A unifying location model on tree graphs based on submodularity properties

Let F be the collection of nonempty subtrees of a given tree T. Each subtree is viewed as a potential facility. Let f{hook} be a real objective function defined on F. The facility location model we consider is to select a subtree minimizing f. This model unifies and generalizes several facility location problems discussed in the literature. We prove that the most common objective functions used in facility location theory possess the submodularity property. In particular, the ellipsoid approach provides a unified framework for polynomial solvability.