Advertisement

Exact Solution of Combined Cutting Stock and Scheduling Problems

  • Nuno Braga
  • Cláudio Alves
  • José Valério de Carvalho
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 682)

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.

Notes

Acknowledgements

This work was supported by FEDER funding through the Programa Operacional Factores de Competitividade - COMPETE and by national funding through the Portuguese Science and Technology Foundation (FCT) in the scope of the project PTDC/EGE-GES/116676/2010.

References

  1. 1.
    Arbib, C., Marinelli, F.: On cutting stock with due dates. Omega 46, 11–20 (2014)CrossRefGoogle Scholar
  2. 2.
    Carlier, J., Clautiaux, F., Moukrim, A.: New reduction procedures and lower bounds for the two-dimensional bin-packing problem with fixed orientation. Comput. Oper. Res. 34, 2223–2250 (2007)CrossRefGoogle Scholar
  3. 3.
    Clautiaux, F., Alves, C., de Carvalho, J.M.V.: A survey of dual-feasible and superadditive functions. Ann. Oper. Res. 179, 317–342 (2010)CrossRefGoogle Scholar
  4. 4.
    Fekete, S., Schepers, J.: New classes of fast lower bounds for bin packing problems. Math. Program. 91, 11–31 (2001)Google Scholar
  5. 5.
    Li, S.: Multi-job cutting stock problem with due dates and release dates. J. Oper. Res. Soc. 47, 490–510 (1996)CrossRefGoogle Scholar
  6. 6.
    Reinertsen, H., Vossen, T.: The one-dimensional cutting stock problem with due dates. Eur. J. Oper. Res. 201, 701–711 (2010)CrossRefGoogle Scholar
  7. 7.
    Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183, 1109–1130 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Nuno Braga
    • 1
  • Cláudio Alves
    • 1
  • José Valério de Carvalho
    • 1
  1. 1.Universidade do MinhoBragaPortugal

Personalised recommendations