Single machine scheduling problems with exponentially time-dependent learning effects

highlights•Introduce exponentially time-dependent learning effect into single machine scheduling problems.•Using SPT to minimize two criteria: makespan and the total flow time.•Obtain the upper bound for the total weighed flow time and maximum lateness.•Consider two special cases of the problem to minimize several regular objectives.

In this paper, we introduce a single-machine scheduling problem with an exponentially time-dependent learning effect. The processing time of a job is assumed to be an exponential function of the total normal processing time of jobs already processed before it. For such a scheduling problem, we first provide the upper bound for the maximum lateness and for the total weighted completion time. Next, we show that problems with the following criteria: makespan, the total completion time, the total weighted completion time, the total earliness/tardiness penalties and the maximum lateness under some agreeable conditions, are polynomially solvable.