Here, we describe the exact formulation of Twyman et al.'s problem-and its efficient computational implementation -as a linear optimization. We demonstrate that the exact formulation is of comparable computation cost and can be implemented in fewer lines of Python code. Furthermore, we show that the errors introduced by using a greedy algorithm can be large and result in qualitative differences in oxidation products. Using this approach, we recompute exact versions of key results of Twyman et al.'s paper and note differences. We also discuss how this strategy can be generalized to consider free energy minimization. ) which can be used to evaluate vacuum stability.