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Abstract

Multi-Commodity Contraflow Problem on Lossy Network with Asymmetric Transit times †

by
Shiva Prakash Gupta
*,
Urmila Pyakurel
and
Tanka Nath Dhamala
Central Department of Mathematics, Tribhuvan University, Kirtipur 44618, Nepal
*
Author to whom correspondence should be addressed.
Presented at the 1st International Electronic Conference on Algorithms, 27 September–10 October 2021; Available online: https://ioca2021.sciforum.net/.
Comput. Sci. Math. Forum 2022, 2(1), 21; https://doi.org/10.3390/IOCA2021-10878
Published: 19 September 2021
(This article belongs to the Proceedings of The 1st International Electronic Conference on Algorithms)

Abstract

:
During the transmission of commodities from one place to another, there may be loss due to death, leakage, damage, or evaporation. To address this problem, each arc of the network contains a gain factor. The network is a lossy network with a gain factor of at most one on each arc. The generalized multi-commodity flow problem deals with routing several distinct goods from specific supply points to the corresponding demand points on an underlying network with minimum loss. The sum of all commodities on each arc does not exceed its capacity. Motivated by the uneven road condition of transportation network topology, we incorporate a contraflow approach with orientation-dependent transit times on arcs and introduce the generalized multi-commodity contraflow problem on a lossy network with orientation-dependent transit times. In general, the generalized dynamic multi-commodity contraflow problem is NP-hard. For a lossy network with a symmetric transit time on anti-parallel arcs, the problem is solved in pseudo-polynomial time. We extend the analytical solution with a symmetric transit time on anti-parallel arcs to asymmetric transit times and present algorithms that solve it within the same time-complexity.

Supplementary Materials

The conference presentation file is available at https://www.mdpi.com/article/10.3390/IOCA2021-10878/s1.

Author Contributions

S.P.G.—conceptualization, investigation and documentation, U.P., and T.N.D.—formal analysis, editing and supervision. All authors have read and agreed to the published version of the manuscript.

Funding

This research work received no specific grants from any funding in the public, commercial or non-profit organizations.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The authors have not used any additional data in this article.

Conflicts of Interest

Authors have no conflict of interest regarding the publication of the paper.
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Share and Cite

MDPI and ACS Style

Gupta, S.P.; Pyakurel, U.; Dhamala, T.N. Multi-Commodity Contraflow Problem on Lossy Network with Asymmetric Transit times. Comput. Sci. Math. Forum 2022, 2, 21. https://doi.org/10.3390/IOCA2021-10878

AMA Style

Gupta SP, Pyakurel U, Dhamala TN. Multi-Commodity Contraflow Problem on Lossy Network with Asymmetric Transit times. Computer Sciences & Mathematics Forum. 2022; 2(1):21. https://doi.org/10.3390/IOCA2021-10878

Chicago/Turabian Style

Gupta, Shiva Prakash, Urmila Pyakurel, and Tanka Nath Dhamala. 2022. "Multi-Commodity Contraflow Problem on Lossy Network with Asymmetric Transit times" Computer Sciences & Mathematics Forum 2, no. 1: 21. https://doi.org/10.3390/IOCA2021-10878

APA Style

Gupta, S. P., Pyakurel, U., & Dhamala, T. N. (2022). Multi-Commodity Contraflow Problem on Lossy Network with Asymmetric Transit times. Computer Sciences & Mathematics Forum, 2(1), 21. https://doi.org/10.3390/IOCA2021-10878

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