  We formulate the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution
of the Deep Inelastic Scattering (DIS) structure functions $F_2$ and $F_{\rm
L}$ at next to leading order in $\alpha_s$ (NLO) directly in terms of the
structure functions rather than parton distributions (PDFs). We call this the
physical basis approach. In practice, we first express the NLO quark singlet
and gluon PDFs in terms of the structure functions $F_2$ and $F_{\rm L}$ in
momentum space. Employing these expressions in the DGLAP evolution, we arrive
at the evolution equations for $F_2$ and $F_{\rm L}$ in the physical basis. We
demonstrate how one is free from defining a factorization scale and scheme when
using the physical basis evolution equations. We also discuss the process of
applying the NLO physical basis to global analysis of LHC cross sections.
