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A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems

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  • Sándor P. Fekete

  • Jörg Schepers

Abstract

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is of crucial importance to have good and easy bounds for an optimal solution. Previous efforts have produced a number of special classes of such bounds. Unfortunately, some of these bounds are somewhat complicated and hard to generalize. We present a new approach for obtaining classes of lower bounds for higher-dimensional packing problems; our bounds improve and simplify several well-known bounds from previous literature. In addition, our approach provides an easy framework for proving correctness of new bounds. This is the second in a series of four articles describing new approaches to higher-dimensional packing. Copyright Springer-Verlag 2004

Suggested Citation

  • Sándor P. Fekete & Jörg Schepers, 2004. "A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 311-329, October.
    • Handle: RePEc:spr:mathme:v:60:y:2004:i:2:p:311-329
    DOI: 10.1007/s001860400376
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