Permutatorial Optimization via the Permutahedron

Abstract: 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.