  Data on $W + D$-meson and $W + c$-jet hadroproduction have recently started
to be included in at least some of the parton distribution function fits,
mainly because of their potential to constrain the strange quark content of the
proton. In this contribution we present predictions for $W + D$-meson and $W +
c$-jet production with NLO QCD accuracy matched to parton shower. We show how
including the latter effects, as well as hadronization, beam remnant and
multiple parton interaction effects present in Shower Monte Carlo codes, is
fundamental to provide consistent comparisons with the current experimental
data by the ATLAS and CMS collaborations, as required for non-biased
extractions of the strange and antistrange quark PDFs.
