  Here we investigate the origin of the dust mass (Mdust) observed in the Milky
Way (MW) and of dust scaling relations found in a sample of local galaxies from
the DGS and KINGFISH surveys. To this aim, we model dust production from
Asymptotic Giant Branch (AGB) stars and supernovae (SNe) in simulated galaxies
forming along the assembly of a Milky Way-like halo in a well resolved cosmic
volume of 4cMpc using the GAMESH pipeline. We explore the impact of different
sets of metallicity and mass-dependent AGB and SN dust yields on the predicted
Mdust. Our results show that models accounting for grain destruction by the SN
reverse shock predict a total dust mass in the MW that is a factor of ~4 lower
than observed, and can not reproduce the observed galaxy-scale relations
between dust and stellar masses, and dust-to-gas ratios and metallicity, with a
smaller discrepancy in galaxies with low metallicity (12 + log(O/H) < 7.5) and
low stellar masses (Mstar < 10^7 Msun). In agreement with previous studies, we
suggest that competing processes in the interstellar medium must be at play to
explain the observed trends. Our result reinforces this conclusion by showing
that it holds independently of the adopted AGB and SN dust yields.
