In its most general case the problem is stated as follows: given a set of n demand points, a space of feasible locations of a facility and a function to calculate the transportation cost between a facility and any demand point, find a location of the facility which minimizes the maximum facility-demand point transportation cost.
There are numerous particular cases of the problem, depending on the choice of the locations both of demand points and facilities, as well as the distance function.
A simple special case is when the feasible locations and demand points are in the plane with Euclidean distance as transportation cost (planar minmax Euclidean facility location problem, Euclidean 1-center problem in the plane, etc.).
Its generalization to n-dimensional Euclidean spaces is known as the smallest enclosing ball problem.
The corresponding problem of minimizing the maximum weight of a path between two selected vertices, in place of a star, is called the minimax path problem.