  The production of weak gauge bosons in association with heavy flavored mesons
at the LHCb conditions is considered, and a detailed study of the different
contributing processes is presented including single (SPS) and double (DPS)
parton scattering mechanisms. We find that the usual DPS factorization formula
needs to be corrected for the limited partonic phase space, and that including
the relevant corrections reduces discrepancies in the associated $ZD$
production. We conclude finally that double parton scattering dominates the
production of same-sign $W^\pm D^\pm$ states, as well as the production of
$W^-$ bosons associated with $B$-mesons. The latter processes can thus be
regarded as new useful DPS indicators.
