### 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) |
---|---|

Pages (from-to) | 201-207 |

Number of pages | 7 |

Journal | Journal of Scheduling |

Volume | 4 |

Issue number | 4 |

DOIs | |

State | Published - 2001 |

### Fingerprint

### Keywords

- Approximation algorithms
- Bin packing
- Complexity

### ASJC Scopus subject areas

- Management Science and Operations Research
- Industrial and Manufacturing Engineering

### Cite this

*Journal of Scheduling*,

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

**Technical note : A note on an open-end bin packing problem.** / Leung, Joseph Y T; Dror, Moshe; Young, Gilbert H.

Research output: Contribution to journal › Article

*Journal of Scheduling*, vol. 4, no. 4, pp. 201-207. https://doi.org/10.1002/jos.75

}

TY - JOUR

T1 - Technical note

T2 - A note on an open-end bin packing problem

AU - Leung, Joseph Y T

AU - Dror, Moshe

AU - Young, Gilbert H.

PY - 2001

Y1 - 2001

N2 - 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 = (p1,p2,...,pn) of n pieces, where pj 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.

AB - 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 = (p1,p2,...,pn) of n pieces, where pj 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.

KW - Approximation algorithms

KW - Bin packing

KW - Complexity

UR - http://www.scopus.com/inward/record.url?scp=0346491951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346491951&partnerID=8YFLogxK

U2 - 10.1002/jos.75

DO - 10.1002/jos.75

M3 - Article

VL - 4

SP - 201

EP - 207

JO - Journal of Scheduling

JF - Journal of Scheduling

SN - 1094-6136

IS - 4

ER -