Abstract
The paper deals with the single-machine scheduling problems with a time-dependent deterioration. By time-dependent deterioration, we mean that the processing time of a job is defined by an increasing function of total normal processing time of jobs in front of it in the sequence. We show that, even with the introduction of time-dependent deterioration to job processing times, the single-machine makespan minimization problem remains polynomially solvable. We also show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times.
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