### Abstract

We consider a variant of the classical one-dimensional bin packing problem, which we call the open-end bin packing problem. Suppose that we are given a list L = (p_{1},p_{2},...,p_{n}) of n pieces, where p_{j} denotes both the name and the size of the jth piece in L, and an infinite collection of infinite-capacity bins. A bin can always accommodate a piece if the bin has not yet reached a level of C or above, but it will be closed as soon as it reaches that level. Our goal is to find a packing that uses the minimum number of bins. In this article, we first show that the open-end bin packing problem remains strongly NP-hard. We then show that any online algorithm must have an asymptotic worst-case ratio of at least 2, and there is a simple online algorithm with exactly this ratio. Finally, we give an offline algorithm that is a folly polynomial approximation scheme with respect to the asymptotic worst-case ratio.

Original language | English (US) |
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Pages (from-to) | 201-207 |

Number of pages | 7 |

Journal | Journal of Scheduling |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2001 |

### Keywords

- Approximation algorithms
- Bin packing
- Complexity

### ASJC Scopus subject areas

- Software
- Engineering(all)
- Management Science and Operations Research
- Artificial Intelligence

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## Cite this

*Journal of Scheduling*,

*4*(4), 201-207. https://doi.org/10.1002/jos.75