Single-machine just-in-time scheduling problem with learning/deterioration effects and past-sequence-dependent delivery times

Just-in-time (JIT) production is widely adopted in industries such as automobile manufacturing and construction engineering, with the goal of completing tasks within predefined time frames. This paper investigates single-machine scheduling problems in a JIT environment, incorporating past-sequence-dependent delivery times and considering two factors that influence processing time: a position-related learning effect that reduces processing time and a time-related deterioration effect that increases it. The objective is to minimise a weighted sum of classical due-window costs and makespan in common/slack/different due windows, in which the classical due window cost includes the earliness and tardiness, the number of early and tardy jobs, as well as the window start time and size, and with the associated weights being position-dependent. By establishing relevant optimality properties, we demonstrate that optimal solutions can be obtained in polynomial-time for common/slack/different due windows.