unbounded knapsack problem

(classic problem)

Definition: Given types of items of different values and volumes, find the most valuable set of items that fit in a knapsack of fixed volume. The number of items of each type is unbounded. This is an NP-hard combinatorial optimization problem.

Formal Definition: There is a knapsack of capacity c > 0 and N types of items. Each item of type t has value v_t > 0 and weight w_t > 0. Find the number n_t > 0 of each type of item such that they fit, ∑_t=1^N n_tw_t ≤ c, and the total value, ∑_t=1^N n_tv_t, is maximized.

Also known as UKP.

See also knapsack problem, fractional knapsack problem.

Author: PEB

More information

demonstration solutions using dynamic programming. formal definition and links to papers. Links to many papers.

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified 28 February 2011.
HTML page formatted Tue Dec 6 16:16:33 2011.

Cite this as:
Paul E. Black, "unbounded knapsack problem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 28 February 2011. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/unboundedKnapsack.html