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It is very challenging to schedule time-constrained cluster tools subject to activity time variation. This work adopts our previously developed real-time control policy to offset the activity time variation in single-arm cluster tools. Then it derives analytical schedulability conditions and efficient scheduling algorithms for the first time. The resultant schedule executed together with the real-time control policy forms a real-time schedule. It is proven optimal in terms of cycle time. A semiconductor wafer production example is used to illustrate the research results.

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