In this paper we introduce a new scheduling model with learning effects 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 makespan and total completion time are polynomially solvable. In addition, we show that the problems to minimize total weighted completion time and maximum lateness are polynomially solvable under certain agreeable conditions. Finally, we present polynomial-time optimal solutions for some special cases of the m-machine flowshop problems to minimize makespan and total completion time.
Cheng et al. REF brought up with a new learning model in which the actual processing time of a job depends on both the job's scheduled position and the processing times of the jobs that are already processed.
Some scheduling problems with sum-of-processing-times-based and job-position-based learning effects
Inf. Sci.
Inf. Sci.
Computer Science