American Journal of Applied Mathematics and Statistics
ISSN (Print): 2328-7306 ISSN (Online): 2328-7292 Website: Editor-in-chief: Mohamed Seddeek
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American Journal of Applied Mathematics and Statistics. 2019, 7(6), 191-195
DOI: 10.12691/ajams-7-6-1
Open AccessArticle

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

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


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.

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

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