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Scheduling with position-dependent weights, due-date assignment and past-sequence-dependent setup times

In this study, we consider single-machine scheduling problems with past-sequence-dependent (denoted by psd) setup times in which the setup times of jobs are proportional to the length of already processed jobs. Under common (CON) and slack (SLK) due-date assignment methods, we prove that the weighted sum of earliness, tardiness and due-date minimization remains polynomially solvable. We also give some extensions for the scheduling problems with psd setup times.