Skip to main content
Log in

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

  • Published:
Networks and Spatial Economics Aims and scope Submit manuscript

Abstract

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.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. Costs in general do not vary linearly with respect to the transportation facility capacity or size. Typically, scale economies or diseconomies exist. Abdulaal and LeBlanc (1979) discussed the cases of linear relationship, scale economies and scale diseconomies in the context of transportation network design problems. If the average investment cost per unit of capacity is declining, then scale economies exist. Empirical data are needed to establish the economies of scale for road construction. This paper assumes a linear relationship between the investment cost and the capacity, for the reasons of simplicity and the requirement of the linear model. The linear case can be regarded as an approximation to the case of scale economies in an expected capacity-increasing range.

References

  • Abdulaal M, LeBlanc LJ (1979) Continuous equilibrium network design models. Transp Res B 13:19–32

    Article  Google Scholar 

  • Atamturk A, Zhang M (2007) Two-stage robust network flow and design under demand uncertainty. Oper Res 55:662–673

    Article  Google Scholar 

  • Ban X, Lu S, Ferris M et al (2009) Risk-averse second-best toll pricing. Proc 18th Int Sympo Transp Traffic Theory 197–218

  • Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23:769–805

    Article  Google Scholar 

  • Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25:1–13

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Ben-Tal A, Nemirovski A (2002) Robust optimization―methodology and applications. Math Program 92:453–480

    Article  Google Scholar 

  • Bertsimas D, Brown DB, Caramanis C (2007) Theory and applications of robust optimization. Available via http://users.ece.utexas.edu/~cmcaram/pubs/RobustOptimizationSV.pdf. Accessed 15 Mar, 2010

  • Daganzo CF (1994) The cell transmission model part I: a simple dynamic representation of highway traffic. Transp Res B 28:269–287

    Article  Google Scholar 

  • Daganzo CF (1995) The cell transmission model part II: network traffic. Transp Res B 29:79–93

    Article  Google Scholar 

  • Karoonsoontawong A, Waller ST (2007) Robust dynamic continuous network design problem. J Transp Res Board 2029:58–71

    Article  Google Scholar 

  • 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 

  • 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 

  • Lou Y, Yin Y, Lawpongpanich S (2009) A robust approach to discrete network designs with demand uncertainty. J Transp Res Board 2090:86–94

    Article  Google Scholar 

  • Lu Y (2007) Robust transportation network design under user equilibrium, Master’s Thesis, MIT, Cambridge, MA.

  • Magnanti TL, Wong RT (1984) Network design and transportation planning: models and algorithms. Transp Sci 18:1–55

    Article  Google Scholar 

  • Minoux M (1989) Network synthesis and optimum network design problems: models, solution methods and applications. Netw 19:313–360

    Article  Google Scholar 

  • Mudchanatongsuk S, Ordonez F, Liu J (2008) Robust solutions for network design under transportation cost and demand uncertainty. J Oper Res Soc 59:652–662

    Article  Google Scholar 

  • Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281

    Article  Google Scholar 

  • Ordonez F, Zhao J (2007) Robust capacity expansion of network flows. Netw 50:136–145

    Article  Google Scholar 

  • Peeta S, Ziliaskopoulos AK (2001) Foundations of dynamic traffic assignment: the past, the present and the future. Network Spatial Econ 1:233–265

    Article  Google Scholar 

  • 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 8:383–406

    Article  Google Scholar 

  • Ukkusuri SV, Mathew T, Waller T (2007) Robust transportation network design under demand uncertainty. Comput Aided Civ Infrastruct Eng 22:6–18

    Article  Google Scholar 

  • Waller ST, Ziliaskopoulos AK (2001) Stochastic dynamic network design problem. J Transp Res Board 1771:106–113

    Article  Google Scholar 

  • Waller ST, Ziliaskopoulos AK (2006) A chance-constrained based stochastic dynamic traffic assignment model: analysis, formulation and solution algorithms. Transp Res C 14:418–427

    Article  Google Scholar 

  • Wardman M (1998) The value of travel time: a review of British evidence. J Transp Econ Policy 32:285–316

    Google Scholar 

  • Yang H, Bell MGH (1998) Models and algorithms for road network design: a review and some new developments. Transp Rev 18:257–278

    Article  Google Scholar 

  • Yao T, Mandala SR, Chung BD (2009) Evacuation transportation planning under uncertainty: a robust optimization approach. Network Spatial Econ 9:171–189

    Article  Google Scholar 

  • Yin Y, Lawpongpanich S (2007) A robust approach to continuous network design with demand uncertainty. Proc 17th Int Sympo Transp Traffic Theory 111–126

  • Zhao Y, Kockelman K (2002) The propagation of uncertainty through travel demand models: an exploratory analysis. Ann Reg Sci 36:145–163

    Article  Google Scholar 

  • Ziliaskopoulos AK (2000) A linear programming model for the single destination system optimum dynamic traffic assignment problem. Transp Sci 34:37–49

    Article  Google Scholar 

Download references

Acknowledgment

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tao Yao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chung, B.D., Yao, T., Xie, C. et al. Robust Optimization Model for a Dynamic Network Design Problem Under Demand Uncertainty. Netw Spat Econ 11, 371–389 (2011). https://doi.org/10.1007/s11067-010-9147-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11067-010-9147-2

Keywords

Navigation