# bin packing problem

(classic problem)

**Definition:**
Determine how to put the most objects in the least number of fixed space bins. More formally, find a *partition* and assignment of a *set* of objects such that a constraint is satisfied or an *objective function* is minimized (or maximized). There are many variants, such as, 3D, 2D, linear, pack by volume, pack by weight, minimize volume, maximize value, fixed shape objects, etc.

**See also**
*knapsack problem*, *cutting stock problem*, *optimization problem*, *strip packing*, *set packing*.

*Note:
A common form of the problem is, what is the least number of bins (containers of fixed volume) needed to hold a set of objects. This problem often appears in manufacturing. For instance, suppose we need a number of pipes of different, specific lengths to plumb a house and we can buy pipe stock in 5 meter lengths. How can we cut the 5-meter pipes to waste as little as possible (minimize the cost of pipe)? *

*
** Thanks to Frank A. Adrian <fadrian@symantec.com>, 28 January 2000.*

Author: PEB

## Implementation

(Icon).
## More information

Limits and references. Suggestions on books and related topics.

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

Entry modified 2 November 2020.

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Cite this as:

Paul E. Black, "bin packing problem", in
*Dictionary of Algorithms and Data Structures* [online], Paul E. Black, ed. 2 November 2020. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/binpacking.html