  Within the framework of a multiphase transport model (AMPT), the $\phi$-meson
production is studied in d+Au collisions at \srt = {200} GeV in the forward
(d-going, $1.2<y<2.2$) and backward (Au-going, $-2.2<y<-1.2$) direction. The
AMPT model with string melting version (parton cascade turning-on) describes
the experimental data well, while the pure hadronic transport scenario of the
AMPT model underestimates the $\phi$-meson production rate in comparison with
the data. Detailed investigations including the rapidity, transverse momentum
and collision system size dependencies of $\phi$-meson nuclear modification
factor indicate that a combination of the initial state effect and a follow-up
parton cascade is required in the AMPT model to describe the data. Similar
calculations are also present in p+Pb collisions at \srt = {5.02} TeV and p+p
collisions at \srt = {2.76} TeV. The findings from a comparison of AMPT model
study with the data are consistent with that at RHIC energy.
