IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v82y2015i1p31-60.html
   My bibliography  Save this article

Computational complexity of convoy movement planning problems

Author

Listed:
  • Ram Gopalan

Abstract

Convoy movement planning problems arise in a number of important logistical contexts, including military planning, railroad optimization and automated guided vehicle routing. In the convoy movement problem (CMP), a set of convoys, with specified origins and destinations, are to be routed with the objective of minimizing either makespan or total flow time, while observing a number of side constraints. This paper characterizes the computational complexity of several restricted classes of CMPs. The principal objective is to identify the most parsimonious set of problem features that make the CMP intractable. A polynomial-time algorithm is provided for the single criterion two-convoy movement problem. The performance of a simple prioritization–idling approximation algorithm is also analyzed for the K-convoy movement problem. Error bounds are developed for the makespan and flow time objectives. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Ram Gopalan, 2015. "Computational complexity of convoy movement planning problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(1), pages 31-60, August.
    • Handle: RePEc:spr:mathme:v:82:y:2015:i:1:p:31-60
    DOI: 10.1007/s00186-015-0503-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00186-015-0503-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00186-015-0503-3?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. J Liu & R K Ahuja & G Şahin, 2008. "Optimal network configuration and capacity expansion of railroads," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(7), pages 911-920, July.
    2. R Gopalan & N S Narayanaswamy, 2009. "Analysis of algorithms for an online version of the convoy movement problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(9), pages 1230-1236, September.
    3. Desrochers, Martin & Soumis, Francois, 1988. "A reoptimization algorithm for the shortest path problem with time windows," European Journal of Operational Research, Elsevier, vol. 35(2), pages 242-254, May.
    4. Burdett, R.L. & Kozan, E., 2010. "A disjunctive graph model and framework for constructing new train schedules," European Journal of Operational Research, Elsevier, vol. 200(1), pages 85-98, January.
    5. Volgenant, A., 2002. "Solving some lexicographic multi-objective combinatorial problems," European Journal of Operational Research, Elsevier, vol. 139(3), pages 578-584, June.
    6. A L Tuson & S A Harrison, 2005. "Problem difficulty of real instances of convoy planning," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(7), pages 763-775, July.
    7. Nirup N. Krishnamurthy & Rajan Batta & Mark H. Karwan, 1993. "Developing Conflict-Free Routes for Automated Guided Vehicles," Operations Research, INFORMS, vol. 41(6), pages 1077-1090, December.
    8. David Kraay & Patrick T. Harker & Bintong Chen, 1991. "Optimal Pacing of Trains in Freight Railroads: Model Formulation and Solution," Operations Research, INFORMS, vol. 39(1), pages 82-99, February.
    9. S.A. Harrison & V.J. Rayward‐Smith, 1999. "Minimal cost linkages in graphs," Annals of Operations Research, Springer, vol. 86(0), pages 295-319, January.
    10. M Kress, 2001. "Efficient strategies for transporting mobile forces," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 310-317, March.
    11. Vis, Iris F.A., 2006. "Survey of research in the design and control of automated guided vehicle systems," European Journal of Operational Research, Elsevier, vol. 170(3), pages 677-709, May.
    12. Sherali, Hanif D., 1982. "Equivalent weights for lexicographic multi-objective programs: Characterizations and computations," European Journal of Operational Research, Elsevier, vol. 11(4), pages 367-379, December.
    13. L. R. Ford & D. R. Fulkerson, 1958. "Constructing Maximal Dynamic Flows from Static Flows," Operations Research, INFORMS, vol. 6(3), pages 419-433, June.
    14. Goldstein, Darin & Shehab, Tariq & Casse, Juan & Lin, Hsiu-Chin, 2010. "On the formulation and solution of the convoy routing problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(4), pages 520-533, July.
    15. Demange, Marc & Ekim, TInaz & de Werra, Dominique, 2009. "A tutorial on the use of graph coloring for some problems in robotics," European Journal of Operational Research, Elsevier, vol. 192(1), pages 41-55, January.
    16. Lee, Yusin & Chen, Chuen-Yih, 2009. "A heuristic for the train pathing and timetabling problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 837-851, September.
    17. Higgins, A. & Kozan, E. & Ferreira, L., 1996. "Optimal scheduling of trains on a single line track," Transportation Research Part B: Methodological, Elsevier, vol. 30(2), pages 147-161, April.
    18. P. N. Ram Kumar & T. T. Narendran, 2009. "A Mathematical Approach for Variable Speed Convoy Movement Problem(CMP)," Defense & Security Analysis, Taylor & Francis Journals, vol. 25(2), pages 137-155, June.
    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. Azar Sadeghnejad-Barkousaraie & Rajan Batta & Moises Sudit, 2017. "Convoy movement problem: a civilian perspective," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 14-33, January.

    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. Mokhtar, Hamid & Krishnamoorthy, Mohan & Dayama, Niraj Ramesh & Kumar, P.N. Ram, 2020. "New approaches for solving the convoy movement problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    2. Azar Sadeghnejad-Barkousaraie & Rajan Batta & Moises Sudit, 2017. "Convoy movement problem: a civilian perspective," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(1), pages 14-33, January.
    3. R Gopalan & N S Narayanaswamy, 2009. "Analysis of algorithms for an online version of the convoy movement problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(9), pages 1230-1236, September.
    4. Alan J. Maniamkot & P. N. Ram Kumar & Mohan Krishnamoorthy & Hamid Mokhtar & Sridharan Rajagopalan, 2022. "Hybridised ant colony optimisation for convoy movement problem," Annals of Operations Research, Springer, vol. 315(2), pages 847-866, August.
    5. Zhou, Wenliang & Tian, Junli & Xue, Lijuan & Jiang, Min & Deng, Lianbo & Qin, Jin, 2017. "Multi-periodic train timetabling using a period-type-based Lagrangian relaxation decomposition," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 144-173.
    6. Elisabeth Lübbecke & Marco E. Lübbecke & Rolf H. Möhring, 2019. "Ship Traffic Optimization for the Kiel Canal," Operations Research, INFORMS, vol. 67(3), pages 791-812, May.
    7. Julia Lange & Frank Werner, 2018. "Approaches to modeling train scheduling problems as job-shop problems with blocking constraints," Journal of Scheduling, Springer, vol. 21(2), pages 191-207, April.
    8. Zhang, Chuntian & Gao, Yuan & Yang, Lixing & Gao, Ziyou & Qi, Jianguo, 2020. "Joint optimization of train scheduling and maintenance planning in a railway network: A heuristic algorithm using Lagrangian relaxation," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 64-92.
    9. Paul Corry & Christian Bierwirth, 2019. "The Berth Allocation Problem with Channel Restrictions," Transportation Science, INFORMS, vol. 53(3), pages 708-727, May.
    10. Wang, Yihui & Tang, Tao & Ning, Bin & Meng, Lingyun, 2017. "Integrated optimization of regular train schedule and train circulation plan for urban rail transit lines," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 105(C), pages 83-104.
    11. Jenny Nossack & Dirk Briskorn & Erwin Pesch, 2018. "Container Dispatching and Conflict-Free Yard Crane Routing in an Automated Container Terminal," Transportation Science, INFORMS, vol. 52(5), pages 1059-1076, October.
    12. Chen, Zebin & Li, Shukai & D’Ariano, Andrea & Yang, Lixing, 2022. "Real-time optimization for train regulation and stop-skipping adjustment strategy of urban rail transit lines," Omega, Elsevier, vol. 110(C).
    13. Lee, Yusin & Chen, Chuen-Yih, 2009. "A heuristic for the train pathing and timetabling problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(8-9), pages 837-851, September.
    14. Min Zhang & Rajan Batta & Rakesh Nagi, 2009. "Modeling of Workflow Congestion and Optimization of Flow Routing in a Manufacturing/Warehouse Facility," Management Science, INFORMS, vol. 55(2), pages 267-280, February.
    15. Wenliang Zhou & Wenzhuang Fan & Xiaorong You & Lianbo Deng, 2019. "Demand-Oriented Train Timetabling Integrated with Passenger Train-Booking Decisions," Sustainability, MDPI, vol. 11(18), pages 1-34, September.
    16. E. Ursavas & Stuart X. Zhu, 2018. "Integrated Passenger and Freight Train Planning on Shared-Use Corridors," Service Science, INFORMS, vol. 52(6), pages 1376-1390, December.
    17. Xuesong Feng & Hanxiao Zhang & Yong Ding & Zhili Liu & Hongqin Peng & Bin Xu, 2013. "A Review Study on Traction Energy Saving of Rail Transport," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-9, September.
    18. Kaspar Schüpbach & Rico Zenklusen, 2013. "An adaptive routing approach for personal rapid transit," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 371-380, June.
    19. Jonas Harbering & Abhiram Ranade & Marie Schmidt & Oliver Sinnen, 2019. "Complexity, bounds and dynamic programming algorithms for single track train scheduling," Annals of Operations Research, Springer, vol. 273(1), pages 479-500, February.
    20. Min, Yun-Hong & Park, Myoung-Ju & Hong, Sung-Pil & Hong, Soon-Heum, 2011. "An appraisal of a column-generation-based algorithm for centralized train-conflict resolution on a metropolitan railway network," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 409-429, February.

    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:spr:mathme:v:82:y:2015:i:1:p:31-60. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.