# The Facilities Location Problem

The Facilities Location Problem

The facilities location problem (also known as the -median problem), in its continuous version, starts with a shape in the plane and seeks to locate hosts so as to minimize the average travel distance if each point goes to the nearest host. This is more familiar in the discrete version, where one has points in the plane and wants to select of them as hosts so as to minimize the total travel distance. When , this is known as the Fermat–Weber problem. In this Demonstration, a discrete version based on a number of points inside the polygon is solved by integer-linear programming (ILP) and the Voronoi diagram of the computed hosts is shown. Such a discrete problem is an approximation to the continuous problem.

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k=1