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Preventive maintenance (PM) scheduling is a very challenging task in semiconductor manufacturing due to the complexity of highly integrated fab tools and systems, the interdependence between PM tasks, and the balancing of work-in-process (WIP) with demand/throughput requirements. In this paper, we propose a two-level hierarchical modeling framework. At the higher level is a model for long-term planning, and at the lower level is a model for short-term PM scheduling. Solving the lower level problem is the focus of this paper. We develop mixed-integer programming (MIP) models for scheduling all due PM tasks for a group of tools, over a planning horizon. Interdependence among different PM tasks, production planning data such as projected WIP levels, manpower constraints, and associated PM time windows and costs, are incorporated in the model. Results of a simulation study comparing the performance of the model-based PM schedule with that of a baseline reference schedule are also presented.