Due-Window Assignment Methods and Scheduling with Generalized Positional-Dependent Weights

We focus on a single-machine scheduling problem with common and slack due-window assignment methods. Both the job sequence and due-windows are decision variables to be determined by the decision maker. We consider the following performance criterion: the total weighted number of early and late jobs plus the total weighted of earliness, tardiness and due-window assignment cost, where the weights depend on the position in which a job is scheduled. Some properties are established, and it is shown that the problem can be solved in O(n(5)) time, where n is the number of jobs. The extensions of the model are to cases of general position-dependent processing times and time-dependent processing times.