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A single-level mixed integer linear formulation for a bi-level discrete network design problem

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  • Farvaresh, Hamid
  • Sepehri, Mohammad Mehdi

Abstract

Discrete network design problem (DNDP) is generally formulated as a bi-level programming. In this paper, a single-level mixed integer linear programming (SL-MILP) formulation for bi-level DNDP is presented. To cope with the dependency of node-link adjacency matrix on new links, travel time function is appropriately modified. The nonlinearity of the travel time function is also removed by means of a convex-combination based linear approximation which takes advantage of a unimodular structure. Two valid inequalities is developed which shorten computation time significantly. The validity of the proposed formulation is examined by two test problems. SL-MILP is able to provide optimal solution.

Suggested Citation

  • Farvaresh, Hamid & Sepehri, Mohammad Mehdi, 2011. "A single-level mixed integer linear formulation for a bi-level discrete network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 623-640, September.
    • Handle: RePEc:eee:transe:v:47:y:2011:i:5:p:623-640
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    Cited by:

    1. Liang, Jinpeng & Wu, Jianjun & Gao, Ziyou & Sun, Huijun & Yang, Xin & Lo, Hong K., 2019. "Bus transit network design with uncertainties on the basis of a metro network: A two-step model framework," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 115-138.
    2. Jianqiang Wang & Wenlong Zhao & Chenglin Liu & Zhipeng Huang, 2023. "A System Optimization Approach for Trains’ Operation Plan with a Time Flexible Pricing Strategy for High-Speed Rail Corridors," Sustainability, MDPI, vol. 15(12), pages 1-22, June.
    3. Hong Zheng & Xiaozheng He & Yongfu Li & Srinivas Peeta, 2017. "Traffic Equilibrium and Charging Facility Locations for Electric Vehicles," Networks and Spatial Economics, Springer, vol. 17(2), pages 435-457, June.
    4. Haque, Khademul & Mishra, Sabyasachee & Golias, Mihalis M., 2021. "Multi-period transportation network investment decision making and policy implications using econometric framework," Research in Transportation Economics, Elsevier, vol. 89(C).
    5. Luan, Mingye & Waller, S.Travis & Rey, David, 2023. "A non-additive path-based reward credit scheme for traffic congestion management," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    6. Wang, Guangmin & Gao, Ziyou & Xu, Meng, 2019. "Integrating link-based discrete credit charging scheme into discrete network design problem," European Journal of Operational Research, Elsevier, vol. 272(1), pages 176-187.
    7. Di, Zhen & Yang, Lixing & Qi, Jianguo & Gao, Ziyou, 2018. "Transportation network design for maximizing flow-based accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 209-238.
    8. Hammad, Ahmed W A & Akbarnezhad, Ali & Rey, David, 2017. "Sustainable urban facility location: Minimising noise pollution and network congestion," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 107(C), pages 38-59.
    9. Wang, Zhaodong & Xie, Siyang & Ouyang, Yanfeng, 2022. "Planning reliable service facility location against disruption risks and last-mile congestion in a continuous space," Transportation Research Part B: Methodological, Elsevier, vol. 165(C), pages 123-140.
    10. Li, Changmin & Yang, Hai & Zhu, Daoli & Meng, Qiang, 2012. "A global optimization method for continuous network design problems," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1144-1158.
    11. Wang, David Z.W. & Liu, Haoxiang & Szeto, W.Y., 2015. "A novel discrete network design problem formulation and its global optimization solution algorithm," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 79(C), pages 213-230.
    12. Beikverdi, Majid & Tehrani, Nasim Ghanbar & Shahanaghi, Kamran, 2024. "A Bi-level model for district-fairness participatory budgeting: Decomposition methods and application," European Journal of Operational Research, Elsevier, vol. 314(1), pages 340-362.
    13. Fontaine, Pirmin & Minner, Stefan, 2014. "Benders Decomposition for Discrete–Continuous Linear Bilevel Problems with application to traffic network design," Transportation Research Part B: Methodological, Elsevier, vol. 70(C), pages 163-172.
    14. Rashidi, Eghbal & Parsafard, Mohsen & Medal, Hugh & Li, Xiaopeng, 2016. "Optimal traffic calming: A mixed-integer bi-level programming model for locating sidewalks and crosswalks in a multimodal transportation network to maximize pedestrians’ safety and network usability," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 91(C), pages 33-50.
    15. Liu, Jiangtao & Zhou, Xuesong, 2016. "Capacitated transit service network design with boundedly rational agents," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 225-250.
    16. Meng Xu & Guangmin Wang & Susan Grant-Muller & Ziyou Gao, 2017. "Joint road toll pricing and capacity development in discrete transport network design problem," Transportation, Springer, vol. 44(4), pages 731-752, July.
    17. Reza Faturechi & Shabtai Isaac & Elise Miller-Hooks & Lei Feng, 2018. "Risk-based models for emergency shelter and exit design in buildings," Annals of Operations Research, Springer, vol. 262(1), pages 185-212, March.
    18. Pirmin Fontaine & Stefan Minner, 2017. "A dynamic discrete network design problem for maintenance planning in traffic networks," Annals of Operations Research, Springer, vol. 253(2), pages 757-772, June.
    19. Hamid Farvaresh & Mohammad Sepehri, 2013. "A Branch and Bound Algorithm for Bi-level Discrete Network Design Problem," Networks and Spatial Economics, Springer, vol. 13(1), pages 67-106, March.

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