Research on single-machine scheduling with position-dependent weights and past-sequence-dependent delivery times

This article studies scheduling problems with past-sequence-dependent delivery times (denoted by psddt) on a single-machine, i.e., the delivery time of a job depends on its waiting time of processing. We prove that the total (discounted) weighted completion time minimization can be solved in O(nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n\log n)$$\end{document} time, where n is the number of jobs, and the weight is a position-dependent weight. For common (denoted by con) and slack (denoted by slk) due-date assignment and position-dependent weights (denoted by pdw), we prove that an objective cost minimization is solvable in O(nlogn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n\log n)$$\end{document} time. The model (i.e., psddt and pdw) can also be extended to position-dependent (time-dependent) processing times.