  We study the interplay of interactions and disorder in a one-dimensional
fermion lattice coupled adiabatically to infinite reservoirs. We employ both
the functional renormalization group (FRG) as well as matrix product state
techniques, which serve as an accurate benchmark for small systems. Using the
FRG, we compute the length- and temperature-dependence of the conductance
averaged over $10^4$ samples for lattices as large as $10^{5}$ sites. We
identify regimes in which non-ohmic power law behavior can be observed and
demonstrate that the corresponding exponents can be understood by adapting
earlier predictions obtained perturbatively for disordered Luttinger liquids.
In presence of both disorder and isolated impurities, the conductance has a
universal single-parameter scaling form. This lays the groundwork for an
application of the functional renormalization group to the realm of many-body
localization.
