Skip to main content
Log in

Robust optimization approach to the design of hub-and-spoke networks

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This paper considers the capacitated single and multiple allocation hub location problems with stochastic demands. The objective is to determine the number of hub facilities, their location and capacities, and allocation of demand to facilities so that the transfer of all the commodities in the network is ensured, while the total system-wide costs are minimized. A robust optimization approach is employed to model the problem and a standard optimization package is used to solve it. Computational results indicate the capability of the presented robust models to immunize the system against parameter perturbations with small cost increase, known as robustness cost.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Alumur SA, Kara BY (2008) Network hub location problems: the state of the art. Eur J Oper Res 190:1–21

    Article  MATH  MathSciNet  Google Scholar 

  2. Alumur SA, Nickel S, Saldanha-da-Gama F (2012) Hub location under uncertainty. Transp Res B 46:529–543

    Article  Google Scholar 

  3. Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Bertsimas D, Thiele A (2004) A robust optimization approach to supply chain management. Lect Notes Comput Sci 3064:86–100

    Article  MathSciNet  Google Scholar 

  6. Birge JR, Louveaux FV (1997) Introduction to stochastic programming. Springer, New York

    MATH  Google Scholar 

  7. Campbell JF (1994) Integer programming formulations of discrete hub location problems. Eur J Oper Res 72:387–405

    Article  MATH  Google Scholar 

  8. Campbell JF, Ernst AT, Krishnamoorthy M (2002) Hub location problems. In: Drezner Z, Hamacher HW (eds) Facility location: applications and theory. Springer, New York, pp 373–407

    Chapter  Google Scholar 

  9. Contreras I, Cordeau JF, Laporte G (2011) Stochastic uncapacitated hub location. Eur J Oper Res 212:518–528

    Article  MATH  MathSciNet  Google Scholar 

  10. El Ghaoui L, Oustry F, Lebret H (1998) Robust solutions to uncertain semi-definite programs. SIAM J Optim 9:33–52

    Article  MATH  Google Scholar 

  11. Ghaffari-Nasab N, Ghazanfari M, Saboury A, Fathollah M (2014) The single allocation hub location problem: a robust optimisation approach. Eur J Ind Eng (in press)

  12. Ghaffari-Nasab N, Jabalameli MS, Aryanezhad MB, Makui A (2013) Modeling and solving the bi-objective capacitated location-routing problem with probabilistic travel times. Int J Adv Manuf Technol 58:391–397

    Google Scholar 

  13. Hosseinijou SA, Bashiri M (2012) Stochastic models for transfer point location problem. Int J Adv Manuf Technol 58:391–397

    Article  Google Scholar 

  14. Love RF, Morris JG, Wesolowsky G (1988) Facility location: models and methods. Eur J Oper Res 38(1):127–128. doi:10.1016/0377-2217(89)90484-0

  15. Louveaux FV (1986) Discrete stochastic location models. Ann Oper Res 6:23–34

    Article  Google Scholar 

  16. Louveaux FV (1993) Stochastic location analysis. Locat Sci 1:127–154

    MATH  Google Scholar 

  17. Marianov V, Serra D (2003) Location models for airline hubs behaving as M/D/c queues. Comput Oper Res 30:983–1003

    Article  MATH  Google Scholar 

  18. Nikoofal ME, Sadjadi SJ (2010) A robust optimization model for p-median problem with uncertain edge lengths. Int J Adv Manuf Technol 50:391–397

    Article  Google Scholar 

  19. O’Kelly ME (1986) The location of interacting hub facilities. Transp Sci 20:92–106

    Article  Google Scholar 

  20. O’Kelly ME (1987) A Quadratic integer program for the location of interacting hub facilities. Eur J Oper Res 32:393–404

    Article  MATH  MathSciNet  Google Scholar 

  21. Ryan SM (2004) Capacity expansion for random exponential demand growth with lead times. Manag Sci 50:740–748

    Article  MATH  Google Scholar 

  22. Skorin-Kapov D, Skorin-Kapov J, O’Kelly M (1996) Tight linear programming relaxations of uncapacitated p-hub median problems. Eur J Oper Res 94:582–593

    Article  MATH  Google Scholar 

  23. Soyster AL (1973) Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21:1154–1157

    Article  MATH  MathSciNet  Google Scholar 

  24. Sim T, Lowe TJ, Thomas B-W (2009) The stochastic p-hub center problem with service-level constraints. Comput Oper Res 36:3166–3177

    Article  MATH  Google Scholar 

  25. Snyder LV (2006) Facility location under uncertainty: a review. IIE Trans 38:537–554

    Article  Google Scholar 

  26. Yang T-H (2009) Stochastic air freight hub location and freight routes planning. Appl Math Model 33:4424–4430

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nader Ghaffari-Nasab.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghaffari-Nasab, N., Ghazanfari, M. & Teimoury, E. Robust optimization approach to the design of hub-and-spoke networks. Int J Adv Manuf Technol 76, 1091–1110 (2015). https://doi.org/10.1007/s00170-014-6330-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-014-6330-5

Keywords

Navigation