We present the application of the ACOT and S-ACOT general mass variable flavor number schemes to proton-proton collisions with particular attention to the production of final states with at least one heavy quark. \textit{Subtraction} and \textit{residual} heavy-quark parton distribution functions are introduced to facilitate the implementation of this scheme at higher orders in perturbative QCD. The calculation of $Z$-boson hadronic production with at least one $b$ jet beyond the lowest order in QCD is considered for illustration purposes.