Seru Scheduling Problems with Multiple Due-Windows Assignment and Learning Effect

This paper deals with seru scheduling problems with multiple due windows assignment and DeJong’s learning effect. Specific time intervals are assigned to jobs with multiple due windows and learning effect is introduced to characterize the decrease of processing times with the accumulation of the working experience. We assume that the set of jobs assigned to each due window is independent, and no inclusion exists between due windows. The objective is to determine the optimal due window positions and sizes, the set of jobs assigned to each due window, and the optimal schedule in each seru to minimize a multidimensional function, which consists of the earliness and tardiness punishment cost, as well as the due window related starting time and size cost. We find that when the number of jobs and the due windows assigned to each seru are pre-specified in advance, the problem can be solved in polynomial time. Meanwhile, the impacts of the due-window allocation strategy and learning effect on the total cost are respectively discussed based on numerical examples and special cases. The results show that if each seru is assigned with the same number of due windows, the total cost can be reduced with the increasing ratio of the due-window number to the to-be-processed job number. Furthermore, with an increasing learning effect, the total cost will be decreased.