Some Single Machine Scheduling Problems with an Actual Time-Dependent and Position-Dependent Learning Effect

Abstract

In this paper, we introduce an actual time-dependent and positiondependent learning effect into single-machine scheduling problems. The learning effect of a job is assumed to be a function of the sum of actual processing times of the jobs already processed and the job’s scheduled position. We show that under certain conditions, the problems with classical objectives such as make-span, sum of kth power of the completion times, total weighted completion time, maximum lateness and number of tardy jobs remain polynomial solvable.