  The Goldberg-Seymour Conjecture for $f$-colorings states that the
$f$-chromatic index of a loopless multigraph is essentially determined by
either a maximum degree or a maximum density parameter. We introduce an
oriented version of $f$-colorings, where now each color class of the
edge-coloring is required to be orientable in such a way that every vertex $v$
has indegree and outdegree at most some specified values $g(v)$ and $h(v)$. We
prove that the associated $(g,h)$-oriented chromatic index satisfies a
Goldberg-Seymour formula. We then present simple applications of this result to
variations of $f$-colorings. In particular, we show that the Linear Arboricity
Conjecture holds for $k$-degenerate loopless multigraphs when the maximum
degree is at least $4k-2$, improving a bound recently announced by Chen, Hao,
and Yu for simple graphs. Finally, we demonstrate that the $(g,h)$-oriented
chromatic index is always equal to its list coloring analogue.
