Some scheduling problems with time-dependent learning effect and deteriorating jobs

Although machine scheduling problems with learning and deteriorating effects consideration have received increasing attention in the recent years, most studies have seldom considered the two phenomena simultaneously. However, learning and deteriorating effects might co-exist in many realistic scheduling situations. Thus, in this article, a model which takes the effects of time-dependent learning and deterioration simultaneously is proposed and applied into some scheduling problems. Under the proposed model, the processing time of a job is determined by a function of its corresponding starting time and positional sequence in each machine. We show that some single machine and flowshop scheduling problems are polynomially solvable with the certain performance measures such as makespan, total completion time, and weighted completion time.