This article considers a single-machine group scheduling problem with due-window assignment, where the jobs are classified into groups and the jobs in the same group must be processed in succession. The goal is to minimize the weighted sum of lateness and due-window assignment cost, where the weights depend on the position in which a job is scheduled (i.e., position-dependent weights). For the common, slack, and different due-window assignment methods, we prove that the problem can be solved

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... ynomially, i.e., in ONlogN time, where N is the number of jobs.