IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v48y2000i2p233-242.html
   My bibliography  Save this article

A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure

Author

Listed:
  • Gregory D. Glockner

    (ILOG, Inc., 1080 Linda Vista Avenue, Mountain View, California 94043)

  • George L. Nemhauser

    (Logistics Engineering Center, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

We consider a dynamic network flow problem where the arc capacities are random variables. This gives a multistage stochastic linear program. We describe the randomness using a multi-scenario approach. Because of the multilayered structure, there are several ways to decompose the linear program. We classify different decomposition schemes, and we develop a scheme called compath decomposition , which is derived from path decomposition for network flows. We give a polynomial-time algorithm to find a cheapest compath that can solve the subproblems resulting from compath decomposition. Finally, compath decomposition is extended to multicommodity flow problems.

Suggested Citation

  • Gregory D. Glockner & George L. Nemhauser, 2000. "A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure," Operations Research, INFORMS, vol. 48(2), pages 233-242, April.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:2:p:233-242
    DOI: 10.1287/opre.48.2.233.12384
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.48.2.233.12384
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.48.2.233.12384?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Peter B. M. Vranas & Dimitris Bertsimas & Amedeo R. Odoni, 1994. "Dynamic Ground-Holding Policies for a Network of Airports," Transportation Science, INFORMS, vol. 28(4), pages 275-291, November.
    2. William C. Jordan & Mark A. Turnquist, 1983. "A Stochastic, Dynamic Network Model for Railroad Car Distribution," Transportation Science, INFORMS, vol. 17(2), pages 123-145, May.
    3. Raymond K. Cheung & Warren B. Powell, 1996. "An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management," Operations Research, INFORMS, vol. 44(6), pages 951-963, December.
    4. Peter B. Vranas & Dimitris J. Bertsimas & Amedeo R. Odoni, 1994. "The Multi-Airport Ground-Holding Problem in Air Traffic Control," Operations Research, INFORMS, vol. 42(2), pages 249-261, April.
    5. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    6. Richetta, Octavio & Odoni, Amedeo R., 1994. "Dynamic solution to the ground-holding problem in air traffic control," Transportation Research Part A: Policy and Practice, Elsevier, vol. 28(3), pages 167-185, May.
    7. Linos F. Frantzeskakis & Warren B. Powell, 1990. "A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems," Transportation Science, INFORMS, vol. 24(1), pages 40-57, February.
    8. Warren B. Powell & Yosef Sheffi & Kenneth S. Nickerson & Kevin Butterbaugh & Susan Atherton, 1988. "Maximizing Profits for North American Van Lines' Truckload Division: A New Framework for Pricing and Operations," Interfaces, INFORMS, vol. 18(1), pages 21-41, February.
    9. Ali, Agha Iqbal & Kennington, Jeff & Shetty, Bala, 1988. "The equal flow problem," European Journal of Operational Research, Elsevier, vol. 36(1), pages 107-115, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hafezalkotob, Ashkan & Makui, Ahmad, 2015. "Cooperative maximum-flow problem under uncertainty in logistic networks," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 593-604.
    2. Maciej Rysz & Mohammad Mirghorbani & Pavlo Krokhmal & Eduardo L. Pasiliao, 2014. "On risk-averse maximum weighted subgraph problems," Journal of Combinatorial Optimization, Springer, vol. 28(1), pages 167-185, July.
    3. Song, Haiqing & Cheung, Raymond K. & Wang, Haiyan, 2014. "An arc-exchange decomposition method for multistage dynamic networks with random arc capacities," European Journal of Operational Research, Elsevier, vol. 233(3), pages 474-487.
    4. Zachary Steever & Chase Murray & Junsong Yuan & Mark Karwan & Marco Lübbecke, 2022. "An Image-Based Approach to Detecting Structural Similarity Among Mixed Integer Programs," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 1849-1870, July.
    5. Gaivoronski, Alexei & Sechi, Giovanni M. & Zuddas, Paola, 2012. "Cost/risk balanced management of scarce resources using stochastic programming," European Journal of Operational Research, Elsevier, vol. 216(1), pages 214-224.
    6. Alexander S. Estes & Michael O. Ball, 2020. "Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem," Transportation Science, INFORMS, vol. 54(4), pages 944-955, July.
    7. Delgado, Felipe & Trincado, Ricardo & Pagnoncelli, Bernardo K., 2019. "A multistage stochastic programming model for the network air cargo allocation under capacity uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 292-307.
    8. Maciej Rysz & Foad Mahdavi Pajouh & Pavlo Krokhmal & Eduardo L. Pasiliao, 2018. "Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights," Annals of Operations Research, Springer, vol. 262(1), pages 89-108, March.
    9. S Opasanon & E Miller-Hooks, 2009. "The Safest Escape problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(12), pages 1749-1758, December.
    10. G Barbarosoǧlu & Y Arda, 2004. "A two-stage stochastic programming framework for transportation planning in disaster response," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(1), pages 43-53, January.
    11. Taesung Hwang & Yanfeng Ouyang, 2015. "Urban Freight Truck Routing under Stochastic Congestion and Emission Considerations," Sustainability, MDPI, vol. 7(6), pages 1-16, May.
    12. Alexander S. Estes & Michael O. Ball, 2021. "Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 785-807, May.
    13. Goldbeck, Nils & Angeloudis, Panagiotis & Ochieng, Washington, 2020. "Optimal supply chain resilience with consideration of failure propagation and repair logistics," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    14. Song, Haiqing & Huang, Huei-Chuen, 2008. "A successive convex approximation method for multistage workforce capacity planning problem with turnover," European Journal of Operational Research, Elsevier, vol. 188(1), pages 29-48, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexander S. Estes & Michael O. Ball, 2020. "Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem," Transportation Science, INFORMS, vol. 54(4), pages 944-955, July.
    2. Gregory A. Godfrey & Warren B. Powell, 2002. "An Adaptive Dynamic Programming Algorithm for Dynamic Fleet Management, I: Single Period Travel Times," Transportation Science, INFORMS, vol. 36(1), pages 21-39, February.
    3. Andreatta, Giovanni & Dell'Olmo, Paolo & Lulli, Guglielmo, 2011. "An aggregate stochastic programming model for air traffic flow management," European Journal of Operational Research, Elsevier, vol. 215(3), pages 697-704, December.
    4. Bard, Jonathan F. & Mohan, Dinesh Natarajan, 2008. "Reallocating arrival slots during a ground delay program," Transportation Research Part B: Methodological, Elsevier, vol. 42(2), pages 113-134, February.
    5. Dimitris Bertsimas & Sarah Stock Patterson, 2000. "The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach," Transportation Science, INFORMS, vol. 34(3), pages 239-255, August.
    6. Huseyin Topaloglu & Warren Powell, 2007. "Incorporating Pricing Decisions into the Stochastic Dynamic Fleet Management Problem," Transportation Science, INFORMS, vol. 41(3), pages 281-301, August.
    7. Crainic, Teodor Gabriel & Laporte, Gilbert, 1997. "Planning models for freight transportation," European Journal of Operational Research, Elsevier, vol. 97(3), pages 409-438, March.
    8. Kammoun, Mohamed Ali & Rezg, Nidhal, 2018. "An efficient hybrid approach for resolving the aircraft routing and rescheduling problem," Journal of Air Transport Management, Elsevier, vol. 71(C), pages 73-87.
    9. Raymond K.-M. Cheung & Warren B. Powell, 2000. "Shape -- A Stochastic Hybrid Approximation Procedure for Two-Stage Stochastic Programs," Operations Research, INFORMS, vol. 48(1), pages 73-79, February.
    10. Mohamed Ali Kammoun & Sadok Turki & Nidhal Rezg, 2020. "Optimization of Flight Rescheduling Problem under Carbon Tax," Sustainability, MDPI, vol. 12(14), pages 1-19, July.
    11. Chen, Yunxiang & Zhao, Yifei & Wu, Yexin, 2024. "Recent progress in air traffic flow management: A review," Journal of Air Transport Management, Elsevier, vol. 116(C).
    12. Bojovic, Nebojsa J., 2002. "A general system theory approach to rail freight car fleet sizing," European Journal of Operational Research, Elsevier, vol. 136(1), pages 136-172, January.
    13. Warren B. Powell & Joel A. Shapiro & Hugo P. Simão, 2002. "An Adaptive Dynamic Programming Algorithm for the Heterogeneous Resource Allocation Problem," Transportation Science, INFORMS, vol. 36(2), pages 231-249, May.
    14. Tassio A. Carvalho & Warren B. Powell, 2000. "A Multiplier Adjustment Method for Dynamic Resource Allocation Problems," Transportation Science, INFORMS, vol. 34(2), pages 150-164, May.
    15. Brunner, Jens O., 2014. "Rescheduling of flights during ground delay programs with consideration of passenger and crew connections," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 72(C), pages 236-252.
    16. Warren B. Powell & Michael T. Towns & Arun Marar, 2000. "On the Value of Optimal Myopic Solutions for Dynamic Routing and Scheduling Problems in the Presence of User Noncompliance," Transportation Science, INFORMS, vol. 34(1), pages 67-85, February.
    17. Shi, Ning & Song, Haiqing & Powell, Warren B., 2014. "The dynamic fleet management problem with uncertain demand and customer chosen service level," International Journal of Production Economics, Elsevier, vol. 148(C), pages 110-121.
    18. Guo, Yechenfeng & Hu, Minghua & Zou, Bo & Hansen, Mark & Zhang, Ying & Xie, Hua, 2022. "Air Traffic Flow Management Integrating Separation Management and Ground Holding: An Efficiency-Equity Bi-objective Perspective," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 394-423.
    19. Dimitris Bertsimas & Sarah Stock Patterson, 1998. "The Air Traffic Flow Management Problem with Enroute Capacities," Operations Research, INFORMS, vol. 46(3), pages 406-422, June.
    20. Raymond K. Cheung & Chuen-Yih Chen, 1998. "A Two-Stage Stochastic Network Model and Solution Methods for the Dynamic Empty Container Allocation Problem," Transportation Science, INFORMS, vol. 32(2), pages 142-162, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:48:y:2000:i:2:p:233-242. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.