GREEDY ALGORITHMS FOR PACKING UNEQUAL SPHERES INTO A CUBOIDAL STRIP OR A CUBOID

Timo Kubach, Andreas Bortfeldt (), Thomas Tilli and Hermann Gehring
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Timo Kubach: Department of Information Systems, University of Hagen, Germany; Profilstrasse 8, 58084 Hagen, Germany
Andreas Bortfeldt: Department of Information Systems, University of Hagen, Germany; Profilstrasse 8, 58084 Hagen, Germany
Thomas Tilli: Department of Information Systems, University of Hagen, Germany; Profilstrasse 8, 58084 Hagen, Germany
Hermann Gehring: Department of Information Systems, University of Hagen, Germany; Profilstrasse 8, 58084 Hagen, Germany

Asia-Pacific Journal of Operational Research (APJOR), 2011, vol. 28, issue 06, pages 739-753

Abstract: Given a finite set of spheres of different sizes, we study the three-dimensional Strip Packing Problem (3D-SPP) as well as the three-dimensional Knapsack Problem (3D-KP). The 3D-SPP asks for a placement of all spheres within a cuboidal strip of fixed width and height so that the variable length of the cuboidal strip is minimized. The 3D-KP requires packing of a subset of the spheres in a given cuboid so that the wasted space is minimized. To solve these problems two greedy algorithms were developed which adapt the algorithms proposed by Huang et al. (2005) to the 3D case with some important enhancements. The resulting methods were tested using the instances provided by Stoyan et al. (2003). Additionally, two series of 12 instances each for the 3D-SPP and for the 3D-KP are introduced and results for these new instances are also reported.

Keywords: Packing; spheres; strip packing problem; knapsack problem; greedy method (search for similar items in EconPapers)
Date: 2011
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