This is a Binary Integer Linear Problem.
The goal is to minimize the number of supply locations needed to cover a set of demand locations. The time it takes to get from a demand location to a supply location cannot exceed r.
Let i ? I be the set of demand locations, and j ? J be the set of potential supply locations which can potentially cover i ? I. Let tij be the travel time between i ? I and j ? J, and r be the maximal time allowed for travel between i and j. Each i ? I is covered only if and only if tij = r. In this problem, i ? I must be covered by at least one j ? J.
Define the objective function and constraints of this problem.