Networks and Spatial Economics

, Volume 11, Issue 2, pp 371–389 | Cite as

Robust Optimization Model for a Dynamic Network Design Problem Under Demand Uncertainty

  • Byung Do Chung
  • Tao Yao
  • Chi Xie
  • Andreas Thorsen


This paper describes a robust optimization approach for a network design problem explicitly incorporating traffic dynamics and demand uncertainty. In particular, we consider a cell transmission model based network design problem of the linear programming type and use box uncertainty sets to characterize the demand uncertainty. The major contribution of this paper is to formulate such a robust network design problem as a tractable linear programming model and demonstrate the model robustness by comparing its solution performance with the nominal solution from the corresponding deterministic model. The results of the numerical experiments justify the modeling advantage of the robust optimization approach and provide useful managerial insights for enacting capacity expansion policies under demand uncertainty.


Network design Dynamic traffic assignment Robust optimization Data uncertainty 



This work was partially supported by the grant awards CMMI-0824640 and CMMI-0900040 from the National Science Foundation.


  1. Abdulaal M, LeBlanc LJ (1979) Continuous equilibrium network design models. Transp Res B 13:19–32CrossRefGoogle Scholar
  2. Atamturk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper Res 55:662–673CrossRefGoogle Scholar
  3. Ban X, Lu S, Ferris M et al (2009) Risk-averse second-best toll pricing. Proc 18th Int Sympo Transp Traffic Theory 197–218Google Scholar
  4. Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23:769–805CrossRefGoogle Scholar
  5. Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25:1–13CrossRefGoogle Scholar
  6. Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424CrossRefGoogle Scholar
  7. Ben-Tal A, Nemirovski A (2002) Robust optimization―methodology and applications. Math Program 92:453–480CrossRefGoogle Scholar
  8. Bertsimas D, Brown DB, Caramanis C (2007) Theory and applications of robust optimization. Available via Accessed 15 Mar, 2010
  9. Daganzo CF (1994) The cell transmission model part I: a simple dynamic representation of highway traffic. Transp Res B 28:269–287CrossRefGoogle Scholar
  10. Daganzo CF (1995) The cell transmission model part II: network traffic. Transp Res B 29:79–93CrossRefGoogle Scholar
  11. Karoonsoontawong A, Waller ST (2007) Robust dynamic continuous network design problem. J Transp Res Board 2029:58–71CrossRefGoogle Scholar
  12. Karoonsoontawong A, Waller ST (2008) Integrated network capacity expansion and traffic signal optimization: robust bi-level dynamic formulation. Network Spatial Econ. doi: 10.1007/s11067-008-9071-x Google Scholar
  13. Lin D, Karoonsoontawong A, Waller ST (2008) A Dantzig-Wolfe decomposition based heuristic scheme for bi-level dynamic network design problem (2008). Network Spatial Econ. doi: 10.1007/s11067-008-9093-4 Google Scholar
  14. Lou Y, Yin Y, Lawpongpanich S (2009) A robust approach to discrete network designs with demand uncertainty. J Transp Res Board 2090:86–94CrossRefGoogle Scholar
  15. Lu Y (2007) Robust transportation network design under user equilibrium, Master’s Thesis, MIT, Cambridge, MA.Google Scholar
  16. Magnanti TL, Wong RT (1984) Network design and transportation planning: models and algorithms. Transp Sci 18:1–55CrossRefGoogle Scholar
  17. Minoux M (1989) Network synthesis and optimum network design problems: models, solution methods and applications. Netw 19:313–360CrossRefGoogle Scholar
  18. Mudchanatongsuk S, Ordonez F, Liu J (2008) Robust solutions for network design under transportation cost and demand uncertainty. J Oper Res Soc 59:652–662CrossRefGoogle Scholar
  19. Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281CrossRefGoogle Scholar
  20. Ordonez F, Zhao J (2007) Robust capacity expansion of network flows. Netw 50:136–145CrossRefGoogle Scholar
  21. Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: the past, the present and the future. Network Spatial Econ 1:233–265CrossRefGoogle Scholar
  22. Ukkusuri SV, Waller ST (2008) Linear programming models for the user and system optimal dynamic network design problem: formulations, comparisons and extensions. NetwOrk Spatial Econ 8:383–406CrossRefGoogle Scholar
  23. Ukkusuri SV, Mathew T, Waller T (2007) Robust transportation network design under demand uncertainty. Comput Aided Civ Infrastruct Eng 22:6–18CrossRefGoogle Scholar
  24. Waller ST, Ziliaskopoulos AK (2001) Stochastic dynamic network design problem. J Transp Res Board 1771:106–113CrossRefGoogle Scholar
  25. Waller ST, Ziliaskopoulos AK (2006) A chance-constrained based stochastic dynamic traffic assignment model: analysis, formulation and solution algorithms. Transp Res C 14:418–427CrossRefGoogle Scholar
  26. Wardman M (1998) The value of travel time: a review of British evidence. J Transp Econ Policy 32:285–316Google Scholar
  27. Yang H, Bell MGH (1998) Models and algorithms for road network design: a review and some new developments. Transp Rev 18:257–278CrossRefGoogle Scholar
  28. Yao T, Mandala SR, Chung BD (2009) Evacuation transportation planning under uncertainty: a robust optimization approach. Network Spatial Econ 9:171–189CrossRefGoogle Scholar
  29. Yin Y, Lawpongpanich S (2007) A robust approach to continuous network design with demand uncertainty. Proc 17th Int Sympo Transp Traffic Theory 111–126Google Scholar
  30. Zhao Y, Kockelman K (2002) The propagation of uncertainty through travel demand models: an exploratory analysis. Ann Reg Sci 36:145–163CrossRefGoogle Scholar
  31. Ziliaskopoulos AK (2000) A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transp Sci 34:37–49CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Byung Do Chung
    • 1
  • Tao Yao
    • 1
  • Chi Xie
    • 2
  • Andreas Thorsen
    • 1
  1. 1.Department of Industrial and Manufacturing EngineeringThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.Center for Transportation Research, Department of Civil, Architectural and Environmental EngineeringThe University of Texas at AustinAustinUSA

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