In mathematics, the quadratic bottleneck assignment problem (QBAP) is one of fundamental combinatorial optimization

Combinatorial optimization

In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects. In many such problems, exhaustive search is not feasible...

 problems in the branch of optimization

Optimization (mathematics)

In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....

 or operations research

Operations research

Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...

, from the category of the facilities location problems.

It is related to the quadratic assignment problem

Quadratic assignment problem

The quadratic assignment problem is one of fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facilities location problems....

 in the same way as the linear bottleneck assignment problem

Linear bottleneck assignment problem

In combinatorial optimization, a field within mathematics, the linear bottleneck assignment problem is similar to the linear assignment problem. In plain words the problem is stated as follows:...

 is related to the linear assignment problem, the "sum" is replaced with "max" in the objective function.

The problem models the following real-life problem:

There are a set of n facilities and a set of n locations. For each pair of locations, a distance is specified and for each pair of facilities a weight or flow is specified (e.g., the amount of supplies transported between the two facilities). The problem is to assign all facilities to different locations with the goal of minimizing the maximum of the distances multiplied by the corresponding flows.