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A general bilevel linear programming formulation of the network design problem

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  • Ben-Ayed, Omar
  • Boyce, David E.
  • Blair, Charles E.

Abstract

A formulation of the network design problem as a bilevel linear program is presented which admits both the convex and concave investment functions. It also allows a more general representation of travel cost functions than a previous formulation by LeBlanc and Boyce (1986).

Suggested Citation

  • Ben-Ayed, Omar & Boyce, David E. & Blair, Charles E., 1988. "A general bilevel linear programming formulation of the network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 22(4), pages 311-318, August.
    • Handle: RePEc:eee:transb:v:22:y:1988:i:4:p:311-318
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    1. Lígia Conceição & Gonçalo Homem de Almeida Correia & José Pedro Tavares, 2020. "The Reversible Lane Network Design Problem (RL-NDP) for Smart Cities with Automated Traffic," Sustainability, MDPI, vol. 12(3), pages 1-22, February.
    2. Elnaz Miandoabchi & Reza Farahani & W. Szeto, 2012. "Bi-objective bimodal urban road network design using hybrid metaheuristics," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 583-621, December.
    3. Jin Qin & Yuxin He & Linglin Ni, 2014. "Quantitative Efficiency Evaluation Method for Transportation Networks," Sustainability, MDPI, vol. 6(12), pages 1-15, November.
    4. Ghavamifar, Ali & Makui, Ahmad & Taleizadeh, Ata Allah, 2018. "Designing a resilient competitive supply chain network under disruption risks: A real-world application," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 115(C), pages 87-109.
    5. Huang, Di & Liu, Zhiyuan & Liu, Pan & Chen, Jun, 2016. "Optimal transit fare and service frequency of a nonlinear origin-destination based fare structure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 1-19.
    6. Teodorović Dušan & Nikolić Miloš, 2023. "Work Zone Scheduling Problem in the Urban Traffic Networks," Economic Themes, Sciendo, vol. 61(1), pages 1-18, March.
    7. Zhong, Tao & Young, Rhonda, 2010. "Multiple Choice Knapsack Problem: Example of planning choice in transportation," Evaluation and Program Planning, Elsevier, vol. 33(2), pages 128-137, May.
    8. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    9. Hecheng Li, 2015. "A genetic algorithm using a finite search space for solving nonlinear/linear fractional bilevel programming problems," Annals of Operations Research, Springer, vol. 235(1), pages 543-558, December.
    10. Ang, Sheng & Liu, Pei & Yang, Feng, 2020. "Intra-Organizational and inter-organizational resource allocation in two-stage network systems," Omega, Elsevier, vol. 91(C).
    11. Elnaz Miandoabchi & Reza Farahani & Wout Dullaert & W. Szeto, 2012. "Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks," Networks and Spatial Economics, Springer, vol. 12(3), pages 441-480, September.
    12. Kalashnikov, Vyacheslav V. & Pérez-Valdés, Gerardo A. & Tomasgard, Asgeir & Kalashnykova, Nataliya I., 2010. "Natural gas cash-out problem: Bilevel stochastic optimization approach," European Journal of Operational Research, Elsevier, vol. 206(1), pages 18-33, October.
    13. Andrew Koh & Simon Shepherd & Agachai Sumalee, 2009. "Second best toll and capacity optimisation in networks: solution algorithm and policy implications," Transportation, Springer, vol. 36(2), pages 147-165, March.
    14. Daniela Leite & Caterina De Bacco, 2024. "Similarity and economy of scale in urban transportation networks and optimal transport-based infrastructures," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    15. Gao, Ge & Sun, Huijun & Wu, Jianjun & Liu, Xinmin & Chen, Weiya, 2018. "Park-and-ride service design under a price-based tradable credits scheme in a linear monocentric city," Transport Policy, Elsevier, vol. 68(C), pages 1-12.
    16. Anny B. Wang & W. Y. Szeto, 2020. "Bounding the Inefficiency of the Reliability-Based Continuous Network Design Problem Under Cost Recovery," Networks and Spatial Economics, Springer, vol. 20(2), pages 395-422, June.
    17. Gao, Ziyou & Wu, Jianjun & Sun, Huijun, 2005. "Solution algorithm for the bi-level discrete network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(6), pages 479-495, July.
    18. Judith Y. T. Wang & Richard D. Connors, 2018. "Urban Growth, Transport Planning, Air Quality and Health: A Multi-Objective Spatial Analysis Framework for a Linear Monocentric City," Networks and Spatial Economics, Springer, vol. 18(4), pages 839-874, December.
    19. Amirali Zarrinmehr & Mahmoud Saffarzadeh & Seyedehsan Seyedabrishami & Yu Marco Nie, 2016. "A path-based greedy algorithm for multi-objective transit routes design with elastic demand," Public Transport, Springer, vol. 8(2), pages 261-293, September.
    20. Ata Allah Taleizadeh & Ali Ghavamifar & Amir Khosrojerdi, 2022. "Resilient network design of two supply chains under price competition: game theoretic and decomposition algorithm approach," Operational Research, Springer, vol. 22(1), pages 825-857, March.
    21. Liming Zhang & Wei Yang & Yuan Yuan & Rui Zhou, 2017. "An Integrated Carbon Policy-Based Interactive Strategy for Carbon Reduction and Economic Development in a Construction Material Supply Chain," Sustainability, MDPI, vol. 9(11), pages 1-15, November.
    22. Wang, Delu & Liu, Yifei & Wang, Yadong & Shi, Xunpeng & Song, Xuefeng, 2020. "Allocation of coal de-capacity quota among provinces in China: A bi-level multi-objective combinatorial optimization approach," Energy Economics, Elsevier, vol. 87(C).
    23. Jen-Jia Lin & Chia-Jung Yu, 2013. "A bikeway network design model for urban areas," Transportation, Springer, vol. 40(1), pages 45-68, January.
    24. Giulio Cantarella & Antonino Vitetta, 2006. "The multi-criteria road network design problem in an urban area," Transportation, Springer, vol. 33(6), pages 567-588, November.

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