Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant

Nsikan Paul Akpan; Okeh Chibuzor Ojoh

doi:doi:10.11648/j.ajsp.20170201.11

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Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant

Nsikan Paul Akpan, Okeh Chibuzor Ojoh

Received: 4 December 2016 Accepted: 13 February 2017 Published: 14 April 2017

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Abstract

In this work, the Karmarkar’s algorithm of the interior point method is compared to the simplex method by ascertaining the effect of interior point algorithm on linear programming problem of high number of variables and study why it is not so popularly used in solving linear programming problems. Six (6) products of coca-cola Hellenic Port Harcourt plant (Coke 50cl, Coke35cl, Fanta 50cl, Fanta 35cl, Sprite 35cl and Schweppes 33cl) and their raw materials (Concentrates, Sugar, Water and Carbon (iv) oxide) respectively were studied. The data were analysed using Scilab 5.5.2 software for Karmarmar’s approach and Tora software for Simplex method and the results are compared. The Karmarkar’s algorithm gave a maximum profit of N70,478,116.00 giving a breakdown that the company should produce 159300 crates of Coke 35cl, 64173 crates of Fanta 50cl, 8419 crates of Coke 50cl, 4876 crates of Fanta 35cl, 1118 crates of Sprite and 7 crates of Schweppes from the available resources to attain the optimal solution. The Simplex gave a maximum profit of N107,666,639.51 giving only the production of about 339482 crates of Schweppes 33cl from the available resources to attain the optimal solution.

DOI	10.11648/j.ajsp.20170201.11
Published in	American Journal of Statistics and Probability (Volume 2, Issue 1, January 2017)
Page(s)	1-8
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

Linear Programming, Interior Point, Karmarkar, Simplex, Duality Gap

References

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[12]	Richard B. and Govindasami N. (1997) “Schaum’s Outline Operations Research” 2nd Edition. MC Graw-Hill Inc. USA.
[13]	Robere Robert (2012) “interior point methods and Linear Programming” University of Toronto.
[14]	Schrijver A. (1986) “The new linear programming Method of karmarkar” Centre for Mathematics and Computer Science, Amsterdam, Netherlands.
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Nsikan Paul Akpan, Okeh Chibuzor Ojoh. (2017). Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant. American Journal of Statistics and Probability, 2(1), 1-8. https://doi.org/10.11648/j.ajsp.20170201.11

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Nsikan Paul Akpan; Okeh Chibuzor Ojoh. Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant. Am. J. Stat. Probab. 2017, 2(1), 1-8. doi: 10.11648/j.ajsp.20170201.11

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AMA Style

Nsikan Paul Akpan, Okeh Chibuzor Ojoh. Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant. Am J Stat Probab. 2017;2(1):1-8. doi: 10.11648/j.ajsp.20170201.11

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@article{10.11648/j.ajsp.20170201.11,
  author = {Nsikan Paul Akpan and Okeh Chibuzor Ojoh},
  title = {Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant},
  journal = {American Journal of Statistics and Probability},
  volume = {2},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.ajsp.20170201.11},
  url = {https://doi.org/10.11648/j.ajsp.20170201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajsp.20170201.11},
  abstract = {In this work, the Karmarkar’s algorithm of the interior point method is compared to the simplex method by ascertaining the effect of interior point algorithm on linear programming problem of high number of variables and study why it is not so popularly used in solving linear programming problems. Six (6) products of coca-cola Hellenic Port Harcourt plant (Coke 50cl, Coke35cl, Fanta 50cl, Fanta 35cl, Sprite 35cl and Schweppes 33cl) and their raw materials (Concentrates, Sugar, Water and Carbon (iv) oxide) respectively were studied. The data were analysed using Scilab 5.5.2 software for Karmarmar’s approach and Tora software for Simplex method and the results are compared. The Karmarkar’s algorithm gave a maximum profit of N70,478,116.00 giving a breakdown that the company should produce 159300 crates of Coke 35cl, 64173 crates of Fanta 50cl, 8419 crates of Coke 50cl, 4876 crates of Fanta 35cl, 1118 crates of Sprite and 7 crates of Schweppes from the available resources to attain the optimal solution. The Simplex gave a maximum profit of N107,666,639.51 giving only the production of about 339482 crates of Schweppes 33cl from the available resources to attain the optimal solution.},
 year = {2017}
}

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TY  - JOUR
T1  - Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant
AU  - Nsikan Paul Akpan
AU  - Okeh Chibuzor Ojoh
Y1  - 2017/04/14
PY  - 2017
N1  - https://doi.org/10.11648/j.ajsp.20170201.11
DO  - 10.11648/j.ajsp.20170201.11
T2  - American Journal of Statistics and Probability
JF  - American Journal of Statistics and Probability
JO  - American Journal of Statistics and Probability
SP  - 1
EP  - 8
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.ajsp.20170201.11
AB  - In this work, the Karmarkar’s algorithm of the interior point method is compared to the simplex method by ascertaining the effect of interior point algorithm on linear programming problem of high number of variables and study why it is not so popularly used in solving linear programming problems. Six (6) products of coca-cola Hellenic Port Harcourt plant (Coke 50cl, Coke35cl, Fanta 50cl, Fanta 35cl, Sprite 35cl and Schweppes 33cl) and their raw materials (Concentrates, Sugar, Water and Carbon (iv) oxide) respectively were studied. The data were analysed using Scilab 5.5.2 software for Karmarmar’s approach and Tora software for Simplex method and the results are compared. The Karmarkar’s algorithm gave a maximum profit of N70,478,116.00 giving a breakdown that the company should produce 159300 crates of Coke 35cl, 64173 crates of Fanta 50cl, 8419 crates of Coke 50cl, 4876 crates of Fanta 35cl, 1118 crates of Sprite and 7 crates of Schweppes from the available resources to attain the optimal solution. The Simplex gave a maximum profit of N107,666,639.51 giving only the production of about 339482 crates of Schweppes 33cl from the available resources to attain the optimal solution.
VL  - 2
IS  - 1
ER  -

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Author Information

Nsikan Paul Akpan

Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Port Harcourt, Nigeria
Okeh Chibuzor Ojoh

Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Port Harcourt, Nigeria

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Nsikan Paul Akpan, Okeh Chibuzor Ojoh. (2017). Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant. American Journal of Statistics and Probability, 2(1), 1-8. https://doi.org/10.11648/j.ajsp.20170201.11

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ACS Style

Nsikan Paul Akpan; Okeh Chibuzor Ojoh. Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant. Am. J. Stat. Probab. 2017, 2(1), 1-8. doi: 10.11648/j.ajsp.20170201.11

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AMA Style

Nsikan Paul Akpan, Okeh Chibuzor Ojoh. Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant. Am J Stat Probab. 2017;2(1):1-8. doi: 10.11648/j.ajsp.20170201.11

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@article{10.11648/j.ajsp.20170201.11,
  author = {Nsikan Paul Akpan and Okeh Chibuzor Ojoh},
  title = {Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant},
  journal = {American Journal of Statistics and Probability},
  volume = {2},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.ajsp.20170201.11},
  url = {https://doi.org/10.11648/j.ajsp.20170201.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajsp.20170201.11},
  abstract = {In this work, the Karmarkar’s algorithm of the interior point method is compared to the simplex method by ascertaining the effect of interior point algorithm on linear programming problem of high number of variables and study why it is not so popularly used in solving linear programming problems. Six (6) products of coca-cola Hellenic Port Harcourt plant (Coke 50cl, Coke35cl, Fanta 50cl, Fanta 35cl, Sprite 35cl and Schweppes 33cl) and their raw materials (Concentrates, Sugar, Water and Carbon (iv) oxide) respectively were studied. The data were analysed using Scilab 5.5.2 software for Karmarmar’s approach and Tora software for Simplex method and the results are compared. The Karmarkar’s algorithm gave a maximum profit of N70,478,116.00 giving a breakdown that the company should produce 159300 crates of Coke 35cl, 64173 crates of Fanta 50cl, 8419 crates of Coke 50cl, 4876 crates of Fanta 35cl, 1118 crates of Sprite and 7 crates of Schweppes from the available resources to attain the optimal solution. The Simplex gave a maximum profit of N107,666,639.51 giving only the production of about 339482 crates of Schweppes 33cl from the available resources to attain the optimal solution.},
 year = {2017}
}

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TY  - JOUR
T1  - Karmarkar’s Approach for Solving Linear Programming Problem for Profit Maximization in Production Industries: NBC Port-Harcourt Plant
AU  - Nsikan Paul Akpan
AU  - Okeh Chibuzor Ojoh
Y1  - 2017/04/14
PY  - 2017
N1  - https://doi.org/10.11648/j.ajsp.20170201.11
DO  - 10.11648/j.ajsp.20170201.11
T2  - American Journal of Statistics and Probability
JF  - American Journal of Statistics and Probability
JO  - American Journal of Statistics and Probability
SP  - 1
EP  - 8
PB  - Science Publishing Group
UR  - https://doi.org/10.11648/j.ajsp.20170201.11
AB  - In this work, the Karmarkar’s algorithm of the interior point method is compared to the simplex method by ascertaining the effect of interior point algorithm on linear programming problem of high number of variables and study why it is not so popularly used in solving linear programming problems. Six (6) products of coca-cola Hellenic Port Harcourt plant (Coke 50cl, Coke35cl, Fanta 50cl, Fanta 35cl, Sprite 35cl and Schweppes 33cl) and their raw materials (Concentrates, Sugar, Water and Carbon (iv) oxide) respectively were studied. The data were analysed using Scilab 5.5.2 software for Karmarmar’s approach and Tora software for Simplex method and the results are compared. The Karmarkar’s algorithm gave a maximum profit of N70,478,116.00 giving a breakdown that the company should produce 159300 crates of Coke 35cl, 64173 crates of Fanta 50cl, 8419 crates of Coke 50cl, 4876 crates of Fanta 35cl, 1118 crates of Sprite and 7 crates of Schweppes from the available resources to attain the optimal solution. The Simplex gave a maximum profit of N107,666,639.51 giving only the production of about 339482 crates of Schweppes 33cl from the available resources to attain the optimal solution.
VL  - 2
IS  - 1
ER  -

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