  The $k$-Supplier problem is an important location problem that has been
actively studied in both general and Euclidean metrics. Many of its variants
have also been studied, primarily on general metrics. We study two variants of
$k$-Supplier, namely Priority $k$-Supplier and $k$-Supplier with Outliers, in
Euclidean metrics. We obtain $(1+\sqrt{3})$-approximation algorithms for both
variants, which are the first improvements over the previously-known factor-$3$
approximation (that is known to be best-possible for general metrics). We also
study the Matroid Supplier problem on Euclidean metrics, and show that it
cannot be approximated to a factor better than $3$ (assuming $P\ne NP$); so the
Euclidean metric offers no improvement in this case.
