Deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times

In this paper, we consider the single-machine setup times scheduling with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We show that the problems to minimize the makespan, the total completion time, and the sum of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathit{\delta}$\end{document}th (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathit{\delta}} \geq 0$\end{document}) power of job completion times are polynomially solvable. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.