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Technical Note---Branch-and-Price-and-Cut Approach to the Robust Network Design Problem Without Flow Bifurcations

Author

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  • Chungmok Lee

    (IT Convergence Technology Research Laboratory, Electronics and Telecommunications Research Institute, Yuseong-gu, Daejeon 305-700, Republic of Korea, Department of Industrial and Systems Engineering, KAIST, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea)

  • Kyungsik Lee

    (Department of Industrial and Management Engineering, Hankuk University of Foreign Studies, Mohyeon-myon, Yongin-si, Gyeonggi-do 449-791, Republic of Korea)

  • Kyungchul Park

    (College of Business Administration, Myongji University, Namgaja-dong, Seodaemun-gu, Seoul 120-728, Republic of Korea)

  • Sungsoo Park

    (Department of Industrial and Systems Engineering, KAIST, Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea)

Abstract

This paper presents a robust optimization approach to the network design problem under traffic demand uncertainty. We consider the specific case of the network design problem in which there are several alternatives in edge capacity installations and the traffic cannot be split over several paths. A new decomposition approach is proposed that yields a strong LP relaxation and enables traffic demand uncertainty to be addressed efficiently through localization of the uncertainty to each edge of the underlying network. A branch-and-price-and-cut algorithm is subsequently developed and tested on a set of benchmark instances.

Suggested Citation

  • Chungmok Lee & Kyungsik Lee & Kyungchul Park & Sungsoo Park, 2012. "Technical Note---Branch-and-Price-and-Cut Approach to the Robust Network Design Problem Without Flow Bifurcations," Operations Research, INFORMS, vol. 60(3), pages 604-610, June.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:3:p:604-610
    DOI: 10.1287/opre.1120.1049
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    References listed on IDEAS

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    1. Sara Mattia, 2010. "The Robust Network Loading Problem with Dynamic Routing," DIS Technical Reports 2010-03, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Ayşegül Altın & Hande Yaman & Mustafa Ç. Pınar, 2011. "The Robust Network Loading Problem Under Hose Demand Uncertainty: Formulation, Polyhedral Analysis, and Computations," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 75-89, February.
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    4. S Mudchanatongsuk & F Ordóñez & J Liu, 2008. "Robust solutions for network design under transportation cost and demand uncertainty," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 652-662, May.
    5. Cynthia Barnhart & Christopher A. Hane & Pamela H. Vance, 2000. "Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems," Operations Research, INFORMS, vol. 48(2), pages 318-326, April.
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    Citations

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    Cited by:

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    2. Artur Alves Pessoa & Michael Poss & Ruslan Sadykov & François Vanderbeck, 2021. "Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty," Operations Research, INFORMS, vol. 69(3), pages 739-754, May.
    3. Chassein, André & Goerigk, Marc & Kurtz, Jannis & Poss, Michael, 2019. "Faster algorithms for min-max-min robustness for combinatorial problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 279(2), pages 308-319.
    4. Seulgi Joung & Seyoung Oh & Kyungsik Lee, 2023. "Comparative analysis of linear programming relaxations for the robust knapsack problem," Annals of Operations Research, Springer, vol. 323(1), pages 65-78, April.
    5. Poss, Michael, 2014. "Robust combinatorial optimization with variable cost uncertainty," European Journal of Operational Research, Elsevier, vol. 237(3), pages 836-845.
    6. Artur Alves Pessoa & Michael Poss, 2015. "Robust Network Design with Uncertain Outsourcing Cost," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 507-524, August.
    7. Seohee Kim & Chungmok Lee, 2021. "A branch and price approach for the robust bandwidth packing problem with queuing delays," Annals of Operations Research, Springer, vol. 307(1), pages 251-275, December.
    8. Zhang, Guowei & Jia, Ning & Zhu, Ning & Adulyasak, Yossiri & Ma, Shoufeng, 2023. "Robust drone selective routing in humanitarian transportation network assessment," European Journal of Operational Research, Elsevier, vol. 305(1), pages 400-428.
    9. Annette M. C. Ficker & Frits C. R. Spieksma & Gerhard J. Woeginger, 2018. "Robust balanced optimization," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 239-266, September.

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