IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v233y2014i3p474-487.html
   My bibliography  Save this article

An arc-exchange decomposition method for multistage dynamic networks with random arc capacities

Author

Listed:
  • Song, Haiqing
  • Cheung, Raymond K.
  • Wang, Haiyan

Abstract

Multistage dynamic networks with random arc capacities (MDNRAC) have been successfully used for modeling various resource allocation problems in the transportation area. However, solving these problems is generally computationally intensive, and there is still a need to develop more efficient solution approaches. In this paper, we propose a new heuristic approach that solves the MDNRAC problem by decomposing the network at each stage into a series of subproblems with tree structures. Each subproblem can be solved efficiently. The main advantage is that this approach provides an efficient computational device to handle the large-scale problem instances with fairly good solution quality. We show that the objective value obtained from this decomposition approach is an upper bound for that of the MDNRAC problem. Numerical results demonstrate that our proposed approach works very well.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:233:y:2014:i:3:p:474-487
    DOI: 10.1016/j.ejor.2013.09.048
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713008096
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.09.048?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. András Prékopa, 1999. "The use of discrete moment bounds in probabilisticconstrained stochastic programming models," Annals of Operations Research, Springer, vol. 85(0), pages 21-38, January.
    2. N. C. P. Edirisinghe & W. T. Ziemba, 1992. "Tight Bounds for Stochastic Convex Programs," Operations Research, INFORMS, vol. 40(4), pages 660-677, August.
    3. Kouwenberg, Roy, 2001. "Scenario generation and stochastic programming models for asset liability management," European Journal of Operational Research, Elsevier, vol. 134(2), pages 279-292, October.
    4. 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.
    5. George B. Dantzig, 1955. "Linear Programming under Uncertainty," Management Science, INFORMS, vol. 1(3-4), pages 197-206, 04-07.
    6. Julia L. Higle & Suvrajeet Sen, 1991. "Stochastic Decomposition: An Algorithm for Two-Stage Linear Programs with Recourse," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 650-669, August.
    7. Hugo P. Simão & Abraham George & Warren B. Powell & Ted Gifford & John Nienow & Jeff Day, 2010. "Approximate Dynamic Programming Captures Fleet Operations for Schneider National," Interfaces, INFORMS, vol. 40(5), pages 342-352, October.
    8. Warren B. Powell & Linos F. Frantzeskakis, 1994. "Restricted Recourse Strategies for Dynamic Networks with Random Arc Capacities," Transportation Science, INFORMS, vol. 28(1), pages 3-23, February.
    9. Julia L. Higle & Wing W. Lowe & Ronald Odio, 1994. "Conditional Stochastic Decomposition: An Algorithmic Interface for Optimization and Simulation," Operations Research, INFORMS, vol. 42(2), pages 311-322, April.
    10. N. C. P. Edirisinghe & W. T. Ziemba, 1994. "Bounds for Two-Stage Stochastic Programs with Fixed Recourse," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 292-313, May.
    11. 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.
    12. Warren B. Powell & Abraham George & Hugo Simão & Warren Scott & Alan Lamont & Jeffrey Stewart, 2012. "SMART: A Stochastic Multiscale Model for the Analysis of Energy Resources, Technology, and Policy," INFORMS Journal on Computing, INFORMS, vol. 24(4), pages 665-682, November.
    13. 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.
    14. 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.
    15. Astrid S. Kenyon & David P. Morton, 2003. "Stochastic Vehicle Routing with Random Travel Times," Transportation Science, INFORMS, vol. 37(1), pages 69-82, February.
    16. 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.
    17. 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.
    18. Birge, John R. & Louveaux, Francois V., 1988. "A multicut algorithm for two-stage stochastic linear programs," European Journal of Operational Research, Elsevier, vol. 34(3), pages 384-392, March.
    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. 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. 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.
    3. Huiying Wen & Yuchen Zeng & Zuogan Tang, 2019. "Sustainability and Resource Equilibrium Evaluation of a Tourism Traffic Network Based on a Tourism Traffic Matching Curve," Sustainability, MDPI, vol. 11(20), pages 1-22, October.

    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. Warren B. Powell, 2016. "Perspectives of approximate dynamic programming," Annals of Operations Research, Springer, vol. 241(1), pages 319-356, June.
    2. 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.
    3. 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.
    4. Fan, Wei & Machemehl, Randy, 2004. "A Multi-stage Monte Carlo Sampling Based Stochastic Programming Model for the Dynamic Vehicle Allocation Problem," 45th Annual Transportation Research Forum, Evanston, Illinois, March 21-23, 2004 208244, Transportation Research Forum.
    5. 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.
    6. Zhou, Shaorui & Zhang, Hui & Shi, Ning & Xu, Zhou & Wang, Fan, 2020. "A new convergent hybrid learning algorithm for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 283(1), pages 33-46.
    7. David P. Morton & R. Kevin Wood, 1999. "Restricted-Recourse Bounds for Stochastic Linear Programming," Operations Research, INFORMS, vol. 47(6), pages 943-956, December.
    8. 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.
    9. Fan, Wei, 2014. "Optimizing Strategic Allocation of Vehicles for One-Way Car-sharing Systems Under Demand Uncertainty," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 53(3).
    10. 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.
    11. Crainic, Teodor Gabriel & Laporte, Gilbert, 1997. "Planning models for freight transportation," European Journal of Operational Research, Elsevier, vol. 97(3), pages 409-438, March.
    12. Jia Shu & Miao Song, 2014. "Dynamic Container Deployment: Two-Stage Robust Model, Complexity, and Computational Results," INFORMS Journal on Computing, INFORMS, vol. 26(1), pages 135-149, February.
    13. Fei, Xin & Gülpınar, Nalân & Branke, Jürgen, 2019. "Efficient solution selection for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 277(3), pages 918-929.
    14. 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.
    15. 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).
    16. Warren Powell & Andrzej Ruszczyński & Huseyin Topaloglu, 2004. "Learning Algorithms for Separable Approximations of Discrete Stochastic Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 814-836, November.
    17. Antoine Sauré & Jonathan Patrick & Martin L. Puterman, 2015. "Simulation-Based Approximate Policy Iteration with Generalized Logistic Functions," INFORMS Journal on Computing, INFORMS, vol. 27(3), pages 579-595, August.
    18. Gabor, A.F. & Dekker, R. & van Dijk, T. & van Scheepstal, P., 2009. "Scheduling deliveries under uncertainty," ERIM Report Series Research in Management ERS-2009-040-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    19. C.H. Rosa & D. Yates, 1994. "Addressing the Issue of Uncertainty Within the Egyptian Agricultural Sector," Working Papers wp94097, International Institute for Applied Systems Analysis.
    20. Dong‐Ping Song & Jonathan Carter, 2008. "Optimal empty vehicle redistribution for hub‐and‐spoke transportation systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(2), pages 156-171, March.

    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:eee:ejores:v:233:y:2014:i:3:p:474-487. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.