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Maximal, Lexicographic, and Dynamic Network Flows

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  • Edward Minieka

    (University of Illinois, Chicago, Illinois)

Abstract

This paper proves two properties of maximal network flows: (1) If there exist a maximal network flow with a given departure pattern at the sources and a maximal flow with a given arrival pattern at the sinks, then there exists a flow that has both this departure pattern at the sources and this arrival pattern at the sinks. (2) There exists a maximal dynamic network flow that simultaneously has a latest (earliest) departure schedule at the sources and an earliest (latest) arrival schedule at the sinks. The paper modifies Ford and Fulkerson's maximal dynamic flow algorithm to construct a maximal dynamic network flow with a latest departure schedule and an earliest arrival schedule.

Suggested Citation

  • Edward Minieka, 1973. "Maximal, Lexicographic, and Dynamic Network Flows," Operations Research, INFORMS, vol. 21(2), pages 517-527, April.
    • Handle: RePEc:inm:oropre:v:21:y:1973:i:2:p:517-527
    DOI: 10.1287/opre.21.2.517
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    Cited by:

    1. Ryo Yamamoto & Atsushi Takizawa, 2019. "Partitioning Vertical Evacuation Areas in Umeda Underground Mall to Minimize the Evacuation Completion Time," The Review of Socionetwork Strategies, Springer, vol. 13(2), pages 209-225, October.
    2. Pursals, Salvador Casadesús & Garzón, Federico Garriga, 2009. "Optimal building evacuation time considering evacuation routes," European Journal of Operational Research, Elsevier, vol. 192(2), pages 692-699, 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. Urmila Pyakurel & Hari Nandan Nath & Stephan Dempe & Tanka Nath Dhamala, 2019. "Efficient Dynamic Flow Algorithms for Evacuation Planning Problems with Partial Lane Reversal," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    5. 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.
    6. Pyakurel, Urmila & Khanal, Durga Prasad & Dhamala, Tanka Nath, 2023. "Abstract network flow with intermediate storage for evacuation planning," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1178-1193.
    7. Nadine Baumann & Martin Skutella, 2009. "Earliest Arrival Flows with Multiple Sources," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 499-512, May.
    8. Bruce Hoppe & Éva Tardos, 2000. "The Quickest Transshipment Problem," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 36-62, February.
    9. 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.
    10. Urmila Pyakurel & Stephan Dempe, 2020. "Network Flow with Intermediate Storage: Models and Algorithms," SN Operations Research Forum, Springer, vol. 1(4), pages 1-23, December.
    11. Urmila Pyakurel & Hari Nandan Nath & Tanka Nath Dhamala, 2019. "Partial contraflow with path reversals for evacuation planning," Annals of Operations Research, Springer, vol. 283(1), pages 591-612, December.
    12. 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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