Scheduling jobs with an exponential sum-of-actual-processing-time-based learning effect

In this paper we consider single-machine scheduling problems with an exponential sum-of-actual-processing-time-based learning effect. By the exponential sum-of-actual-processing-time-based learning effect, we mean that the processing time of a job is defined by an exponential function of the sum of the actual processing times of the already processed jobs. For the proposed learning model, we show that under certain conditions, the makespan minimization problem, the sum of the θθth (θ>0θ>0) powers of completion times minimization problem, and some special cases of the total weighted completion time minimization problem and the maximum lateness minimization problem all remain polynomially solvable.