An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem

P. Gayathri; K. R. Subramanian

doi:doi:10.11648/j.ijssam.20160104.14

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An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem

P. Gayathri, K. R. Subramanian

Published in International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 4)

Received: 15 September 2016 Accepted: 10 October 2016 Published: 9 November 2016

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Abstract

The fuzzy transportation problem in which available commodity frequently moves from one source to another source or destination before reaching its actual destination is called a fuzzy transshipment problem. In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: From a source to any another source, from a destination to another destination, and from a destination to any source. In the proposed method all the parameters are represented by trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem with transshipment is solved. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems with transshipment occurring in real life situations.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 1, Issue 4)
DOI	10.11648/j.ijssam.20160104.14
Page(s)	58-62
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

Transportation Problem, Fuzzy Transshipment Problem, Trapezoidal Fuzzy Numbers

References

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[2]	King GA, Logan SH (1964) Optimum location, number, and size of processing plants with raw product and final product shipments. J Farm Econ 46: 94–108.
[3]	Judge GG, Havlicek J, Rizek RL (1965) An interregional model: its formulation and application to thelivestock industry. Agric Econ Rev 17: 1–9.
[4]	Hurt VG, Tramel TE (1965) Alternative formulations of the transshipment problem. J Farm Econ 47 (3): 763–773.
[5]	Brigden MEV (1974) A variant of transportation problem in which the constraints are of mixed type. Oper Res Quaterly 25 (3): 437–445.
[6]	Klingmana D, Russel R (1975) Solving constrained transportation problems. Oper Res 23 (1): 91–105.
[7]	Garg R, Prakash S (1985) Time minimizing transshipment problem. Indian J Pure Appl Math 16 (5): 449–460.
[8]	Gupta A, Khanna S, Puri MC (1992) Paradoxical situations in transportation problems. Cah CentEtudesde Rech Operationnell 34: 37–49.
[9]	Gupta A, Khanna S, Puri MC (1993) A paradox in linear fractional transportation problems with mixedconstraints. Optimization 27: 375– 387.
[10]	Arora SR, Khurana A (2004) Three dimensional fixed charge bicriterion indefinite quadratictransportation problem. Yugoslavia J Oper Res 14 (1): 83–97.
[11]	Dahiya K, Verma V (2007) Capacitated transportation problem with bounds on the rim conditions. Eur JOper Res 178: 718–737.
[12]	Khurana A, Thirwani D, Arora SR (2009) An algorithm for solving fixed charge bi-criterion indefinitequadratic transportation problem with restricted flow. Int J Optim Theory Methods Appl 1 (4): 367–380.
[13]	Khurana A, Arora SR (2011) Fixed charge bi-criterion indefinite quadratic transportation problem withenhanced flow. Rev Investig Operacional 32: 133–145.
[14]	Khurana A, Verma T, Arora SR (2012) An algorithmfor solving time minimizing transshipmentproblem. Int J Manag Sci Eng Manag 7 (3): 192–199.
[15]	Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Applications. Academic, New York (1980).

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APA Style

P. Gayathri, K. R. Subramanian. (2016). An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem. International Journal of Systems Science and Applied Mathematics, 1(4), 58-62. https://doi.org/10.11648/j.ijssam.20160104.14

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ACS Style

P. Gayathri; K. R. Subramanian. An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem. Int. J. Syst. Sci. Appl. Math. 2016, 1(4), 58-62. doi: 10.11648/j.ijssam.20160104.14

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AMA Style

P. Gayathri, K. R. Subramanian. An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem. Int J Syst Sci Appl Math. 2016;1(4):58-62. doi: 10.11648/j.ijssam.20160104.14

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@article{10.11648/j.ijssam.20160104.14,
  author = {P. Gayathri and K. R. Subramanian},
  title = {An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {58-62},
  doi = {10.11648/j.ijssam.20160104.14},
  url = {https://doi.org/10.11648/j.ijssam.20160104.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160104.14},
  abstract = {The fuzzy transportation problem in which available commodity frequently moves from one source to another source or destination before reaching its actual destination is called a fuzzy transshipment problem. In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: From a source to any another source, from a destination to another destination, and from a destination to any source. In the proposed method all the parameters are represented by trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem with transshipment is solved. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems with transshipment occurring in real life situations.},
 year = {2016}
}

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TY  - JOUR
T1  - An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem
AU  - P. Gayathri
AU  - K. R. Subramanian
Y1  - 2016/11/09
PY  - 2016
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JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
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AB  - The fuzzy transportation problem in which available commodity frequently moves from one source to another source or destination before reaching its actual destination is called a fuzzy transshipment problem. In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: From a source to any another source, from a destination to another destination, and from a destination to any source. In the proposed method all the parameters are represented by trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem with transshipment is solved. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems with transshipment occurring in real life situations.
VL  - 1
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Author Information

P. Gayathri

Department of Mathematics, A.V.C.College (Autonomous), Mannampandal, Mayiladuthurai
K. R. Subramanian

Department of Computer Applications, Srimati Indira Gandhi College, Trichy, Tamilnadu, India

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APA Style

P. Gayathri, K. R. Subramanian. (2016). An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem. International Journal of Systems Science and Applied Mathematics, 1(4), 58-62. https://doi.org/10.11648/j.ijssam.20160104.14

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ACS Style

P. Gayathri; K. R. Subramanian. An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem. Int. J. Syst. Sci. Appl. Math. 2016, 1(4), 58-62. doi: 10.11648/j.ijssam.20160104.14

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AMA Style

P. Gayathri, K. R. Subramanian. An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem. Int J Syst Sci Appl Math. 2016;1(4):58-62. doi: 10.11648/j.ijssam.20160104.14

Copy | Download

@article{10.11648/j.ijssam.20160104.14,
  author = {P. Gayathri and K. R. Subramanian},
  title = {An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {1},
  number = {4},
  pages = {58-62},
  doi = {10.11648/j.ijssam.20160104.14},
  url = {https://doi.org/10.11648/j.ijssam.20160104.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20160104.14},
  abstract = {The fuzzy transportation problem in which available commodity frequently moves from one source to another source or destination before reaching its actual destination is called a fuzzy transshipment problem. In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: From a source to any another source, from a destination to another destination, and from a destination to any source. In the proposed method all the parameters are represented by trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem with transshipment is solved. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems with transshipment occurring in real life situations.},
 year = {2016}
}

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TY  - JOUR
T1  - An Algorithm to Solve Fuzzy Trapezoidal Transshipment Problem
AU  - P. Gayathri
AU  - K. R. Subramanian
Y1  - 2016/11/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ijssam.20160104.14
DO  - 10.11648/j.ijssam.20160104.14
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 58
EP  - 62
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20160104.14
AB  - The fuzzy transportation problem in which available commodity frequently moves from one source to another source or destination before reaching its actual destination is called a fuzzy transshipment problem. In this paper, a new method is proposed to find the fuzzy optimal solution of fuzzy transportation problems with the following transshipment: From a source to any another source, from a destination to another destination, and from a destination to any source. In the proposed method all the parameters are represented by trapezoidal fuzzy numbers. To illustrate the proposed method a fuzzy transportation problem with transshipment is solved. The proposed method is easy to understand and to apply for finding the fuzzy optimal solution of fuzzy transportation problems with transshipment occurring in real life situations.
VL  - 1
IS  - 4
ER  -

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