  For a given digraph $D$ and distinct $u,v \in V(D)$, we denote by
$\lambda_D(u,v)$ the local arc-connectivity from $u$ to $v$. Further, we define
the total arc-connectivity $tac(D)$ of $D$ to be $\sum_{\{u,v\}\subseteq
V(D)}\lambda_D(u,v)+\lambda_D(v,u)$. We show that, given a graph $G$ and an
integer $k$, it is NP-complete to decide whether $G$ has an orientation
$\vec{G}$ satisfying $tac(\vec{G})\geq k$. This answers a question of Pekec. On
the positive side, we show that the corresponding maximization problem admits a
$\frac{2}{3}$-approximation algorithm.
