  The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum
cardinality of a set $S$ of black vertices (whereas vertices in $V(G)-S$ are
colored white) such that $V(G)$ is turned black after finitely many
applications of "the color-change rule": a white vertex is converted black if
it is the only white neighbor of a black vertex. The \emph{strong metric
dimension}, $sdim(G)$, of a graph $G$ is the minimum among cardinalities of all
strong resolving sets: $W \subseteq V(G)$ is a \emph{strong resolving set} of
$G$ if for any $u, v \in V(G)$, there exists an $x \in W$ such that either $u$
lies on an $x-v$ geodesic or $v$ lies on an $x-u$ geodesic. In this paper, we
prove that $Z(G) \le sdim(G)+3r(G)$ for a connected graph $G$, where $r(G)$ is
the cycle rank of $G$. Further, we prove the sharp bound $Z(G) \leq sdim(G)$
when $G$ is a tree or a unicyclic graph, and we characterize trees $T$
attaining $Z(T)=sdim(T)$. It is easy to see that $sdim(T+e)-sdim(T)$ can be
arbitrarily large for a tree $T$; we prove that $sdim(T+e) \ge sdim(T)-2$ and
show that the bound is sharp.
