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Network Flow with Intermediate Storage: Models and Algorithms

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  • Urmila Pyakurel

    (Tribhuvan University)

  • Stephan Dempe

    (TU Bergakademie Freiberg)

Abstract

Various network flow models, such as a flow maximization, a time minimization, a cost minimization, or a combination of them, have already been investigated. In most of the cases, they are considered subject to the flow conservation constraints. Here, we investigate the network flow models with intermediate storage, i.e., the inflow may be greater than the outflow at intermediate nodes. We introduce a maximum static and a maximum dynamic flow problem where an intermediate storage is allowed. Then, polynomial time algorithms are presented to solve these problems in two terminal general networks. We also study the earliest arrival property of the maximum dynamic flow in two terminal series-parallel networks and present its efficient solution procedure with intermediate storage. Moreover, we introduce a dynamic contraflow model with intermediate storage and present a polynomial time algorithm to solve the maximum dynamic contraflow problem in two terminal networks. We also solve an earliest arrival contraflow problem with intermediate storage. Our investigation is focused to solve the evacuation planning problem where the intermediate storage is permitted.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:snopef:v:1:y:2020:i:4:d:10.1007_s43069-020-00033-0
    DOI: 10.1007/s43069-020-00033-0
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    References listed on IDEAS

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    7. 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.
    8. 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.
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    Cited by:

    1. Shiva Prakash Gupta & Urmila Pyakurel & Tanka Nath Dhamala, 2023. "Multi-commodity flow problem on lossy network with partial lane reversals," Annals of Operations Research, Springer, vol. 323(1), pages 45-63, April.
    2. Durga Prasad Khanal & Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2022. "Efficient Algorithms for Abstract Flow with Partial Switching," SN Operations Research Forum, Springer, vol. 3(4), pages 1-17, December.
    3. 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.
    4. Bayram, Vedat & Yaman, Hande, 2024. "A joint demand and supply management approach to large scale urban evacuation planning: Evacuate or shelter-in-place, staging and dynamic resource allocation," European Journal of Operational Research, Elsevier, vol. 313(1), pages 171-191.

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