Performance guarantees for one-dimensional bin packing

Edward G. Coffman, J. Csirik

Research output: Chapter

25 Citations (Scopus)

Abstract

Let a1, …, an be a given collection of items with sizes s (ai) > 0, 1 ≤ i ≤ n. In mathematical terms, bin packing is a problem of partitioning the set {ai} under a sum constraint: Divide {ai} 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 {ai}, or equivalently, to minimize the trim loss or waste (the total board length used minus the sum of the s (ai)). 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 languageEnglish
Title of host publicationHandbook of Approximation Algorithms and Metaheuristics
PublisherCRC Press
Pages32-1-32-18
ISBN (Electronic)9781420010749
ISBN (Print)1584885505, 9781584885504
DOIs
Publication statusPublished - jan. 1 2007

ASJC Scopus subject areas

  • Computer Science(all)

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    Coffman, E. G., & Csirik, J. (2007). Performance guarantees for one-dimensional bin packing. In Handbook of Approximation Algorithms and Metaheuristics (pp. 32-1-32-18). CRC Press. https://doi.org/10.1201/9781420010749