Due-window assignment scheduling problems with position-dependent weights on a single machine

This article deals with an integrated optimization problem of production scheduling and common due-window assignment on a single machine. The objective is to minimize the total cost, which is a weighted sum function of earliness and tardiness, due-window starting time, and due-window size, where the weights only depend on their position in a sequence (i.e. position-dependent weights). A polynomial time solution algorithm is provided for the corresponding problem. The problem can also be extended to slack due-windows assignment and general position-dependent processing times. It is proved that both these extensions remain polynomially solvable.