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American Journal of Applied Mathematics and Statistics. 2019, 7(6), 191-195
DOI: 10.12691/AJAMS-7-6-1
Original Research

The Fuzzy Minimum Cost Flow Problem with the Fuzzy Time-Windows

Nasser A. El-Sherbeny1,

1Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt

Pub. Date: November 25, 2019
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Cite this paper

Nasser A. El-Sherbeny. The Fuzzy Minimum Cost Flow Problem with the Fuzzy Time-Windows. American Journal of Applied Mathematics and Statistics. 2019; 7(6):191-195. doi: 10.12691/AJAMS-7-6-1

Abstract

The Minimum Cost Flow Problem (MCFP) is a well-known combinatorial optimization and a logical distribution problem. The MCFP is an NP-hard problem with many applications in logistic networks and computer networks. The Fuzzy Minimum Cost Flow Problem with Fuzzy Time-Windows (FMCFPFTW) is an extension of the MCFP. The goal of the problem is to find the minimum amount of the fuzzy flow from the source to the sink that satisfies all constraints of the fuzzy shortest dynamic f-augmenting path with the fuzzy dynamic residual network. We consider a generalized fuzzy version of the MCFP of the fuzzy network. We propose the mathematical model of the FMCFPFTW. Finally, a new algorithm of the FMCFPFTW is presented.

Keywords

combinatorial optimization, minimum cost flow, time-windows, fuzzy time-windows

Copyright

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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