Given n item types, each having an associated profit and weight, and a container of given capacity, the unbounded knapsack problem is to determine the number of items of each type to be selected so that the corresponding total profit is a maximum and the corresponding total weight does not exceed the capacity. The authors present upper bounds, dominance relations, and an approach-based on the definition of a core problem-to the exact solution of very large instances of the problem. They give the results of computational experiments on randomly generated test problems involving up to 250000 item types.
