  We discuss production of four-jet final state $pp \rightarrow j j j j X$ in
proton-proton collisions at the LHC through the mechanism of double-parton
scattering (DPS) in the context of jets with large rapidity separation. The DPS
contributions are calculated within the so-called factorized Ansatz and each
step of DPS is calculated in the LO collinear approximation. The LO pQCD
calculations are shown to give a reasonably good descritption of recent CMS and
ATLAS data on inclusive jet production and therefore this formalism can be used
to reliably estimate the DPS effects. Relative contribution of DPS is growing
at large rapidity distance between jets. This is consistent with our experience
from previous studies of double-parton scattering effects in the case of open
and hidden charm production. The calculated differential cross sections as a
function of rapidity distance between the most remote in rapidity jets are
compared with recent results of LL and NLL BFKL calculations for
Mueller-Navelet (MN) jet production at $\sqrt{s} = 7$ TeV. The DPS contribution
to widely rapidity separated jet production is carefully studied for the
present energy $\sqrt{s}$ = 7 TeV and also at the nominal LHC energy $\sqrt{s}$
= 14 TeV and in different ranges of jet transverse momenta. The differential
cross section as a function of dijet transverse momenta as well as
two-dimensional ($p_{T}(y_{min})\times p_{T}(y_{max})$)-plane correlations for
DPS mechanism are also presented. Some ideas how the DPS effects could be
studied in the case of double dijet production are suggested.
