Single-machine group scheduling with a general learning effect

This paper investigates some single-machine scheduling problems with a general learning effect and the group technology assumption. A setup time is incurred whenever the single machine transfers job processing from a family to another family. By the general learning effect, we mean that the actual group setup time depends not only on the total setup time of the groups already processed but also on its scheduled position, and the actual processing time of a job in a certain group depends not only on the total normal processing time of the jobs already processed in the group but also on its scheduled position. We show that the makespan minimisation problem remains polynomially solvable under the proposed models. We also show that the problems of minimising the total completion time, the total weighted completion time and the discounted total weighted completion time of all jobs have polynomial optimal solutions under certain conditions.