Sensitivity Analysis of Linear Programming in Decision Making Model

Shek AhmedDepartment of Mathematics; University of Barishal; Barishal; Jakia Sultana; Tanzila Yeasmin Nilu; Shamima Islam

doi:doi:10.11648/j.ijtam.20210703.12

Sensitivity Analysis of Linear Programming in Decision Making Model

Shek AhmedDepartment of Mathematics, University of Barishal, Barishal, Jakia Sultana, Tanzila Yeasmin Nilu, Shamima Islam

Published in International Journal of Theoretical and Applied Mathematics (Volume 7, Issue 3)

Received: 23 April 2021 Accepted: 11 May 2021 Published: 31 May 2021

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Abstract

The term Sensitivity Analysis (SA), sometimes called the post optimality analysis, refers to an analysis of the effect on the optimal solution of changes in the parameters of problem on the current optimal solution. Simplex method is an iterative procedure which gives the optimal solution to a Linear Programming Problem (LPP) in a finite number of steps or gives an indication that there is an unbounded solution whereas SA serves as an integral part of solving LPP and is normally carried out after getting optimal solution. In this research work, Sensitivity Analysis is used to understand the effect of a set of independent variables on some dependent variable under certain specific conditions. In order to determine the possible effect of independent parameters, we considered the changes in the input data of the optimal solution. This notion is actually based on the idea of Sensitivity Analysis. And it is found that all the possible alternative decision making converges in the neighborhood of the optimal solution. To avoid numerical complexity, we use LINDO software to show the changes in the input data and optimal solution.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 7, Issue 3)
DOI	10.11648/j.ijtam.20210703.12
Page(s)	53-56
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), 2021. Published by Science Publishing Group

Keywords

Linear Programming Problem (LPP), Sensitivity Analysis (SA), Simplex Method (SM), Shadow Price, Basic and Non-basic Variable

References

[1]	Adler I, Monteiro R. D. C. (1992), A geometric view of parametric linear programming, Algorithmica Vol: 161-176.
[2]	M. A. I. Bhuiyan and Shek Ahmed. 2017. A new Computer Oriented Technique for solving Linear Programming Problem Using Bender’s Decomposition Method. Barishal University Journal Part 1. Vol 4 (2): 413-426.
[3]	Tanzila Yeasmin Nilu, Shek Ahmed and M. A. I. Bhuiyan 2017. A Study of Sensitivity Analysis in Linear Programming problem and its Implementation in Real Life. Green University Bangladesh Journal of Science and Engineering, Vol 4 (1): 85-92.
[4]	Winston, W. L., 1994. Linear Programming: Applications and Algorithm, Dunbury Press, Bellmont, California, U.S.A.
[5]	Hashnayne Ahmed and Shek Ahmed 2019. A Comparative Study on Harvesting Plan Predicting insurance with Two-Stage Stochastic Analysis. International Journal on data Science and Technology. 5 (4): 73-82.
[6]	Dahiya K, Verma V (2005), Sensitivity analysis in linear programming with bounded variables, ASOR Bulletin 24 (3), 2-19.
[7]	Tanzila Yeasmin Nilu, Shek Ahmed and Hashnayne Ahmed 2020. Analysis of Diet Choice towards a Proper Nutrition Plan by Linear Programming. Science Journal of Applied Mathematics and Statistics. 2020; 8 (5): 59-66.
[8]	Yang B. H. (1990), “A study on sensitivity analysis for a non-extreme optimal solution in linear programming”, Ph. D. Thesis, Seoul National University, Republic of Korea.
[9]	Tanzila Yeasmin Nilu, Hashnayne Ahmed and Shek Ahmed 2019. Mathematical Modeling for Launch Vessel Operators at Internal Waterways Transportation in Bangladesh, Green University Bangladesh Journal of Science and Engineering, Vol 6 (1): 46-53.
[10]	Jansen B, JJ de Jong, Ross C, Terlaky T (1997), Sensitivity analysis in linear programming: just be careful, European Journal of Operational Research 101, 15-28.
[11]	Monteiro R. D. C., Mehrotra S (1996), “A general parametric approach and its implications to sensitivity analysis in interior point methods, Mathematical Programming” 92, 65-82.
[12]	Murty K. G. (1976), Linear and combinatorial programming, John Wiley & Sons INC., New York London Sydney Toronto.
[13]	Park C, Kim W, Lee S, Park S (2004), Positive sensitivity analysis in linear programming, Asia-Pacific Journal of Operational Research 21 (1), 53-68.
[14]	Roos. CT., Terlaky T, Vial (1997), Theory and algorithms for linear optimization, New York, John Wiley & Sons.
[15]	Taha, H. A., Operations research: An introduction, 8th Ed. Pearson Princeton hall.

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APA Style

Shek AhmedDepartment of Mathematics, University of Barishal, Barishal, Jakia Sultana, Tanzila Yeasmin Nilu, et al. (2021). Sensitivity Analysis of Linear Programming in Decision Making Model. International Journal of Theoretical and Applied Mathematics, 7(3), 53-56. https://doi.org/10.11648/j.ijtam.20210703.12

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ACS Style

Shek AhmedDepartment of Mathematics; University of Barishal; Barishal; Jakia Sultana; Tanzila Yeasmin Nilu, et al. Sensitivity Analysis of Linear Programming in Decision Making Model. Int. J. Theor. Appl. Math. 2021, 7(3), 53-56. doi: 10.11648/j.ijtam.20210703.12

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AMA Style

Shek AhmedDepartment of Mathematics, University of Barishal, Barishal, Jakia Sultana, Tanzila Yeasmin Nilu, et al. Sensitivity Analysis of Linear Programming in Decision Making Model. Int J Theor Appl Math. 2021;7(3):53-56. doi: 10.11648/j.ijtam.20210703.12

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@article{10.11648/j.ijtam.20210703.12,
  author = {Shek AhmedDepartment of Mathematics and University of Barishal and Barishal and Jakia Sultana and Tanzila Yeasmin Nilu and Shamima Islam},
  title = {Sensitivity Analysis of Linear Programming in Decision Making Model},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {7},
  number = {3},
  pages = {53-56},
  doi = {10.11648/j.ijtam.20210703.12},
  url = {https://doi.org/10.11648/j.ijtam.20210703.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20210703.12},
  abstract = {The term Sensitivity Analysis (SA), sometimes called the post optimality analysis, refers to an analysis of the effect on the optimal solution of changes in the parameters of problem on the current optimal solution. Simplex method is an iterative procedure which gives the optimal solution to a Linear Programming Problem (LPP) in a finite number of steps or gives an indication that there is an unbounded solution whereas SA serves as an integral part of solving LPP and is normally carried out after getting optimal solution. In this research work, Sensitivity Analysis is used to understand the effect of a set of independent variables on some dependent variable under certain specific conditions. In order to determine the possible effect of independent parameters, we considered the changes in the input data of the optimal solution. This notion is actually based on the idea of Sensitivity Analysis. And it is found that all the possible alternative decision making converges in the neighborhood of the optimal solution. To avoid numerical complexity, we use LINDO software to show the changes in the input data and optimal solution.},
 year = {2021}
}

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TY  - JOUR
T1  - Sensitivity Analysis of Linear Programming in Decision Making Model
AU  - Shek AhmedDepartment of Mathematics
AU  - University of Barishal
AU  - Barishal
AU  - Jakia Sultana
AU  - Tanzila Yeasmin Nilu
AU  - Shamima Islam
Y1  - 2021/05/31
PY  - 2021
N1  - https://doi.org/10.11648/j.ijtam.20210703.12
DO  - 10.11648/j.ijtam.20210703.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 53
EP  - 56
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20210703.12
AB  - The term Sensitivity Analysis (SA), sometimes called the post optimality analysis, refers to an analysis of the effect on the optimal solution of changes in the parameters of problem on the current optimal solution. Simplex method is an iterative procedure which gives the optimal solution to a Linear Programming Problem (LPP) in a finite number of steps or gives an indication that there is an unbounded solution whereas SA serves as an integral part of solving LPP and is normally carried out after getting optimal solution. In this research work, Sensitivity Analysis is used to understand the effect of a set of independent variables on some dependent variable under certain specific conditions. In order to determine the possible effect of independent parameters, we considered the changes in the input data of the optimal solution. This notion is actually based on the idea of Sensitivity Analysis. And it is found that all the possible alternative decision making converges in the neighborhood of the optimal solution. To avoid numerical complexity, we use LINDO software to show the changes in the input data and optimal solution.
VL  - 7
IS  - 3
ER  -

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Author Information

Shek AhmedDepartment of Mathematics
University of Barishal
Barishal
Jakia Sultana

Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh
Tanzila Yeasmin Nilu

Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh
Shamima Islam

Department of Computer Science and Engineering, Green University of Bangladesh, Dhaka, Bangladesh

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Plain Text BibTeX RIS

APA Style

Shek AhmedDepartment of Mathematics, University of Barishal, Barishal, Jakia Sultana, Tanzila Yeasmin Nilu, et al. (2021). Sensitivity Analysis of Linear Programming in Decision Making Model. International Journal of Theoretical and Applied Mathematics, 7(3), 53-56. https://doi.org/10.11648/j.ijtam.20210703.12

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ACS Style

Shek AhmedDepartment of Mathematics; University of Barishal; Barishal; Jakia Sultana; Tanzila Yeasmin Nilu, et al. Sensitivity Analysis of Linear Programming in Decision Making Model. Int. J. Theor. Appl. Math. 2021, 7(3), 53-56. doi: 10.11648/j.ijtam.20210703.12

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AMA Style

Shek AhmedDepartment of Mathematics, University of Barishal, Barishal, Jakia Sultana, Tanzila Yeasmin Nilu, et al. Sensitivity Analysis of Linear Programming in Decision Making Model. Int J Theor Appl Math. 2021;7(3):53-56. doi: 10.11648/j.ijtam.20210703.12

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@article{10.11648/j.ijtam.20210703.12,
  author = {Shek AhmedDepartment of Mathematics and University of Barishal and Barishal and Jakia Sultana and Tanzila Yeasmin Nilu and Shamima Islam},
  title = {Sensitivity Analysis of Linear Programming in Decision Making Model},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {7},
  number = {3},
  pages = {53-56},
  doi = {10.11648/j.ijtam.20210703.12},
  url = {https://doi.org/10.11648/j.ijtam.20210703.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20210703.12},
  abstract = {The term Sensitivity Analysis (SA), sometimes called the post optimality analysis, refers to an analysis of the effect on the optimal solution of changes in the parameters of problem on the current optimal solution. Simplex method is an iterative procedure which gives the optimal solution to a Linear Programming Problem (LPP) in a finite number of steps or gives an indication that there is an unbounded solution whereas SA serves as an integral part of solving LPP and is normally carried out after getting optimal solution. In this research work, Sensitivity Analysis is used to understand the effect of a set of independent variables on some dependent variable under certain specific conditions. In order to determine the possible effect of independent parameters, we considered the changes in the input data of the optimal solution. This notion is actually based on the idea of Sensitivity Analysis. And it is found that all the possible alternative decision making converges in the neighborhood of the optimal solution. To avoid numerical complexity, we use LINDO software to show the changes in the input data and optimal solution.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Sensitivity Analysis of Linear Programming in Decision Making Model
AU  - Shek AhmedDepartment of Mathematics
AU  - University of Barishal
AU  - Barishal
AU  - Jakia Sultana
AU  - Tanzila Yeasmin Nilu
AU  - Shamima Islam
Y1  - 2021/05/31
PY  - 2021
N1  - https://doi.org/10.11648/j.ijtam.20210703.12
DO  - 10.11648/j.ijtam.20210703.12
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 53
EP  - 56
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20210703.12
AB  - The term Sensitivity Analysis (SA), sometimes called the post optimality analysis, refers to an analysis of the effect on the optimal solution of changes in the parameters of problem on the current optimal solution. Simplex method is an iterative procedure which gives the optimal solution to a Linear Programming Problem (LPP) in a finite number of steps or gives an indication that there is an unbounded solution whereas SA serves as an integral part of solving LPP and is normally carried out after getting optimal solution. In this research work, Sensitivity Analysis is used to understand the effect of a set of independent variables on some dependent variable under certain specific conditions. In order to determine the possible effect of independent parameters, we considered the changes in the input data of the optimal solution. This notion is actually based on the idea of Sensitivity Analysis. And it is found that all the possible alternative decision making converges in the neighborhood of the optimal solution. To avoid numerical complexity, we use LINDO software to show the changes in the input data and optimal solution.
VL  - 7
IS  - 3
ER  -

Copy | Download