Skip to main content

Robust Scheduling with Logic-Based Benders Decomposition

  • Conference paper
  • First Online:
Operations Research Proceedings 2014

Part of the book series: Operations Research Proceedings ((ORP))

Abstract

We study project scheduling at a large IT services delivery center in which there are unpredictable delays. We apply robust optimization to minimize tardiness while informing the customer of a reasonable worst-case completion time, based on empirically determined uncertainty sets. We introduce a new solution method based on logic-based Benders decomposition. We show that when the uncertainty set is polyhedral, the decomposition simplifies substantially, leading to a model of tractable size. Preliminary computational experience indicates that this approach is superior to a mixed integer programming model solved by state-of-the-art software.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press (2009)

    Google Scholar 

  2. Bertsimas, D., Brown, D.B., Caramanis, C.: Theory and applications of robust optimization. SIAM Rev. 53(3), 464–501 (2011)

    Google Scholar 

  3. Bertsimas, D., Pachamanova, D., Sim, M.: Robust linear optimization under general norms. Oper. Res. Lett. 32, 510–516 (2004)

    Article  Google Scholar 

  4. Bertsimas, D., Sim, M.: The price of robustness. Oper. Res. 52(1), 35–53 (2004)

    Article  Google Scholar 

  5. Bertsimas, D., Thiele, A.: Robust and data-driven optimization: modern decision-making under uncertainty. Tutorials Oper. Res. 4, 122–195 (2006)

    Google Scholar 

  6. Ciré, A.A., Çoban, E., Hooker, J.N.: Mixed integer programming versus logic-based Benders decomposition for planning and scheduling. In: Gomes, C., Sellmann, M., (eds.) CPAIOR 2013, Lecture Notes in Computer Science, vol. 7874, pp. 325–331, Springer (2013)

    Google Scholar 

  7. Harjunkoski, I., Grossmann, I.E.: A decomposition approach for the scheduling of a steel plant production. Comput. Chem. Eng. 25, 1647–1660 (2001)

    Article  Google Scholar 

  8. Hooker, J.N.: Integrated Methods for Optimization, 2nd edn. Springer (2012)

    Google Scholar 

  9. Hooker, J.N.: Logic-based Benders decomposition. In INFORMS National Meeting (fall), New Orleans (1995)

    Google Scholar 

  10. Hooker, J.N.: An integrated method for planning and scheduling to minimize tardiness. Constraints 11, 139–157 (2006)

    Article  Google Scholar 

  11. Hooker, J.N.: Planning and scheduling by logic-based Benders decomposition. Oper. Res. 55, 588–602 (2007)

    Article  Google Scholar 

  12. Hooker, J.N., Ottosson, G.: Logic-based Benders decomposition. Math. Program. 96, 33–60 (2003)

    Google Scholar 

  13. Hooker, J.N., Yan, H.: Logic circuit verification by Benders decomposition. In: Saraswat, V., Van Hentenryck, P. (eds.) Principles and Practice of Constraint Programming: The Newport Papers, pp. 267–288. MIT Press, Cambridge, MA (1995)

    Google Scholar 

  14. Jain, V., Grossmann, I.E.: Algorithms for hybrid MILP/CP models for a class of optimization problems. INFORMS J. Comput. 13, 258–276 (2001)

    Article  Google Scholar 

  15. Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21(5), 1154–1157 (1973)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elvin Coban .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Coban, E., Heching, A., Hooker, J.N., Scheller-Wolf, A. (2016). Robust Scheduling with Logic-Based Benders Decomposition. In: Lübbecke, M., Koster, A., Letmathe, P., Madlener, R., Peis, B., Walther, G. (eds) Operations Research Proceedings 2014. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-28697-6_15

Download citation

Publish with us

Policies and ethics