Single-machine scheduling problems with a learning effect matrix

Scheduling problems with learning effects have been widely studied in numerous publication. However, the learning effect might accelerate, especially in the steel plates and the human interaction systems. In this paper, we propose a new scheduling model with a learning effect matrix. We show that the makespan and the total completion time problems can be optimally solved in polynomial time. We present heuristic sequencing rules and analyze the worst-case bounds for performance ratios to minimize the total weighted completion time, the maximum lateness, and the total tardiness. We also show that these heuristic rules can be optimal under some agreeable conditions between the normal processing times and job due dates or weights.