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


  • John J. Jarvis

    (Georgia Institute of Technology)

  • H. Donald Ratliff

    (Georgia Institute of Technology)


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

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    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.

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    network models: theory; dynamic flows;


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