Some single-machine scheduling problems with the extended sum-of-processing-time-based aging effect

In this paper, we analyze some single machine scheduling problems with the aging effect. We extend the sum-of-processing-time-based aging model such that the fatigue caused by each job to the machine is equal to a non-increasing function dependent on the normal processing time of a job and the aging effect is job dependent. Although the proposed model is more general and describes more precisely the real-life settings, we show that the special cases of the maximum completion time and the maximum lateness minimization problems with this model are still polynomially solvable. However, we prove the maximum completion time minimization problem with the sum-of-processing-time-based aging model is strongly NP-hard if some jobs have deadlines and constant processing times. On this basis, we show that the maximum lateness minimization problem with this aging model is also strongly NP-hard.