  For a positive integer $r$, let $f(r)$ denote the smallest number such that
any 2-edge connected mixed graph with radius $r$ has an oriented radius of at
most $f(r)$. Recently, Babu, Benson, and Rajendraprasad significantly improved
the upper bound of $f(r)$ by establishing that $f(r) \leq 1.5r^2 + r + 1$, see
[Improved bounds for the oriented radius of mixed multigraphs, J. Graph Theory,
103 (2023), 674-689]. Additionally, they demonstrated that if each edge of a
graph $G$ is contained within a cycle of length at most $\eta$, then the
oriented radius of $G$ is at most $1.5r\eta$. The authors' results were derived
through Observation 1, which served as the foundation for the development of
Algorithm ORIENTOUT and Algorithm ORIENTIN. By integrating these algorithms,
they obtained the improved bounds. However, an error has been identified in
Observation 1, necessitating revisions to Algorithm ORIENTOUT and Algorithm
ORIENTIN. In this note, we address the error and propose the necessary
modifications to both algorithms, thereby ensuring the correctness of the
conclusions.
