Minimising total completion time on single-machine scheduling with new integrated maintenance activities

A single-machine scheduling problem with new maintenance activities is examined in this paper. In the scheduling literature, it is often assumed that the interval between maintenance activities is fixed or within a specified time frame. However, this assumption may not hold true in many real-world situations, such as the maintenance activities in wafer manufacturing of semiconductor. Before the wafer manufacturing process starts, it is imperative that the wafers go through a number of cleaning operations to avoid contamination. Using a cleaning agent as the main material of wafer cleaning, the contamination will be dissolved and removed from wafer surface. In case of contamination being accumulated substantial and going beyond a permitted value, the cleaning agent is highly likely to damage the wafer surfaces. Thus, the interval between maintenance activities in the wafer manufacturing process is deemed irregular. The objective function of the proposed problem is to minimise total completion time. Addressing the problem, a binary integer programming model is formulated in this paper. Furthermore, with the research problem being NP-hard, a heuristic based on two special properties is proposed to address the problem. To evaluate and validate the proposed heuristic, a new lower bound is further developed. Extensive experiments have been conducted showing that the proposed heuristic efficiently yields a near-optimal solution with an average percentage error of 15.4 from lower bound.