Sample preparation is an essential step in biochemical reactions. Reactants must be diluted to achieve given target concentrations in sample preparation. Since some reactants like costly reagents and infant's blood are valuable, their usage should be minimized during dilution. In this paper, we propose an optimal reactant minimization algorithm, GORMA, for sample preparation on digital microfluidic biochips. GORMA adopts a systematic method to exhaustively check all possible dilution solutions and then identifies the one with minimal reactant usage and waste through maximal droplet sharing. Experimental results show that GORMA outperforms all the existing methods in reactant usage. Meanwhile, the waste amount is reduced up to 30% as compared with existing waste minimization methods. Moreover, GORMA requires only 0.6% more operations on average when compared with an operation-minimal dilution method.