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Multi-commodity flow problem on lossy network with partial lane reversals

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Abstract

During the transmission of several different commodities from respective sources to the sinks, there may be loss due to leakage, evaporation, or damage. The generalized multi-commodity flow problem on a lossy network deals with the transshipment of these commodities from the origin nodes to the destination nodes − not violating the capacity constraints on each arc with minimum loss. Partial lane reversal strategy makes traffic systematic and smooth by flipping the orientation of necessary road segments that improve the flow value and significantly minimize the loss. In this paper, we introduce maximum generalized static multi-commodity flow, maximum generalized dynamic multi-commodity flow, and generalized earliest arrival multi-commodity flow problems on a lossy network with partial lane reversals, and present algorithms to solve these problems in pseudo-polynomial time complexity. We also present a fully polynomial-time approximation scheme for the maximum generalized dynamic multi-commodity flow problem with partial lane reversals.

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Acknowledgements

The first author thanks the University Grants Commission, Nepal, for his Ph.D. research fellowship and the second author thanks to the Alexander von Humboldt Foundation for Digital Cooperation Fellowship (August 1, 2021 - January 31, 2022) and for Remote Cooperation Aboard Fellowship (March 1 - August 30, 2022). The authors would also like to thank the anonymous referees and the editor for their valuable suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Tri-Chandra Multiple Campus, Tribhuvan University, Kathmandu, Nepal

    Shiva Prakash Gupta

  2. Central Department of Mathematics, Tribhuvan University, Kathmandu, Nepal

    Urmila Pyakurel & Tanka Nath Dhamala

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  1. Shiva Prakash Gupta
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  2. Urmila Pyakurel
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  3. Tanka Nath Dhamala
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Correspondence to Urmila Pyakurel.

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Gupta, S.P., Pyakurel, U. & Dhamala, T.N. Multi-commodity flow problem on lossy network with partial lane reversals. Ann Oper Res 323, 45–63 (2023). https://doi.org/10.1007/s10479-023-05210-y

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