Single Machine Scheduling Problems with Job-Position-Based and Sum-of-Processing-Times-Based Learning Effect

In this paper we consider a new scheduling model with learning effect, in which the actual processing time of a job is a function of the total normal processing times of the jobs already processed and of the job´s scheduled position. We show that the single machine problems to minimize the makespan and the total completion time are polynomially solvable. In addition, we show by counterexample that the weighted shortest processing time (WSPT) rule is not optimal for the problems to minimize the total weighted completion time, but it is optimal when the processing times and weights are under certain disagreeable condition.