Single-machine lot scheduling with variable lot processing times

This research addresses single-machine lot scheduling problems, with a focus on minimizing the total weighted completion time. The following properties for the lots are assumed: the lots have the same capacity, each lot may contain several orders of different sizes, the size of each order is less than or equal to the identical capacity, and orders must be processed at most in two consecutive lots. To date, lot scheduling researchers have assumed that all lots have identical processing times. In this study, variable lot processing times are considered; specifically, the setting where the processing time of the lots is position dependent, reflecting general position-dependent processing time properties, e.g. learning/ageing effects. Three special cases are examined: minimizing the total completion time, minimizing the makespan, and minimizing the linear combination of the makespan and the total completion time. All problems are shown to be solved in polynomial time.