A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques

Zahidul Islam Sohag; Md. Asadujjaman

doi:doi:10.11648/j.ml.20180402.11

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A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques

Zahidul Islam Sohag, Md. Asadujjaman

Published in Mathematics Letters (Volume 4, Issue 2)

Received: 22 April 2018 Accepted: 24 May 2018 Published: 14 June 2018

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Abstract

In this paper, we initiated New Average Method with various kinds of mean techniques to solve multi-objective linear programming problem. In this method multi-objective functions are converted into single objective function by using different kinds of mean techniques. Also an algorithm of New Average Method is suggested for solving multi-objective linear programming problem. We illustrate numerical problem using Chandra Sen’s Method, Average Method and New Average Method. The numerical result in this paper indicates that New Average Method gives promising result than Chandra Sen’s Method and Average Method. Also we observed that, in New Average Method, Harmonic mean technique gives better result than other mean techniques like as Quadratic mean, Arithmetic mean, Identric mean, Logarithmic mean, Geometric mean techniques.

Published in	Mathematics Letters (Volume 4, Issue 2)
DOI	10.11648/j.ml.20180402.11
Page(s)	25-33
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), 2018. Published by Science Publishing Group

Keywords

Multi-objective Linear Programming Problem, Average Method, New Average Method, Harmonic Mean

References

[1]	Gass S. I., “Linear Programming Methods and Application”, McGraw-Hill, Inc., 1985.
[2]	Sen. Chandra, A new approach for multi-objective rural development planning, The Indian Economic Journal, Vol. 30, No.4, PP.91-96, 1983.
[3]	Sulaiman N. A. and Sadiq G. W., “Solving the linear multi-objective programming problems; using mean and median values”, Al-Rafiden Journal of Computer Sciences and Mathematical, University of Mosul, Vol.3, No.1, PP. 69-83, 2006.
[4]	Sulaiman, N. A. and Mustafa R. B., “Using harmonic mean to solve multi-objective linear programming problems”, American Journal of Operations Research, Vol. 6, No. 1, PP. 25-30, 2016.
[5]	Nahar Samsun and Alim Md. Abdul, “A new geometric average technique to solve multi-objective linear fractional programming problem and comparison with new arithmetic average technique”, IOSR Journal of Mathematics, Vol. 13, No. 3, PP. 39-52, 2017.
[6]	Nahar Samsun and Alim Md. Abdul, “A statistical averaging method to solve multi objective linear programming problem”, International Journal of Science and Research, Volume 6 Issue 8, August 2017.
[7]	A. Abdil-Kadir, M. S and Sulaiman, And N. A., “An approach for multi objective fractional programming”, Journal of the College of Education, Univ. Salahaddin, Vol. 3, Pp. 1-5, 1993.
[8]	Najmaddin A. Sulaiman, Rebaz B. Mustafa, “ Using harmonic mean to solve multi-objective linear programming problems”, Americam Journal of operations Reasearch, 2016, 6, 25-30.
[9]	Najmaddin A. Sulaiman, Abdul-Qader, “Optimal transformation technique to solve multi-objective linear programming problem”, Journal of Kirkuk University – scientific studies, vol. 3, No. 2, 2008.
[10]	H. Akhtar, G. Modi, S. Duraphe, “Transforming and optimizing multi-objective quadratic fractional programming problem”, International Journal of Statistics and Applied Mathematics 2017; 2(1): 01-05.
[11]	N. A. Sulaiman, G. W. Sadiq, B. K. Abdulrahim, “ New arithmetic average technique to solve multi-objective linear fractional programming problem and it is comparison with other techniques”, IJRRAS 18 (2), February 2014.
[12]	N. A. Suleiman, M. A. Nawkhass, “Transforming and solving multi-objective quadratic fractional programming problems by optimal average of maximin & minimax techniques”, American Journal of Operational Research 2013, 3(3): 92-98.
[13]	H. Akhtar, G. Modi, “An approach for solving multi-objective linear fractional programming problem and it’s comparison with other techniques”, Intearnational Journal of Scientific and Innovative Mathematical Reasearch (IJSIMR), volume 5, Issue 11, 2017, pp- 1-5.
[14]	Sulaiman, N. A. & Salih A. D., “ Using mean and median values to solve linear fractional multi-objective programming problem”, Zanco Journal for Pure and Applied Science, Salahaddin-Erbil University, Vol. 22, No.5, 2010.

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APA Style

Zahidul Islam Sohag, Md. Asadujjaman. (2018). A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques. Mathematics Letters, 4(2), 25-33. https://doi.org/10.11648/j.ml.20180402.11

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ACS Style

Zahidul Islam Sohag; Md. Asadujjaman. A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques. Math. Lett. 2018, 4(2), 25-33. doi: 10.11648/j.ml.20180402.11

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AMA Style

Zahidul Islam Sohag, Md. Asadujjaman. A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques. Math Lett. 2018;4(2):25-33. doi: 10.11648/j.ml.20180402.11

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@article{10.11648/j.ml.20180402.11,
  author = {Zahidul Islam Sohag and Md. Asadujjaman},
  title = {A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques},
  journal = {Mathematics Letters},
  volume = {4},
  number = {2},
  pages = {25-33},
  doi = {10.11648/j.ml.20180402.11},
  url = {https://doi.org/10.11648/j.ml.20180402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180402.11},
  abstract = {In this paper, we initiated New Average Method with various kinds of mean techniques to solve multi-objective linear programming problem. In this method multi-objective functions are converted into single objective function by using different kinds of mean techniques. Also an algorithm of New Average Method is suggested for solving multi-objective linear programming problem. We illustrate numerical problem using Chandra Sen’s Method, Average Method and New Average Method. The numerical result in this paper indicates that New Average Method gives promising result than Chandra Sen’s Method and Average Method. Also we observed that, in New Average Method, Harmonic mean technique gives better result than other mean techniques like as Quadratic mean, Arithmetic mean, Identric mean, Logarithmic mean, Geometric mean techniques.},
 year = {2018}
}

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TY  - JOUR
T1  - A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques
AU  - Zahidul Islam Sohag
AU  - Md. Asadujjaman
Y1  - 2018/06/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180402.11
DO  - 10.11648/j.ml.20180402.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 25
EP  - 33
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180402.11
AB  - In this paper, we initiated New Average Method with various kinds of mean techniques to solve multi-objective linear programming problem. In this method multi-objective functions are converted into single objective function by using different kinds of mean techniques. Also an algorithm of New Average Method is suggested for solving multi-objective linear programming problem. We illustrate numerical problem using Chandra Sen’s Method, Average Method and New Average Method. The numerical result in this paper indicates that New Average Method gives promising result than Chandra Sen’s Method and Average Method. Also we observed that, in New Average Method, Harmonic mean technique gives better result than other mean techniques like as Quadratic mean, Arithmetic mean, Identric mean, Logarithmic mean, Geometric mean techniques.
VL  - 4
IS  - 2
ER  -

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Author Information

Zahidul Islam Sohag

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh
Md. Asadujjaman

Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

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APA Style

Zahidul Islam Sohag, Md. Asadujjaman. (2018). A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques. Mathematics Letters, 4(2), 25-33. https://doi.org/10.11648/j.ml.20180402.11

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ACS Style

Zahidul Islam Sohag; Md. Asadujjaman. A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques. Math. Lett. 2018, 4(2), 25-33. doi: 10.11648/j.ml.20180402.11

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AMA Style

Zahidul Islam Sohag, Md. Asadujjaman. A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques. Math Lett. 2018;4(2):25-33. doi: 10.11648/j.ml.20180402.11

Copy | Download

@article{10.11648/j.ml.20180402.11,
  author = {Zahidul Islam Sohag and Md. Asadujjaman},
  title = {A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques},
  journal = {Mathematics Letters},
  volume = {4},
  number = {2},
  pages = {25-33},
  doi = {10.11648/j.ml.20180402.11},
  url = {https://doi.org/10.11648/j.ml.20180402.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180402.11},
  abstract = {In this paper, we initiated New Average Method with various kinds of mean techniques to solve multi-objective linear programming problem. In this method multi-objective functions are converted into single objective function by using different kinds of mean techniques. Also an algorithm of New Average Method is suggested for solving multi-objective linear programming problem. We illustrate numerical problem using Chandra Sen’s Method, Average Method and New Average Method. The numerical result in this paper indicates that New Average Method gives promising result than Chandra Sen’s Method and Average Method. Also we observed that, in New Average Method, Harmonic mean technique gives better result than other mean techniques like as Quadratic mean, Arithmetic mean, Identric mean, Logarithmic mean, Geometric mean techniques.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - A Proposed New Average Method for Solving Multi-Objective Linear Programming Problem Using Various Kinds of Mean Techniques
AU  - Zahidul Islam Sohag
AU  - Md. Asadujjaman
Y1  - 2018/06/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180402.11
DO  - 10.11648/j.ml.20180402.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 25
EP  - 33
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180402.11
AB  - In this paper, we initiated New Average Method with various kinds of mean techniques to solve multi-objective linear programming problem. In this method multi-objective functions are converted into single objective function by using different kinds of mean techniques. Also an algorithm of New Average Method is suggested for solving multi-objective linear programming problem. We illustrate numerical problem using Chandra Sen’s Method, Average Method and New Average Method. The numerical result in this paper indicates that New Average Method gives promising result than Chandra Sen’s Method and Average Method. Also we observed that, in New Average Method, Harmonic mean technique gives better result than other mean techniques like as Quadratic mean, Arithmetic mean, Identric mean, Logarithmic mean, Geometric mean techniques.
VL  - 4
IS  - 2
ER  -

Copy | Download