  In this work, we address the problem of longitudinal spin polarization of the
$\Lambda$ hyperons produced in relativistic heavy-ion collisions. We combine a
relativistic kinetic-theory framework that includes spin degrees of freedom
treated in a classical way with the freeze-out parametrization used in previous
investigations. The use of the kinetic theory allows us to incorporate
dissipative corrections (due to the thermal shear and gradients of thermal
vorticity) into the Pauli-Lubanski vector that determines spin polarization and
can be directly compared with the experimental data. As in earlier similar
studies, it turns out that a successful description of data can only be
achieved with additional assumptions -- in our case, they involve the use of
projected thermal vorticity and a suitably adjusted time for spin relaxation
($\tau_s$). From our analysis, we find that $\tau_s \sim 5$ fm/$c$, which is
comparable with other estimates.
