  This paper is devoted to Wiener index of directed graphs, more precisely of
directed grids. The grid $G_{m,n}$ is the Cartesian product $P_m\Box P_n$ of
paths on $m$ and $n$ vertices, and in a particular case when $m=2$, it is a
called the ladder graph $L_n$. Kraner \v{S}umenjak et al. proved that the
maximum Wiener index of a digraph, which is obtained by orienting the edges of
$L_n$, is obtained when all layers isomorphic to one factor are directed paths
directed in the same way except one (corresponding to an endvertex of the other
factor) which is a directed path directed in the opposite way. Then they
conjectured that the natural generalization of this orientation to $G_{m,n}$
will attain the maximum Wiener index among all orientations of $G_{m,n}$. In
this paper we disprove the conjecture by showing that a comb-like orientation
of $G_{m,n}$ has significiantly bigger Wiener index.
