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In this paper, we focus on real-life settings that require the development of new models of flowshop scheduling problems, where job processing times can increase with the number of processed jobs due to the aging effect and decrease by the allocation of additional resource. We analyse the makespan minimization flowshop problem with such model and also with the aging effect only. We prove that the considered problems and their special cases are still polynomially solvable under given conditions, and on their basis, we provide optimal polynomial time solution algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we analyze some single machine scheduling problems with the aging effect. We extend the sum-of-processing-time-based aging model such that the fatigue caused by each job to the machine is equal to a non-increasing function dependent on the normal processing time of a job and the aging effect is job dependent. Although the proposed model is more general and describes more precisely the real-life settings, we show that the special cases of the maximum completion time and the maximum lateness minimization problems with this model are still polynomially solvable. However, we prove the maximum completion time minimization problem with the sum-of-processing-time-based aging model is strongly NP-hard if some jobs have deadlines and constant processing times. On this basis, we show that the maximum lateness minimization problem with this aging model is also strongly NP-hard. [ABSTRACT FROM AUTHOR]