  In the article, we study associated production of prompt $J/\psi(\Upsilon)$
and $D-$mesons in the improved color evaporation model using the high-energy
factorization approach as it is realized in the Monte-Carlo event generator
KaTie. The modified Kimber-Martin-Ryskin-Watt model for unintegrated parton
distribution functions is used. We predict cross sections for associated
$J/\psi(\Upsilon)$ and $D-$meson hadroproduction via the single and double
parton scattering mechanisms using the set of model parameters which has been
fixed early for description of prompt single and pair heavy quarkonium
production at the LHC energies. We found the results of calculations agree with
the LHCb Collaboration data at the energies $\sqrt{s} = 7,8$ TeV and we present
theoretical predictions for the energy $\sqrt{s} = 13$ TeV .
