IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v198y2009i2p405-411.html
   My bibliography  Save this article

A Lagrangian relaxation approach to large-scale flow interception problems

Author

Listed:
  • Gzara, Fatma
  • Erkut, Erhan

Abstract

The paper presents a tight Lagrangian bound and an efficient dual heuristic for the flow interception problem. The proposed Lagrangian relaxation decomposes the problem into two subproblems that are easy to solve. Information from one of the subproblems is used within a dual heuristic to construct feasible solutions and is used to generate valid cuts that strengthen the relaxation. Both the heuristic and the relaxation are integrated into a cutting plane method where the Lagrangian bound is calculated using a subgradient algorithm. In the course of the algorithm, a valid cut is added and integrated efficiently in the second subproblem and is updated whenever the heuristic solution improves. The algorithm is tested on randomly generated test problems with up to 500 vertices, 12,483 paths, and 43 facilities. The algorithm finds a proven optimal solution in more than 75% of the cases, while the feasible solution is on average within 0.06% from the upper bound.

Suggested Citation

  • Gzara, Fatma & Erkut, Erhan, 2009. "A Lagrangian relaxation approach to large-scale flow interception problems," European Journal of Operational Research, Elsevier, vol. 198(2), pages 405-411, October.
    • Handle: RePEc:eee:ejores:v:198:y:2009:i:2:p:405-411
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00742-X
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    2. Bazaraa, Mokhtar S. & Sherali, Hanif D., 1981. "On the choice of step size in subgradient optimization," European Journal of Operational Research, Elsevier, vol. 7(4), pages 380-388, August.
    3. John Hodgson, M., 1981. "The location of public facilities intermediate to the journey to work," European Journal of Operational Research, Elsevier, vol. 6(2), pages 199-204, February.
    4. Oded Berman & Richard C. Larson & Nikoletta Fouska, 1992. "Optimal Location of Discretionary Service Facilities," Transportation Science, INFORMS, vol. 26(3), pages 201-211, August.
    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. Ghaddar, Bissan & Naoum-Sawaya, Joe & Kishimoto, Akihiro & Taheri, Nicole & Eck, Bradley, 2015. "A Lagrangian decomposition approach for the pump scheduling problem in water networks," European Journal of Operational Research, Elsevier, vol. 241(2), pages 490-501.
    2. Marković, Nikola & Ryzhov, Ilya O. & Schonfeld, Paul, 2017. "Evasive flow capture: A multi-period stochastic facility location problem with independent demand," European Journal of Operational Research, Elsevier, vol. 257(2), pages 687-703.
    3. Miyagawa, Masashi, 2010. "Distributions of rectilinear deviation distance to visit a facility," European Journal of Operational Research, Elsevier, vol. 205(1), pages 106-112, August.
    4. Mohammad Nezhad, Ali & Manzour, Hasan & Salhi, Said, 2013. "Lagrangian relaxation heuristics for the uncapacitated single-source multi-product facility location problem," International Journal of Production Economics, Elsevier, vol. 145(2), pages 713-723.

    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. Nadjib Brahimi & Stéphane Dauzère-Pérès & Najib M. Najid, 2006. "Capacitated Multi-Item Lot-Sizing Problems with Time Windows," Operations Research, INFORMS, vol. 54(5), pages 951-967, October.
    2. Miyagawa, Masashi, 2010. "Distributions of rectilinear deviation distance to visit a facility," European Journal of Operational Research, Elsevier, vol. 205(1), pages 106-112, August.
    3. Nourbakhsh, Seyed Mohammad & Ouyang, Yanfeng, 2010. "Optimal fueling strategies for locomotive fleets in railroad networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1104-1114, September.
    4. Tragantalerngsak, Suda & Holt, John & Ronnqvist, Mikael, 1997. "Lagrangian heuristics for the two-echelon, single-source, capacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 102(3), pages 611-625, November.
    5. Bayraktar, O. Baturhan & Günneç, Dilek & Salman, F. Sibel & Yücel, Eda, 2022. "Relief Aid Provision to En Route Refugees: Multi-Period Mobile Facility Location with Mobile Demand," European Journal of Operational Research, Elsevier, vol. 301(2), pages 708-725.
    6. Tong, Daoqin & Ren, Fang & Mack, James, 2012. "Locating farmers’ markets with an incorporation of spatio-temporal variation," Socio-Economic Planning Sciences, Elsevier, vol. 46(2), pages 149-156.
    7. Berman, Obed, 1995. "The maximizing market size discretionary facility location problem with congestion," Socio-Economic Planning Sciences, Elsevier, vol. 29(1), pages 39-46, March.
    8. Marković, Nikola & Ryzhov, Ilya O. & Schonfeld, Paul, 2017. "Evasive flow capture: A multi-period stochastic facility location problem with independent demand," European Journal of Operational Research, Elsevier, vol. 257(2), pages 687-703.
    9. Michel Gendreau & Gilbert Laporte & Isabelle Parent, 2000. "Heuristics for the location of inspection stations on a network," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(4), pages 287-303, June.
    10. Lorena, Luiz Antonio N. & Goncalves Narciso, Marcelo, 2002. "Using logical surrogate information in Lagrangean relaxation: An application to symmetric traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 138(3), pages 473-483, May.
    11. Simin Huang & Rajan Batta & Rakesh Nagi, 2005. "Distribution network design: Selection and sizing of congested connections," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 701-712, December.
    12. John Hodgson, M. & Rosing, K. E. & Leontien, A. & Storrier, G., 1996. "Applying the flow-capturing location-allocation model to an authentic network: Edmonton, Canada," European Journal of Operational Research, Elsevier, vol. 90(3), pages 427-443, May.
    13. Bai, Yun & Ouyang, Yanfeng & Pang, Jong-Shi, 2016. "Enhanced models and improved solution for competitive biofuel supply chain design under land use constraints," European Journal of Operational Research, Elsevier, vol. 249(1), pages 281-297.
    14. Wolosewicz, Cathy & Dauzère-Pérès, Stéphane & Aggoune, Riad, 2015. "A Lagrangian heuristic for an integrated lot-sizing and fixed scheduling problem," European Journal of Operational Research, Elsevier, vol. 244(1), pages 3-12.
    15. M Diaby & A L Nsakanda, 2006. "Large-scale capacitated part-routing in the presence of process and routing flexibilities and setup costs," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(9), pages 1100-1112, September.
    16. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    17. Mutsunori Yagiura & Toshihide Ibaraki & Fred Glover, 2004. "An Ejection Chain Approach for the Generalized Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 133-151, May.
    18. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    19. Shangyao Yan & Chun-Ying Chen & Chuan-Che Wu, 2012. "Solution methods for the taxi pooling problem," Transportation, Springer, vol. 39(3), pages 723-748, May.
    20. Chou, Chang-Chi & Chiang, Wen-Chu & Chen, Albert Y., 2022. "Emergency medical response in mass casualty incidents considering the traffic congestions in proximity on-site and hospital delays," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).

    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:198:y:2009:i:2:p:405-411. 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.