A unified approach to single-machine scheduling with position-based processing times, machine availability, and job rejection

We present a unified approach to single-machine scheduling with position-based processing times, an availability constraint, and job rejection. The approach uses two general position-based processing time functions to model both the learning and aging effects in scheduling. In addition, taking machine availability and job rejection into consideration, the models are more realistic, which seek to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. We present fully polynomial-time approximation schemes to address the two NP-hard problems.