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A Distributionally Robust Joint Chance Constrained Optimization Model for the Dynamic Network Design Problem under Demand Uncertainty


  • Hua Sun


  • Ziyou Gao


  • W. Szeto


  • Jiancheng Long


  • Fangxia Zhao



This paper develops a distributionally robust joint chance constrained optimization model for a dynamic network design problem (NDP) under demand uncertainty. The major contribution of this paper is to propose an approach to approximate a joint chance-constrained Cell Transmission Model (CTM) based System Optimal Dynamic Network Design Problem with only partial distributional information of uncertain demand. The proposed approximation is tighter than two popular benchmark approximations, namely the Bonferroni’s inequality and second-order cone programming (SOCP) approximations. The resultant formulation is a semidefinite program which is computationally efficient. A numerical experiment is conducted to demonstrate that the proposed approximation approach is superior to the other two approximation approaches in terms of solution quality. The proposed approximation approach may provide useful insights and have broader applicability in traffic management and traffic planning problems under uncertainty. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Hua Sun & Ziyou Gao & W. Szeto & Jiancheng Long & Fangxia Zhao, 2014. "A Distributionally Robust Joint Chance Constrained Optimization Model for the Dynamic Network Design Problem under Demand Uncertainty," Networks and Spatial Economics, Springer, vol. 14(3), pages 409-433, December.
  • Handle: RePEc:kap:netspa:v:14:y:2014:i:3:p:409-433
    DOI: 10.1007/s11067-014-9236-8

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    References listed on IDEAS

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    Cited by:

    1. Kathryn M. Schumacher & Richard Li‐Yang Chen & Amy E.M. Cohn & Jeremy Castaing, 2016. "Algorithm to solve a chance‐constrained network capacity design problem with stochastic demands and finite support," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(3), pages 236-246, April.
    2. Liu, Ming & Liu, Xin & Chu, Feng & Zheng, Feifeng & Chu, Chengbin, 2019. "Distributionally robust inventory routing problem to maximize the service level under limited budget," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 126(C), pages 190-211.
    3. Lingyun Meng & Xiaojie Luan & Xuesong Zhou, 2016. "A Train Dispatching Model Under a Stochastic Environment: Stable Train Routing Constraints and Reformulation," Networks and Spatial Economics, Springer, vol. 16(3), pages 791-820, September.
    4. Khooban, Zohreh & Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y., 2015. "Mixed network design using hybrid scatter search," European Journal of Operational Research, Elsevier, vol. 247(3), pages 699-710.
    5. Bakker, Hannah & Dunke, Fabian & Nickel, Stefan, 2020. "A structuring review on multi-stage optimization under uncertainty: Aligning concepts from theory and practice," Omega, Elsevier, vol. 96(C).
    6. Ming Liu & Rongfan Liu & E Zhang & Chengbin Chu, 0. "Eco-friendly container transshipment route scheduling problem with repacking operations," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-26.
    7. Chang, Zhiqi & Song, Shiji & Zhang, Yuli & Ding, Jian-Ya & Zhang, Rui & Chiong, Raymond, 2017. "Distributionally robust single machine scheduling with risk aversion," European Journal of Operational Research, Elsevier, vol. 256(1), pages 261-274.


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