In the assignment problem, one tries to find $f$ such that the cost function $$ \sum_{a\in A} C(a,f(a)) $$ is minimized. Here $f$ is a bijection between sets $A$ and $B$ of equal finite cardinality, and $C$ is a cost function $A\times B \to \mathbb R$.
My question: is there a name for the problem to minimize $$ \max_{a\in A} \, C(a,f(a)) $$ over bijections $f$ as above?
Thanks in advance for any replies or references.