Which algorithm to use for a very simple ranking problem?

Currently, I have a dataset with 10 features that results in a ranking of 4 items, i.e. [1,2,3,4], [4,3,1,2], [3,2,4,1] or any $4!$ permutations that can arise from the ranking.

What algorithms are there to train a model for this? Making it a categorical variable with 24 items seems like a silly way to do this. Another silly way seems to be to transform the data into something like

$x_1$, $item_1$, 4
$x_1$, $item_2$, 3
$x_1$, $item_3$, 1
$x_1$, $item_4$, 2
$x_2$, $item_1$, 1
$\cdots$

and solve it as a regression problem, but that seems silly, since it's not including the semantics of ranking, and because ranking is a discrete function.

I don't need a hefty algorithm, maybe something simple on the level of logistic regression, but unsure what algorithm suits the purpose.