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Maximum flow in hybrid network with intermediate storage

Author

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  • Badri Prasad Pangeni

    (Department of Mathematics, Prithvi Narayan Campus)

  • Tanka Nath Dhamala

    (Tribhuvan University)

Abstract

When uncertain and random arcs coexist with non-deterministic arc capacities in network optimization issues, chance space is used as the product of uncertain and probability space to arrive at the required answer. In order to determine the maximum flow in the hybrid network in this study, the intermediate storage at the vertices together with both uncertain and random arcs are introduced. The maximum flow model based on chance measure is first transformed into its deterministic equivalent by using the self dual and measure inversion properties, as well as a theorem on inverse uncertain distribution and the same qualities for probability measure. The intermediate vertices’ deterministic storing capability to the extent that it allows them to record the flow that is headed toward them is taken into account. As a generic solution to the issue, an algorithm for the maximum flow is then developed using the maximum flow distribution theorem. An illustrative example is provided to demonstrate the models’ and algorithms’ efficacy and level of efficiency. Additionally, a graphic comparison of the change in maximum flow values with and without intermediate storage is included.

Suggested Citation

  • Badri Prasad Pangeni & Tanka Nath Dhamala, 2025. "Maximum flow in hybrid network with intermediate storage," OPSEARCH, Springer;Operational Research Society of India, vol. 62(2), pages 833-849, June.
    • Handle: RePEc:spr:opsear:v:62:y:2025:i:2:d:10.1007_s12597-024-00816-7
    DOI: 10.1007/s12597-024-00816-7
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    References listed on IDEAS

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    1. Edward Minieka, 1973. "Maximal, Lexicographic, and Dynamic Network Flows," Operations Research, INFORMS, vol. 21(2), pages 517-527, April.
    2. Urmila Pyakurel & Tanka Nath Dhamala & Stephan Dempe, 2017. "Efficient continuous contraflow algorithms for evacuation planning problems," Annals of Operations Research, Springer, vol. 254(1), pages 335-364, July.
    3. George S. Fishman, 1987. "The Distribution of Maximum Flow with Applications to Multistate Reliability Systems," Operations Research, INFORMS, vol. 35(4), pages 607-618, August.
    4. 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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