Complexity with day-independent processing times

Determine the computational complexity of the maximal fairness problem in repetitive single-machine scheduling when every client’s job has a processing time independent of the day, p_{ij}=p_j for every job, under the total completion-time and lateness criteria.

Background

The special case p_{ij}=p_j models settings in which each client submits the same job in every period. The paper notes practical applications such as repeated healthcare treatments performed on the same machine, where the same treatment is administered during each visit.

Although the paper establishes several hardness results for related maximal fairness variants—including waiting time and tardiness cases—the computational complexity of the day-independent-processing-time special case is not established for the completion-time and lateness criteria.