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Network Flow with Intermediate Storage: Models and Algorithms

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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.

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Acknowledgments

The first author acknowledges the support of Alexander von Humboldt Foundation to her post doctoral research stay (November 2017–October 2019) at TU Bergakademie, Freiberg, Germany and her return fellowship (November 2019–October 2020) at Central Department of Mathematics, TU, Nepal. The authors would also like to thank the anonymous reviewers for their constructive suggestions.

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Authors and Affiliations

  1. Central Department of Mathematics, Tribhuvan University, P.O.Box 13143, Kathmandu, Nepal

    Urmila Pyakurel

  2. Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, Freiberg, Germany

    Stephan Dempe

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  1. Urmila Pyakurel
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Correspondence to Urmila Pyakurel.

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Pyakurel, U., Dempe, S. Network Flow with Intermediate Storage: Models and Algorithms. SN Oper. Res. Forum 1, 37 (2020). https://doi.org/10.1007/s43069-020-00033-0

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