  A water company decides to expand its network with a set of water lines, but
it cannot build them all at once. However, it starts reaping benefits from a
partial expansion. In what order should the company build the lines? We
formalize a class of permutatorial problems with combinatorial/continuous
subproblems capturing applications of incremental deployment. We show that, for
additive/linear objective functions, efficient polyhedral methods for the
subproblems extend to the permutatorial problem. Our main technical ingredient
is the permutahedron.
