  Lattice polyhedra $Q_1$ and $Q_2$ with the same tail cone are said to be
normally located if every lattice point in the Minkowski sum $Q_1+Q_2$ is the
sum of lattice points from $Q_1$ and $Q_2$, respectively. We prove that if the
normal fan of $Q_1$ refines the normal fan of $Q_2$, then there is a positive
integer $k$ such that for any positive integer $s$ the polyhedra $skQ_1$ and
$skQ_2$ are normally located. This result is based on an interpretation of the
problem in terms of graded algebras and earlier results on surjectivity of the
multiplicaiton map on homogeneous components. Also we provide an example of two
lattice triangles $P$ and $Q$ on the plane such that for any positive integer
$k$ the triangles $kP$ and $kQ$ are not normally located.
