Single machine SLK/DIF due window assignment problem with learning effect and deteriorating jobs

We study a single-machine scheduling and due window assignment problem, in which job processing times are defined by functions of their starting times (deteriorating effect) and positions in the sequence (learning effect). The problem is to determine the optimal due windows and the processing sequence simultaneously to minimize costs for earliness, tardiness, the window location, window size and makespan. We show that the problem remains polynomially solvable under the proposed model for two popular due window assignment methods: The slack due date assignment method (usually referred to as SLK) and the unrestricted due date assignment method (usually referred to as DIF).