Skip to main content
SpringerLink
Log in

Benders Decomposition

  • Living reference work entry
  • First Online:
Encyclopedia of Optimization

  • 132 Accesses

Abstract

Abstract Text

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4(1):238–252

    Article  MathSciNet  MATH  Google Scholar 

  2. Birge JR, Louveaux F (1997) Introduction to stochastic programming. Springer, Berlin

    MATH  Google Scholar 

  3. Conejo AJ, Castillo E, Minguez R, Garcia-Bertrand R (2006) Decomposition techniques in mathematical programming: engineering and science applications. Springer, Berlin

    MATH  Google Scholar 

  4. Geoffrion AM (1972) Generalized benders decomposition. J Optim Theory Appl 10(1):237–260

    Article  MathSciNet  MATH  Google Scholar 

  5. Lohmann T, Rebennack S (2017) Tailored benders decomposition for a long-term power expansion model with short-term demand response. Manag Sci 63(6):2027–2048

    Article  Google Scholar 

  6. Pereira MVF, Pinto LMVG (1991) Multi-stage stochastic optimization applied to energy planning. Math Program 52(1):359–375

    Article  MathSciNet  MATH  Google Scholar 

  7. Rahmaniani R, Crainic TG, Gendreau M, Rei W (2017) The benders decomposition algortihm: a literature review. Eur J Oper Res 259(1):801–817

    Article  MATH  Google Scholar 

  8. Rebennack S (2016) Combining sampling-based and scenario-based nested benders decomposition methods: application to stochastic dual dynamic programming. Math Program 156(1):343–389

    Article  MathSciNet  MATH  Google Scholar 

  9. Rebennack S, Prokopyev OA, Singh B (2020) Two-stage stochastic minimum s-t cut problems: formulations, complexity and decomposition algorithms. Networks 75(3):235–258

    Article  MathSciNet  Google Scholar 

  10. Sudermann-Merx N, Rebennack S, Timpe C (2021) Crossing minimal edge-constrained layout planning using benders decomposition production and operations management. Prod Oper Manag (accepted)

    Google Scholar 

  11. Van Dinter J, Rebennack S, Kallrath J, Denholm P, Newman A (2013) The unit commitment model with concave emissions costs: a hybrid benders’ decomposition with nonconvex master problems. Ann Oper Res 210(1):361–386

    Article  MathSciNet  MATH  Google Scholar 

  12. Vanderbeck F, Wolsey LA (2010) Reformulation and decomposition of integer programs. In 50 years of integer programming. Springer, Berlin, pp 1958–2008

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Marcel Sinske & Steffen Rebennack

Authors
  1. Marcel Sinske
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steffen Rebennack
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marcel Sinske .

Editor information

Editors and Affiliations

  1. Department of Industrial & Systems Engin, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

  2. Departmentl of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Oleg A. Prokopyev

Rights and permissions

Reprints and permissions

Copyright information

© 2023 Springer Nature Switzerland AG

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Sinske, M., Rebennack, S. (2023). Benders Decomposition. In: Pardalos, P.M., Prokopyev, O.A. (eds) Encyclopedia of Optimization. Springer, Cham. https://doi.org/10.1007/978-3-030-54621-2_726-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-54621-2_726-1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-54621-2

  • Online ISBN: 978-3-030-54621-2

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

Publish with us

Policies and ethics

Search

Navigation