A note on single-machine scheduling with deteriorating jobs

In many real life applications, jobs deteriorate at a certain rate while waiting to be processed. This paper introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. We show that the single-machine makespan minimization problem remains polynomially solvable under the proposed model. We also show that an optimal schedule of the total completion time minimization problem is polynomially solvable under some cases and V -shaped with respect to job deterioration rates for other cases.