Flow Shop Scheduling Problems with General Learning Effect under Dominant Machines

This paper considers a flow shop scheduling model with general learning effect under dominant machines in which the actual processing time of a job is not only a function of the total actual processing time of the jobs already processed, but also a function of the job's scheduled position. The paper shows that the problems to minimize the makespan and the sum of the kth power of completion times are polynomially solvable under the proposed model. It further shows that the problems to minimize the total weighted completion time and the maximum lateness are polynomially solvable under certain conditions.