Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning

Job deterioration and machine learning co-exist in various real life scheduling settings. This paper studies several single machine scheduling problems under the joint effect of nonlinear job deterioration and time-dependent learning. We assume that the processing time of a job increases when its processing is delayed. In addition, it is assumed that the machine undergoes a learning process, decreasing the time required to process a given job. The following objectives are considered: the makespan, the sum of completion times (square) and the maximum lateness. We derive polynomial-time optimal solutions for all the objectives.