In this paper, the scheduling problems for due date assignment with position-dependent weights are studied. The goal is to find the optimal job processing sequence in two modes of common/slack due date assignment with the linear weighted sum of minimal due date and tardiness, where the weights are position-dependents weights. By proving a series of properties, the calculation methods of due date are obtained, and then the two kinds of due date assignment problems are transformed into functions related to job processing time. According to coefficient corresponding to each job, the specific solution algorithms are given to obtain the optimal job sequence, and the corresponding optimal common/slack due date. The algorithms are verified to solve the problems in polynomial time by numerical examples.