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Exact Solution of Combined Cutting Stock and Scheduling Problems

In: Computational Management Science

Author

Listed:
  • Nuno Braga

    (Universidade do Minho)

  • Cláudio Alves

    (Universidade do Minho)

  • José Valério de Carvalho

    (Universidade do Minho)

Abstract

The combination of cutting and packing with scheduling has been addressed recently by various authors considering both one- and two-dimensional instances. These problems consist essentially in finding the cutting plan that minimizes a function of the wastage and tardiness related to the items delivery given a set of due dates (and possibly release dates). As shown by other authors, some of these models may not be exact due to the definition of the time periods on which they rely. In this paper, we explore an exact and compact assignment formulation for the combined cutting stock and scheduling. The model is general in the sense that it applies to instances with any level of demand per item. To strengthen the model, we resort to knapsack-based inequalities derived using dual-feasible functions. Up to now, these functions have been used mainly to derive lower bounds for cutting and packing problems. Different computational experiments performed on benchmark instances illustrate their potential as an effective cutting plane tool.

Suggested Citation

  • Nuno Braga & Cláudio Alves & José Valério de Carvalho, 2016. "Exact Solution of Combined Cutting Stock and Scheduling Problems," Lecture Notes in Economics and Mathematical Systems, in: Raquel J. Fonseca & Gerhard-Wilhelm Weber & João Telhada (ed.), Computational Management Science, edition 1, pages 131-139, Springer.
    • Handle: RePEc:spr:lnechp:978-3-319-20430-7_17
    DOI: 10.1007/978-3-319-20430-7_17
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    Cited by:

    1. de Lima, Vinícius L. & Alves, Cláudio & Clautiaux, François & Iori, Manuel & Valério de Carvalho, José M., 2022. "Arc flow formulations based on dynamic programming: Theoretical foundations and applications," European Journal of Operational Research, Elsevier, vol. 296(1), pages 3-21.
    2. Kennedy A. G. Araújo & Tibérius O. Bonates & Bruno A. Prata & Anselmo R. Pitombeira-Neto, 2021. "Heterogeneous prestressed precast beams multiperiod production planning problem: modeling and solution methods," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 660-693, October.
    3. Polyakovskiy, Sergey & M’Hallah, Rym, 2021. "Just-in-time two-dimensional bin packing," Omega, Elsevier, vol. 102(C).

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