  A semi-proper orientation of a given graph $G$, denoted by $(D,w)$, is an
orientation $D$ with a weight function $w: A(D)\rightarrow \mathbb{Z}_+$, such
that the in-weight of any adjacent vertices are distinct, where the in-weight
of $v$ in $D$, denoted by $w^-_D(v)$, is the sum of the weights of arcs towards
$v$. The semi-proper orientation number of a graph $G$, denoted by
$\overrightarrow{\chi}_s(G)$, is the minimum of maximum in-weight of $v$ in $D$
over all semi-proper orientation $(D,w)$ of $G$. This parameter was first
introduced by Dehghan (2019). When the weights of all edges eqaul to one, this
parameter is equal to the proper orientation number of $G$. The optimal
semi-proper orientation is a semi-proper orientation $(D,w)$ such that
$\max_{v\in V(G)}w_D^-(v)=\overrightarrow{\chi}_s(G)$.
  Ara\'ujo et al. (2016) showed that $\overrightarrow{\chi}(G)\le 7$ for every
cactus $G$ and the bound is tight. We prove that for every cactus $G$,
$\overrightarrow{\chi}_s(G) \le 3$ and the bound is tight. Ara\'{u}jo et al.
(2015) asked whether there is a constant $c$ such that
$\overrightarrow{\chi}(G)\le c$ for all outerplanar graphs $G.$ While this
problem remains open, we consider it in the weighted case. We prove that for
every outerplanar graph $G,$ $\overrightarrow{\chi}_s(G)\le 4$ and the bound is
tight.
