  In this article, we present a Next-to-Leading Order (NLO) QCD analysis to
study the role and influence of different schemes on simultaneous determination
of the Parton Distribution Functions (PDFs) and strong coupling,
$\alpha_s(M^2_Z)$. We perform our analysis based on three different data sets,
HERA I and II combined data, H1-ZEUS charm combined data, and H1 and ZEUS
beauty production cross sections data, in two different Thorne-Roberts (TR or
RT) and Thorne-Roberts Optimal (RT OPT) schemes. We show in going from RT
scheme to RT OPT scheme, in addition of reduction the uncertainty of some PDFs,
specially for the gluon distribution, we get $\sim 0.4$~\% and $\sim
0.7$~\%~improvement in the fit quality and $\sim 0.9$~\% and $\sim
1.6$~\%~improvement for the strong coupling, $\alpha_s(M^2_Z)$, without and
with heavy flavor contributions, respectively.
