimizing the number of late jobs. In the studied problem, the processing times of the jobs are defined by positional learning effects. A recent paper proposed a polynomial time algorithm for the case with a common due date and conjectured the general problem to be NP-hard. We confirm that the general problem is strongly NP-hard and show that the studied problem remains NP-hard even if there are only two different due-date values.