  We investigate the contribution of inelastic and elastic processes to single
inclusive hadron production in proton-proton and proton (deuteron)-nucleus
collisions at RHIC and the LHC. Using the hybrid formulation which includes
both elastic and inelastic contributions, supplemented with the
running-coupling Balitsky-Kovchegov equation, we get a good description of RHIC
data. It is shown that inclusion of the inelastic terms makes the transverse
momentum dependence of the production cross section steeper in the mid-rapidity
region but does not affect the cross section in the very forward region. The
inelastic processes also lead to a sharper increase of the nuclear modification
factor R_{pA} with increasing p_T. We also make predictions for the nuclear
modification factor in proton-nucleus collisions at the LHC (\sqrt{s}=4.4 and
8.8 TeV) at various rapidities using the Color Glass Condensate framework.
