  Given a set $S$ of $m$ point sites in a simple polygon $P$ of $n$ vertices,
we consider the problem of computing the geodesic farthest-point Voronoi
diagram for $S$ in $P$. It is known that the problem has an $\Omega(n+m\log m)$
time lower bound. Previously, a randomized algorithm was proposed [Barba, SoCG
2019] that can solve the problem in $O(n+m\log m)$ expected time. The previous
best deterministic algorithms solve the problem in $O(n\log \log n+ m\log m)$
time [Oh, Barba, and Ahn, SoCG 2016] or in $O(n+m\log m+m\log^2 n)$ time [Oh
and Ahn, SoCG 2017]. In this paper, we present a deterministic algorithm of
$O(n+m\log m)$ time, which is optimal. This answers an open question posed by
Mitchell in the Handbook of Computational Geometry two decades ago.
