IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v28y1982i1p106-109.html
   My bibliography  Save this article

Note---Some Equivalent Objectives for Dynamic Network Flow Problems

Author

Listed:
  • John J. Jarvis

    (Georgia Institute of Technology)

  • H. Donald Ratliff

    (Georgia Institute of Technology)

Abstract

Many important problems can be modeled as dynamic (time-expanded) network flow problems. For example, in building evacuation we might use twenty nodes to represent a room at 3 minute intervals over an hour, and use arcs to indicate the feasible passages, over time, among the various rooms. The purpose of this note is to demonstrate that it is possible to satisfy at least three important objectives simultaneously in a maximal dynamic network flow problem. These are (1) construction of an earliest arrival schedule (i.e., a solution which maximizes flow in the first p periods, for every p), (2) minimization of the period at which the last unit of flow arrives at the sink, and (3) minimization of the average time for all flow to arrive at the sink.

Suggested Citation

  • John J. Jarvis & H. Donald Ratliff, 1982. "Note---Some Equivalent Objectives for Dynamic Network Flow Problems," Management Science, INFORMS, vol. 28(1), pages 106-109, January.
  • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:1:p:106-109
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.28.1.106
    Download Restriction: no

    Citations

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


    Cited by:

    1. Bish, Douglas R. & Sherali, Hanif D., 2013. "Aggregate-level demand management in evacuation planning," European Journal of Operational Research, Elsevier, vol. 224(1), pages 79-92.
    2. Ismaila Abderhamane Ndiaye & Emmanuel Neron & Antoine Jouglet, 2017. "Macroscopic evacuation plans for natural disasters," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 231-272, January.
    3. repec:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2302-5 is not listed on IDEAS
    4. Bretschneider, S. & Kimms, A., 2011. "A basic mathematical model for evacuation problems in urban areas," Transportation Research Part A: Policy and Practice, Elsevier, vol. 45(6), pages 523-539, July.
    5. Xiaozheng He & Srinivas Peeta, 2014. "Dynamic Resource Allocation Problem for Transportation Network Evacuation," Networks and Spatial Economics, Springer, vol. 14(3), pages 505-530, December.
    6. Bretschneider, S. & Kimms, A., 2012. "Pattern-based evacuation planning for urban areas," European Journal of Operational Research, Elsevier, vol. 216(1), pages 57-69.
    7. repec:pal:jorsoc:v:56:y:2005:i:6:d:10.1057_palgrave.jors.2601875 is not listed on IDEAS
    8. Jian Li & Kaan Ozbay, 2015. "Evacuation Planning with Endogenous Transportation Network Degradations: A Stochastic Cell-Based Model and Solution Procedure," Networks and Spatial Economics, Springer, vol. 15(3), pages 677-696, September.
    9. Yu-Ting Hsu & Srinivas Peeta, 2015. "Clearance Time Estimation for Incorporating Evacuation Risk in Routing Strategies for Evacuation Operations," Networks and Spatial Economics, Springer, vol. 15(3), pages 743-764, September.
    10. Fry, John & Binner, Jane M., 2016. "Elementary modelling and behavioural analysis for emergency evacuations using social media," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1014-1023.

    More about this item

    Keywords

    network models: theory; dynamic flows;

    Statistics

    Access and download statistics

    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:ormnsc:v:28:y:1982:i:1:p:106-109. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mirko Janc). General contact details of provider: http://edirc.repec.org/data/inforea.html .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.