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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
    DOI: 10.1287/mnsc.28.1.106
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    Cited by:

    1. Hong Zheng & Yi-Chang Chiu, 2011. "A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem," Transportation Science, INFORMS, vol. 45(1), pages 121-137, February.
    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. Urmila Pyakurel & Tanka Nath Dhamala, 2017. "Continuous Dynamic Contraflow Approach for Evacuation Planning," Annals of Operations Research, Springer, vol. 253(1), pages 573-598, June.
    4. 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.
    5. Bretschneider, S. & Kimms, A., 2012. "Pattern-based evacuation planning for urban areas," European Journal of Operational Research, Elsevier, vol. 216(1), pages 57-69.
    6. Douglas Bish & Esra Agca & Roger Glick, 2014. "Decision support for hospital evacuation and emergency response," Annals of Operations Research, Springer, vol. 221(1), pages 89-106, October.
    7. K L Poh & K W Choo & C G Wong, 2005. "A heuristic approach to the multi-period multi-commodity transportation problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 708-718, June.
    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. 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.
    10. Matthew R. Silver & Olivier L. de Weck, 2007. "Time‐expanded decision networks: A framework for designing evolvable complex systems," Systems Engineering, John Wiley & Sons, vol. 10(2), pages 167-188, June.
    11. Sadegh Mirshekarian, 2015. "Enhanced Time‐Expanded Decision Network: The Original TDN and More," Systems Engineering, John Wiley & Sons, vol. 18(4), pages 415-429, July.
    12. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2007. "Fast, Fair, and Efficient Flows in Networks," Operations Research, INFORMS, vol. 55(2), pages 215-225, April.
    13. 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.
    14. Natashia Boland & Mike Hewitt & Luke Marshall & Martin Savelsbergh, 2017. "The Continuous-Time Service Network Design Problem," Operations Research, INFORMS, vol. 65(5), pages 1303-1321, October.
    15. Nadine Baumann & Martin Skutella, 2009. "Earliest Arrival Flows with Multiple Sources," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 499-512, May.
    16. Lichun Chen & Elise Miller‐Hooks, 2008. "The building evacuation problem with shared information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(4), pages 363-376, June.
    17. H. W. Hamacher & S. Tufekci, 1987. "On the use of lexicographic min cost flows in evacuation modeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(4), pages 487-503, August.
    18. 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.
    19. 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.
    20. Hong Zheng & Yi-Chang Chiu & Pitu B. Mirchandani, 2015. "On the System Optimum Dynamic Traffic Assignment and Earliest Arrival Flow Problems," Transportation Science, INFORMS, vol. 49(1), pages 13-27, February.
    21. Tanka Nath Dhamala & Urmila Pyakurel & Ram Chandra Dhungana, 2018. "Abstract Contraflow Models and Solution Procedures for Evacuation Planning," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 10(4), pages 89-100, August.

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    Keywords

    network models: theory; dynamic flows;

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