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.