Uncapacitated Lot-Sizing Problems with Start-Up Costs

We consider the uncapacitated economic lot-sizing problem with start-up costs as a mixed integer program. A family of strong valid inequalities is derived for the class as well as a polynomial separation algorithm. It is then shown how equivalent, or possibly stronger, formulations are obtained by the introduction of auxiliary variables. Finally, some limited computational results for a single item model and a multi-item model with changeover costs are reported.