# The school location problem

I’ve spent a few days thinking about a facility location problem that we might call the *school location problem.* The goal is to place \(n\) schools to serve \(m\) families, such that the *furthest* distance between any family and their *nearest* school is *minimized.* This problem is almost a \(k\)-means or ellipsoid fitting problem, but its unusual “minimin” form makes it computationally challenging.

In the video below, and associated Jupyter notebook (Github, HTML viewer), I discuss the formulation of this problem, show to express it as a mixed-integer second-order convex program, and then solve a small instance using the Julia/JuMP/Juniper/SCS stack.