Sample preparation is an essential step in almost all bioprotocols, which can be efficiently achieved via a sequence of mixing steps called mixing graph. In the literature, several techniques have been reported to determine a mixing graph with the minimal number of mixing steps, the minimal usage of reagent fluids, the minimal wastage, or sometimes a combination of them. The retention time of a flow-based microfluidic biochip (FMB) is defined as the maximum duration for which a fluid can be stored within a microchannel without any fluid leakage. However, the retention time has not yet been considered as a scheduling constraint during the automation of the sample preparation using an FMB in order to obtain the scheduled mixing graphs. In this article, we propose a retention time-aware scheduling method called time-aware list scheduling (TALS), which can be used with the state-of-the-art methods, and a new satisfiability-based mixing algorithm called time-aware sample preparation (TASP) to obtain the scheduled mixing graph for a target ratio satisfying the retention time constraint and the number of available on-chip mixers in an FMB. Simulation results suggest that on an average TALS always outperforms a baseline scheduling method while scheduling any mixing graph, whereas TASP can determine the optimal and scheduled mixing graphs compared to the existing mixing methods combined with TALS.