Dynamic Knapsack Sets and Capacitated Lot-Sizing.

A dynamic knapsack set is a natural generalization of the 0-1 knapsack set with a continuous variable studied recently.For dynamic knapsack sets a large family of facet-defining inequalities, called dynamic knapsack inequalities, are derived by fixing variables to one and then lifting. Surprisingly such inequalities have the simultaneous lifting property, and for small instances provide a significant proportion of all the facet-defining inequalities.