A polyhedral study of lot-sizing with supplier selection

The traditional lot-sizing problem is to find the least cost production lot-sizes in several time periods. We consider the lot-sizing model together with simultaneous selection of suppliers, which have variable and fixed costs. We study the underlying polytope. We provide valid inequalities for the uncapacitated case and we give sufficient and necessary conditions for facet-defining inequalities. We also give a full description of the underlying polyhedron. For the general capacitated case, we show how to derive several families of valid inequalities from standard lot-sizing valid inequalities.