Semiconductor manufacturing systems consist of highly complex and constrained processes owing to the requirement for high-quality wafers and dynamic customer orders. This study focuses on waiting time constraints to achieve high-quality wafers, with missing operations, to manufacture different types of orders, which are common scheduling requirements in semiconductor manufacturing systems. Waiting time constraints limit the waiting times between consecutive machines. Although sequential steps are modelled as a flow shop, some jobs can skip some steps in the flow shop. Such jobs can accordingly skip certain machines in the flow shop, which is called ‘missing operations’. This research investigates a scheduling problem for a flow shop with waiting time constraints and missing operations. A mathematical programming formulation and scheduling algorithms are proposed to operate such a flow shop efficiently. Through computational experiments, the proposed algorithms were evaluated, and analysis of various parameters for waiting time constraints and missing operations was conducted.

This study considers a scheduling problem for a flow shop with urgent jobs and limited waiting times. The urgent jobs and limited waiting times are major considerations for scheduling in semiconductor manufacturing systems. The objective function is to minimize a weighted sum of total tardiness of urgent jobs and the makespan of normal jobs. This problem is formulated in mixed integer programming (MIP). By using a commercial optimization solver, the MIP can be used to find an optimal solution. However, because this problem is proved to be NP-hard, solving to optimality requires a significantly long computation time for a practical size problem. Therefore, this study adopts metaheuristic algorithms to obtain a good solution quickly. To complete this, two metaheuristic algorithms (an iterated greedy algorithm and a simulated annealing algorithm) are proposed, and a series of computational experiments were performed to examine the effectiveness and efficiency of the proposed algorithms.