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Dual-Feasible Functions for Integer Programming and Combinatorial Optimization pp 91–123Cite as

Applications for Cutting and Packing Problems

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Part of the book series: EURO Advanced Tutorials on Operational Research ((EUROATOR))

Abstract

Dual-feasible functions have been designed specifically for the cutting-stock problem. As shown in Chap. 1, they arise naturally from the dual of the classical formulation of Gilmore and Gomory for this problem. Since many problems can be modeled using a similar formulation, it makes sense to explore the concept of dual-feasible function within a more general class of applications. A first approach is to considermulti-dimensional dual-feasible functions,which can be used to derive lower bounds for the vector packing problem. Here, we also consider different packing problems with more complicated subproblems such as multi-dimensional orthogonal packing and packing with conflicts. Dual-feasible functions can still be derived in these cases.

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Authors and Affiliations

  1. Department of Production and Systems, University of Minho, Braga, Portugal

    Cláudio Alves & José Valério de Carvalho

  2. Institut de Mathématiques de Bordeaux, University of Bordeaux, Talence, France

    François Clautiaux

  3. Centro Algoritmi, University of Minho, Braga, Portugal

    Jürgen Rietz

Authors
  1. Cláudio Alves
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  2. François Clautiaux
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  3. José Valério de Carvalho
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  4. Jürgen Rietz
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Alves, C., Clautiaux, F., de Carvalho, J.V., Rietz, J. (2016). Applications for Cutting and Packing Problems. In: Dual-Feasible Functions for Integer Programming and Combinatorial Optimization. EURO Advanced Tutorials on Operational Research. Springer, Cham. https://doi.org/10.1007/978-3-319-27604-5_4

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