Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem

Samsun Nahar; Samima Akther; Mohammad Abdul Alim

doi:doi:10.11648/j.ml.20180403.12

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Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem

Samsun Nahar, Samima Akther, Mohammad Abdul Alim

Published in Mathematics Letters (Volume 4, Issue 3)

Received: 2 October 2018 Accepted: 26 October 2018 Published: 14 November 2018

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Abstract

In this paper, statistical averaging method (arithmetic mean, geometric mean) and new statistical averaging method (new arithmetic mean, new geometric mean) have been proposed for extreme point multi-objective linear programming problem (EPMOLPP). Extreme point can be taken from graphical representation of linear programming problem (LPP). Graphical solution of LPP has been discussed in this research The objective of this method is for making single objective from multi-objective extreme point linear programming problem. Chandra Sen’s method is for making single objective from multi-objective linear programming problem (MOLPP). Here Chandra Sen’s method has also been used to solve EPMOLPP. An algorithm and program solution have been given for our proposed method to solve such type of problems. A numerical example is given and the result in Table 2 indicates that the proposed technique gives better results.

Published in	Mathematics Letters (Volume 4, Issue 3)
DOI	10.11648/j.ml.20180403.12
Page(s)	44-50
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

Extreme Point Linear Programming Problem, Statistical Averaging Method, New Statistical Averaging Method, Extreme Point Multi-Objective Linear Programming Problem (EPMOLPP)

References

[1]	M. S. Abdul-Kadir and N. A. Sulaiman, “An approach for multi objective fractional programming problem”, Journal of the College of Education, University of Salahaddin, vol. 3. pp 1-5, 1993.
[2]	N. A. Sulaiman and R. B. Mustafa, “Using harmonic mean to solve multi-objective linear programming problems”, American journal of operations Research, 6, 25-30, 2016.
[3]	S. Nahar and M. A. Alim, “A New Geometric Average Technique to Solve Multi-Objective Linear Fractional Programming Problem and Comparison with New Arithmetic Average Technique”, IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. vol. 13, issue 3 ver. 1, pp 39-52, DOI: 10.9790/5728-1303013952, 2017.
[4]	S. H. Frederick and J. L. Gerald, "introduction to operations research" seventh edition published by McGraw-Hill, an imprint of The McGraw-Hill companies, inc., 1221, 2001.
[5]	B. K. Abdulrahim, “On Extreme Point Quadratic Fractional Programming Problem” Applied Mathematical Sciences, Vol. 8, no. 6, 261 – 277, 2014.
[6]	M. A. Nawkhass, “On Solving Quadratic Fractional Programming Problems” M. Sc. Thesis, Salahaddin university Erbil Iraq, 2014.
[7]	S. Nahar and M. A. Alim , “Weighted Sum Method for Making Single Objective from Multi-objective Linear Programming Problem (MOLPP) and Comparison with Chandra Sen’s Method”, (accepted) BSME conference (BUET), 2018.
[8]	S. Nahar and M. A. Alim, “A New Statistical Averaging Method to Solve Multi-Objective Linear Programming Problem, ” International Journal of Science and Research (IJSR), ISSN: 2319-7064, Vol. 6 No. 8, 2017.
[9]	N. A. Sulaiman, R. M. Abdullah and S. O. Abdul, “Using Optimal Geometric Average Technique to Solve Extreme Point Multi- Objective Quadratic Programming Problems” Journal of Zankoi Sulaimani, Part- A. (Pure Applied Science), 2016.
[10]	T. Hossain, M. R. Arefin and M. A. Islam, “An Alternative Approach for Solving Extreme Point Linear and Linear Fractional Programming Problem” Dhaka University. J. Sci. vol.63. no.2, pp 77-84, 2015.
[11]	N. A. Sulaiman, “Extreme Point Quadratic Programming Techniques” M. Sc. Thesis, University of Salahaddin, Erbil/Iraq, 1989.
[12]	A. O. Hamad-Amin, “An Adaptive Arithmetic Average Transformation Technique for Solving MOLPP”, M. Sc. Thesis, University of Koya, Koya/Iraq, 2008.
[13]	M. J. L. Kirby, H. R. Love, and S. Kanti, “Cutting Plan Algorithm for Extreme Point Mathematical Programming", Cashier. Ducentre D Etudes De Recherche Operationelle, vol.14, no.1 pp 27-42, 1972.
[14]	C. Sen, “A New Approach for Multi objective Rural Development Planning”, The Indian Economic Journal, vol.30, pp.91-96.
[15]	T. Sottiner, “Operation Research with GNU Linear Programming Kit”, University of Vassa, August 2009.

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APA Style

Samsun Nahar, Samima Akther, Mohammad Abdul Alim. (2018). Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem. Mathematics Letters, 4(3), 44-50. https://doi.org/10.11648/j.ml.20180403.12

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ACS Style

Samsun Nahar; Samima Akther; Mohammad Abdul Alim. Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem. Math. Lett. 2018, 4(3), 44-50. doi: 10.11648/j.ml.20180403.12

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AMA Style

Samsun Nahar, Samima Akther, Mohammad Abdul Alim. Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem. Math Lett. 2018;4(3):44-50. doi: 10.11648/j.ml.20180403.12

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@article{10.11648/j.ml.20180403.12,
  author = {Samsun Nahar and Samima Akther and Mohammad Abdul Alim},
  title = {Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem},
  journal = {Mathematics Letters},
  volume = {4},
  number = {3},
  pages = {44-50},
  doi = {10.11648/j.ml.20180403.12},
  url = {https://doi.org/10.11648/j.ml.20180403.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180403.12},
  abstract = {In this paper, statistical averaging method (arithmetic mean, geometric mean) and new statistical averaging method (new arithmetic mean, new geometric mean) have been proposed for extreme point multi-objective linear programming problem (EPMOLPP). Extreme point can be taken from graphical representation of linear programming problem (LPP). Graphical solution of LPP has been discussed in this research The objective of this method is for making single objective from multi-objective extreme point linear programming problem. Chandra Sen’s method is for making single objective from multi-objective linear programming problem (MOLPP). Here Chandra Sen’s method has also been used to solve EPMOLPP. An algorithm and program solution have been given for our proposed method to solve such type of problems. A numerical example is given and the result in Table 2 indicates that the proposed technique gives better results.},
 year = {2018}
}

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TY  - JOUR
T1  - Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem
AU  - Samsun Nahar
AU  - Samima Akther
AU  - Mohammad Abdul Alim
Y1  - 2018/11/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180403.12
DO  - 10.11648/j.ml.20180403.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 44
EP  - 50
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180403.12
AB  - In this paper, statistical averaging method (arithmetic mean, geometric mean) and new statistical averaging method (new arithmetic mean, new geometric mean) have been proposed for extreme point multi-objective linear programming problem (EPMOLPP). Extreme point can be taken from graphical representation of linear programming problem (LPP). Graphical solution of LPP has been discussed in this research The objective of this method is for making single objective from multi-objective extreme point linear programming problem. Chandra Sen’s method is for making single objective from multi-objective linear programming problem (MOLPP). Here Chandra Sen’s method has also been used to solve EPMOLPP. An algorithm and program solution have been given for our proposed method to solve such type of problems. A numerical example is given and the result in Table 2 indicates that the proposed technique gives better results.
VL  - 4
IS  - 3
ER  -

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Author Information

Samsun Nahar

Department of Basic Sciences & Humanities, University of Asia Pacific, Dhaka, Bangladesh
Samima Akther

Department of Mathematics, University of Barisal, Barisal, Bangladesh
Mohammad Abdul Alim

Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka, Bangladesh

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Plain Text BibTeX RIS

APA Style

Samsun Nahar, Samima Akther, Mohammad Abdul Alim. (2018). Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem. Mathematics Letters, 4(3), 44-50. https://doi.org/10.11648/j.ml.20180403.12

Copy | Download

ACS Style

Samsun Nahar; Samima Akther; Mohammad Abdul Alim. Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem. Math. Lett. 2018, 4(3), 44-50. doi: 10.11648/j.ml.20180403.12

Copy | Download

AMA Style

Samsun Nahar, Samima Akther, Mohammad Abdul Alim. Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem. Math Lett. 2018;4(3):44-50. doi: 10.11648/j.ml.20180403.12

Copy | Download

@article{10.11648/j.ml.20180403.12,
  author = {Samsun Nahar and Samima Akther and Mohammad Abdul Alim},
  title = {Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem},
  journal = {Mathematics Letters},
  volume = {4},
  number = {3},
  pages = {44-50},
  doi = {10.11648/j.ml.20180403.12},
  url = {https://doi.org/10.11648/j.ml.20180403.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180403.12},
  abstract = {In this paper, statistical averaging method (arithmetic mean, geometric mean) and new statistical averaging method (new arithmetic mean, new geometric mean) have been proposed for extreme point multi-objective linear programming problem (EPMOLPP). Extreme point can be taken from graphical representation of linear programming problem (LPP). Graphical solution of LPP has been discussed in this research The objective of this method is for making single objective from multi-objective extreme point linear programming problem. Chandra Sen’s method is for making single objective from multi-objective linear programming problem (MOLPP). Here Chandra Sen’s method has also been used to solve EPMOLPP. An algorithm and program solution have been given for our proposed method to solve such type of problems. A numerical example is given and the result in Table 2 indicates that the proposed technique gives better results.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Statistical Averaging Method and New Statistical Averaging Method for Solving Extreme Point Multi–Objective Linear Programming Problem
AU  - Samsun Nahar
AU  - Samima Akther
AU  - Mohammad Abdul Alim
Y1  - 2018/11/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180403.12
DO  - 10.11648/j.ml.20180403.12
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 44
EP  - 50
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180403.12
AB  - In this paper, statistical averaging method (arithmetic mean, geometric mean) and new statistical averaging method (new arithmetic mean, new geometric mean) have been proposed for extreme point multi-objective linear programming problem (EPMOLPP). Extreme point can be taken from graphical representation of linear programming problem (LPP). Graphical solution of LPP has been discussed in this research The objective of this method is for making single objective from multi-objective extreme point linear programming problem. Chandra Sen’s method is for making single objective from multi-objective linear programming problem (MOLPP). Here Chandra Sen’s method has also been used to solve EPMOLPP. An algorithm and program solution have been given for our proposed method to solve such type of problems. A numerical example is given and the result in Table 2 indicates that the proposed technique gives better results.
VL  - 4
IS  - 3
ER  -

Copy | Download