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

Shiva Prakash Gupta (), Urmila Pyakurel () and Tanka Nath Dhamala ()
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Shiva Prakash Gupta: Tribhuvan University
Urmila Pyakurel: Tribhuvan University
Tanka Nath Dhamala: Tribhuvan University

Annals of Operations Research, 2023, vol. 323, issue 1, No 3, 45-63

Abstract: 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.

Keywords: Network flow; Generalized multi-commodity flow; Lossy network; Lane reversals; Primary: 90B10; 90C27; 68Q25; Secondary: 90B06; 90B20. (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10479-023-05210-y

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