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An Algorithm for Universal Maximal Dynamic Flows in a Network

Author

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  • W. L. Wilkinson

    (The George Washington University, Washington, D.C.)

Abstract

This paper presents a modification to the Ford-Fulkerson algorithm for maximal dynamic flow in a time-weighted, capacitated network. The modification is mild, as conjectured by Gale, and produces a shipping schedule representing what has been termed the universal maximal dynamic flow. The universal feature is that, in constructing a schedule for P periods, this same schedule is maximal when truncated to p less than P periods. A numerical example compares the temporally repeated and universal-type solutions.

Suggested Citation

  • W. L. Wilkinson, 1971. "An Algorithm for Universal Maximal Dynamic Flows in a Network," Operations Research, INFORMS, vol. 19(7), pages 1602-1612, December.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:7:p:1602-1612
    DOI: 10.1287/opre.19.7.1602
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    Cited by:

    1. 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.
    2. 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.
    3. Nadine Baumann & Martin Skutella, 2009. "Earliest Arrival Flows with Multiple Sources," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 499-512, May.
    4. Horst Hamacher & Stephanie Heller & Benjamin Rupp, 2013. "Flow location (FlowLoc) problems: dynamic network flows and location models for evacuation planning," Annals of Operations Research, Springer, vol. 207(1), pages 161-180, August.
    5. 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.
    6. 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.

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