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The invention of microfluidic lab-on-a-chip alleviates the burden of traditional biochemical laboratory procedures which are often very expensive. Device miniaturization and increasing design complexity have mandated a shift in digital microfluidic lab-on-a-chip design from traditional manual design to computer-aided design (CAD) methodologies. As an important procedure in the lab-on-a-chip layout CAD, the lab-on-a-chip component placement determines the physical location and the starting time of each operation such that the overall completion time is minimized while satisfying nonoverlapping constraint, resource constraint, and scheduling constraint. In this paper, a multiscale variation-aware optimization technique based on integer linear programming is proposed for the lab-on-a-chip component placement. The simulation results demonstrate that without considering variations, our technique always satisfies the design constraints and largely outperforms the state-of-the-art approach, with up to 65.9% reduction in completion time. When considering variations, the variation-unaware design has the average yield of 2%, while our variation-aware technique always satisfies the yield constraint with only 7.7% completion time increase.