### Abstract

Let a_{1}, …, a_{n} be a given collection of items with sizes s (a_{i}) > 0, 1 ≤ i ≤ n. In mathematical terms, bin packing is a problem of partitioning the set {a_{i}} under a sum constraint: Divide {a_{i}} into a minimum number of blocks, called bins, such that the sum of the sizes of the items in each bin is at most a given capacity C > 0. To avoid trivialities, it is assumed that all item sizes fall in (0, C]. Research into bin packing and its many variants, which began some 35 years ago [1,2], continues to be driven by a countless variety of applications in the engineering and information sciences. The following examples give an idea of the scope of the applications: • (Stock cutting) Lumber with a fixed cross section comes in a standard board C units in length. The items are demands for pieces that must be cut from such boards. The objective is to minimize the number of boards (bins) used for the pieces {a_{i}}, or equivalently, to minimize the trim loss or waste (the total board length used minus the sum of the s (a_{i})). It is easy to see that this type of application extends to industries that supply cable, tubing, cord, tape, and so on from standard lengths.

Original language | English |
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Title of host publication | Handbook of Approximation Algorithms and Metaheuristics |

Publisher | CRC Press |

Pages | 32-1-32-18 |

ISBN (Electronic) | 9781420010749 |

ISBN (Print) | 1584885505, 9781584885504 |

DOIs | |

Publication status | Published - jan. 1 2007 |

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*Handbook of Approximation Algorithms and Metaheuristics*(pp. 32-1-32-18). CRC Press. https://doi.org/10.1201/9781420010749