In semiconductor wafer production, a cleaning operation is essential for removing surface residues left on wafers after various processing steps. This step takes up approximately 30% of the total fabrication time, making it as important as other major production stages. A wet station is typically composed of a transport single-arm robot and several processing tanks that are arranged in a linear topology configuration. In contrast to cluster tools whose processing modules are arranged in a radial layout, the time taken for the robot to move between tanks in a cleaning tool varies and cannot be considered identical. Under such circumstances, different assignment schemes of tanks to cleaning steps and robot access sequences to the tanks at a step can influence the performance of a wafer cleaning tool, which further complicates the scheduling problem. Our main objective of this paper was to identify the optimal arrangement of allocating tanks to processing steps and the best access route of the robot under various scenarios for maximizing the cleaning efficiency of a wet station. To achieve this goal, a Mixed Integer Programming (MIP) model based on Timed Petri Nets (TPN) was established to determine the optimal cyclic schedule along with the corresponding assignment scheme and cycle time. The practicality of the proposed model was further validated through experimental studies. Our results demonstrated that the proposed model can significantly improve the performance, reduces the average cycle time by 6.66%, and increases throughput by 7.14% compared to traditional scheduling methods. Moreover, the MIP solver obtained optimal schedules within minutes for typical wet station scales, confirming its computational efficiency and practical applicability.
Citation: Luetao Li, Naiqi Wu, Yan Qiao, Siwei Zhang, Jie Li, Yang Bai. An Efficient Mixed Integer Programming Model for Wet Station Scheduling Problems Based on Timed Petri Nets[J]. Journal of Industrial and Management Optimization, 2026, 22(4): 1956-1980. doi: 10.3934/jimo.2026072
In semiconductor wafer production, a cleaning operation is essential for removing surface residues left on wafers after various processing steps. This step takes up approximately 30% of the total fabrication time, making it as important as other major production stages. A wet station is typically composed of a transport single-arm robot and several processing tanks that are arranged in a linear topology configuration. In contrast to cluster tools whose processing modules are arranged in a radial layout, the time taken for the robot to move between tanks in a cleaning tool varies and cannot be considered identical. Under such circumstances, different assignment schemes of tanks to cleaning steps and robot access sequences to the tanks at a step can influence the performance of a wafer cleaning tool, which further complicates the scheduling problem. Our main objective of this paper was to identify the optimal arrangement of allocating tanks to processing steps and the best access route of the robot under various scenarios for maximizing the cleaning efficiency of a wet station. To achieve this goal, a Mixed Integer Programming (MIP) model based on Timed Petri Nets (TPN) was established to determine the optimal cyclic schedule along with the corresponding assignment scheme and cycle time. The practicality of the proposed model was further validated through experimental studies. Our results demonstrated that the proposed model can significantly improve the performance, reduces the average cycle time by 6.66%, and increases throughput by 7.14% compared to traditional scheduling methods. Moreover, the MIP solver obtained optimal schedules within minutes for typical wet station scales, confirming its computational efficiency and practical applicability.
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Luetao Li, Naiqi Wu, Yan Qiao, Siwei Zhang, Jie Li, Yang Bai. An Efficient Mixed Integer Programming Model for Wet Station Scheduling Problems Based on Timed Petri Nets[J]. Journal of Industrial and Management Optimization, 2026, 22(4): 1956-1980. doi: 10.3934/jimo.2026072
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