On the Capacitated Lot Sizing and Continuous Knapsack Polyhedra

We consider the single item capacitated lot sizing problem a well known produc tion planning model that often arises in practical applications and derive new classes of valid inequalities for it We also derive new easily computable valid inequalities for the continuous knapsack problem The continuous knapsack problem has been introduced recently and has been shown to provide a useful relaxation of mixed integer programs Finally we show that by studying an appropriate continuous knapsack relaxation of the capacitated lot sizing problem it is possible to de rive strengthenings of most of the known classes of inequalities for the capacitated lot sizing problem