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

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.
Cite This Article
  • 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
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    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
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    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
  • Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

  • Department of Mathematics, University of Dhaka, Dhaka, Bangladesh

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