Assignment problem with sum replaced by max 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.
In the geometric setting, where $C(x,y) = \|x - y \|$, this formulation is called the bottleneck matching problem. It's possible that this is the generic term for it (I've seen this formulation used in the Kleinberg-Tardos algorithms book for MSTs).