The Minimum Size Instance of a Pallet Loading Problem Equivalence Class

Abstract

The Pallet Loading Problem (PLP) maximizes the number of identical rectangular boxes placed within a rectangular pallet. Boxes may be rotated 90 deg so long as they are packed with edges parallel to the pallet's edges, i.e., in an orthogonal packing. This paper defines the Minimum Size Instance (MSI) of an equivalence class of PLP, and shows that every class has one and only one MSI. We develop bounds on the dimensions of box and pallet for the MSI of any class. Applying our new bounds on MSI dimensions, we present an algorithm for MSI generation and use it to enumerate all 3,080,730 equivalence classes with an area ratio (pallet area divided by box area) smaller than 101 boxes. Previous work only provides bounds on the ratio of box dimensions and only considers a subset of all classes presented here.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2007
Accession Number
ADA520439

Entities

People

  • Gustavo H. Martins
  • Robert F. Dell

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  • Materials and Manufacturing Processes

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  • Algorithms
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  • Computer science

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