“Assign” also rubs me the wrong way because it’s a needless nouning of a verb. The word is “assignment” and it’s only four letters longer.
assign
ə-sīn′
transitive verb
1. To select for a duty or office; appoint: synonym: appoint.
2. To set apart for a particular purpose or place in a particular category; designate: synonym: allocate.
3. To give out as a task; allot.