Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem<br />
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Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake; Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake

doi:doi:10.11648/j.ajam.20231105.11

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Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake, Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake

Published in American Journal of Applied Mathematics (Volume 11, Issue 5)

Received: 1 August 2023 Accepted: 21 August 2023 Published: 28 October 2023

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Abstract

A transportation problem (TP) is a specific part of a linear programming problem that arises in a collection of contexts and has received much attention in the literature. Minimizing transportation costs or time (one objective) is one of the primary goals of transportation problem-solving approaches. Supply, demand, and unit transportation costs may be uncertain in real-life applications due to many factors, such as multiple objectives. The goal of this paper is to look at the fuzzy transportation problem (FTP), which is crucial in TP with multiple objectives. In the literature, numerous techniques for dealing with FTPs are proposed. The cost, supply, and demand values of the FTPs are taken as symmetric triangular fuzzy numbers and then converted into crisp values using ranking techniques to solve the FTP. The initial solution is then obtained by Vogel’s approximation method (VAM), and the optimal solution is obtained by the modified distribution method (MODI). The proposed method is based on the Modified Fractional Knapsack Problem and introduces a new approach to solving the triangular fuzzy transportation problem. This paper analyses an alternative method using the fractional knapsack problem, which was modified using a minimum ratio test. To express the efficiency of the proposed method, it is compared with existing methods in the literature.

Published in	American Journal of Applied Mathematics (Volume 11, Issue 5)
DOI	10.11648/j.ajam.20231105.11
Page(s)	77-88
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fractional Knapsack Problem, Fuzzy Transportation Problem, Harmonic Mean, Initial Feasible Solution, Minimum Ratio Test, Triangular Fuzzy Numbers

References

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APA Style

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake, Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake. (2023). Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem . American Journal of Applied Mathematics, 11(5), 77-88. https://doi.org/10.11648/j.ajam.20231105.11

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ACS Style

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake; Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake. Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem . Am. J. Appl. Math. 2023, 11(5), 77-88. doi: 10.11648/j.ajam.20231105.11

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AMA Style

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake, Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake. Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem . Am J Appl Math. 2023;11(5):77-88. doi: 10.11648/j.ajam.20231105.11

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@article{10.11648/j.ajam.20231105.11,
  author = {Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake and Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake},
  title = {Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem

	
},
  journal = {American Journal of Applied Mathematics},
  volume = {11},
  number = {5},
  pages = {77-88},
  doi = {10.11648/j.ajam.20231105.11},
  url = {https://doi.org/10.11648/j.ajam.20231105.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20231105.11},
  abstract = {A transportation problem (TP) is a specific part of a linear programming problem that arises in a collection of contexts and has received much attention in the literature. Minimizing transportation costs or time (one objective) is one of the primary goals of transportation problem-solving approaches. Supply, demand, and unit transportation costs may be uncertain in real-life applications due to many factors, such as multiple objectives. The goal of this paper is to look at the fuzzy transportation problem (FTP), which is crucial in TP with multiple objectives. In the literature, numerous techniques for dealing with FTPs are proposed. The cost, supply, and demand values of the FTPs are taken as symmetric triangular fuzzy numbers and then converted into crisp values using ranking techniques to solve the FTP. The initial solution is then obtained by Vogel’s approximation method (VAM), and the optimal solution is obtained by the modified distribution method (MODI). The proposed method is based on the Modified Fractional Knapsack Problem and introduces a new approach to solving the triangular fuzzy transportation problem. This paper analyses an alternative method using the fractional knapsack problem, which was modified using a minimum ratio test. To express the efficiency of the proposed method, it is compared with existing methods in the literature.
},
 year = {2023}
}

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TY  - JOUR
T1  - Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem

	

AU  - Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake
AU  - Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake
Y1  - 2023/10/28
PY  - 2023
N1  - https://doi.org/10.11648/j.ajam.20231105.11
DO  - 10.11648/j.ajam.20231105.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 77
EP  - 88
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20231105.11
AB  - A transportation problem (TP) is a specific part of a linear programming problem that arises in a collection of contexts and has received much attention in the literature. Minimizing transportation costs or time (one objective) is one of the primary goals of transportation problem-solving approaches. Supply, demand, and unit transportation costs may be uncertain in real-life applications due to many factors, such as multiple objectives. The goal of this paper is to look at the fuzzy transportation problem (FTP), which is crucial in TP with multiple objectives. In the literature, numerous techniques for dealing with FTPs are proposed. The cost, supply, and demand values of the FTPs are taken as symmetric triangular fuzzy numbers and then converted into crisp values using ranking techniques to solve the FTP. The initial solution is then obtained by Vogel’s approximation method (VAM), and the optimal solution is obtained by the modified distribution method (MODI). The proposed method is based on the Modified Fractional Knapsack Problem and introduces a new approach to solving the triangular fuzzy transportation problem. This paper analyses an alternative method using the fractional knapsack problem, which was modified using a minimum ratio test. To express the efficiency of the proposed method, it is compared with existing methods in the literature.

VL  - 11
IS  - 5
ER  -

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Author Information

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake

Department of Mathematics, Faculty of Natural Sciences, The Open University of Sri Lanka, Nugegoda, Sri Lanka
Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake

Department of Applied Sciences, Faculty of Physical Sciences, Rajarata University of Sri Lanka, Anuradhapura, Sri Lanka

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APA Style

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake, Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake. (2023). Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem . American Journal of Applied Mathematics, 11(5), 77-88. https://doi.org/10.11648/j.ajam.20231105.11

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ACS Style

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake; Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake. Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem . Am. J. Appl. Math. 2023, 11(5), 77-88. doi: 10.11648/j.ajam.20231105.11

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AMA Style

Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake, Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake. Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem . Am J Appl Math. 2023;11(5):77-88. doi: 10.11648/j.ajam.20231105.11

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@article{10.11648/j.ajam.20231105.11,
  author = {Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake and Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake},
  title = {Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem

	
},
  journal = {American Journal of Applied Mathematics},
  volume = {11},
  number = {5},
  pages = {77-88},
  doi = {10.11648/j.ajam.20231105.11},
  url = {https://doi.org/10.11648/j.ajam.20231105.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20231105.11},
  abstract = {A transportation problem (TP) is a specific part of a linear programming problem that arises in a collection of contexts and has received much attention in the literature. Minimizing transportation costs or time (one objective) is one of the primary goals of transportation problem-solving approaches. Supply, demand, and unit transportation costs may be uncertain in real-life applications due to many factors, such as multiple objectives. The goal of this paper is to look at the fuzzy transportation problem (FTP), which is crucial in TP with multiple objectives. In the literature, numerous techniques for dealing with FTPs are proposed. The cost, supply, and demand values of the FTPs are taken as symmetric triangular fuzzy numbers and then converted into crisp values using ranking techniques to solve the FTP. The initial solution is then obtained by Vogel’s approximation method (VAM), and the optimal solution is obtained by the modified distribution method (MODI). The proposed method is based on the Modified Fractional Knapsack Problem and introduces a new approach to solving the triangular fuzzy transportation problem. This paper analyses an alternative method using the fractional knapsack problem, which was modified using a minimum ratio test. To express the efficiency of the proposed method, it is compared with existing methods in the literature.
},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Solving Triangular Fuzzy Transportation Problem Using Modified Fractional Knapsack Problem

	

AU  - Ekanayake Mudiyanselage Tharika Dewanmini Kumari Ekanayake
AU  - Ekanayake Mudiyanselage Uthpala Senerath Bandara Ekanayake
Y1  - 2023/10/28
PY  - 2023
N1  - https://doi.org/10.11648/j.ajam.20231105.11
DO  - 10.11648/j.ajam.20231105.11
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 77
EP  - 88
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20231105.11
AB  - A transportation problem (TP) is a specific part of a linear programming problem that arises in a collection of contexts and has received much attention in the literature. Minimizing transportation costs or time (one objective) is one of the primary goals of transportation problem-solving approaches. Supply, demand, and unit transportation costs may be uncertain in real-life applications due to many factors, such as multiple objectives. The goal of this paper is to look at the fuzzy transportation problem (FTP), which is crucial in TP with multiple objectives. In the literature, numerous techniques for dealing with FTPs are proposed. The cost, supply, and demand values of the FTPs are taken as symmetric triangular fuzzy numbers and then converted into crisp values using ranking techniques to solve the FTP. The initial solution is then obtained by Vogel’s approximation method (VAM), and the optimal solution is obtained by the modified distribution method (MODI). The proposed method is based on the Modified Fractional Knapsack Problem and introduces a new approach to solving the triangular fuzzy transportation problem. This paper analyses an alternative method using the fractional knapsack problem, which was modified using a minimum ratio test. To express the efficiency of the proposed method, it is compared with existing methods in the literature.

VL  - 11
IS  - 5
ER  -

Copy | Download