  A {\it semi-proper orientation} of a given graph $G$ is a function $(D,w)$
that assigns an orientation $D(e)$ and a positive integer weight $ w(e)$ to
each edge $e$ such that for every two adjacent vertices $v$ and $u$,
$S_{(D,w)}(v) \neq S_{(D,w)}(u) $, where $S_{(D,w)}(v) $ is the sum of the
weights of edges with head $v$ in $D$. The {\it semi-proper orientation number}
of a graph $G$, denoted by $\overrightarrow{\chi}_s (G)$, is $ \min_{(D,w)\in
\Gamma} \max_{v\in V(G)} S_{(D,w)}(v) $, where $\Gamma$ is the set of all
semi-proper orientations of $G$. The {\it optimal semi-proper orientation} is a
semi-proper orientation $(D,w)$ such that $ \max_{v\in V(G)} S_{(D,w)}(v)=
\overrightarrow{\chi}_s (G) $. In this work, we show that every graph $G$ has
an optimal semi-proper orientation $(D,w)$ such that the weight of each edge is
one or two. Next, we show that determining whether a given planar graph $G$
with $\overrightarrow{\chi}_s (G)=2 $ has an optimal semi-proper orientation
$(D,w)$ such that the weight of each edge is one is NP-complete. Finally, we
prove that the problem of determining the semi-proper orientation number of
planar bipartite graphs is NP-hard.
