An Innovative Algorithmic Approach for Solving Profit Maximization Problems

Abul Kalam Azad; Mosharraf Hossain

doi:doi:10.11648/j.ml.20180401.11

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An Innovative Algorithmic Approach for Solving Profit Maximization Problems

Abul Kalam Azad, Mosharraf Hossain

Published in Mathematics Letters (Volume 4, Issue 1)

Received: 10 December 2017 Accepted: 25 December 2017 Published: 19 January 2018

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Abstract

The new algorithmic technique developed in this article to solve the profit maximization problems using transportation algorithm of Transportation Problem (TP) has three basic parts; first converting the maximization problem into the minimization problem, second formatting the Total Opportunity Table (TOT) from the converted Transportation Table (TT), and last allocations of profits using the Row Average Total Opportunity Value (RATOV) and Column Average Total Opportunity Value (CATOV). The current algorithm considers the average of the cell values of the TOT along each row identified as RATOV and the average of the cell values of the TOT along each column identified as CATOV. Allocations of profits are started in the cell along the row or column which has the highest RATOVs or CATOVs. The Initial Basic Feasible Solution (IBFS) obtained by the current method is better than some other familiar methods which is discussed in this paper with the three different sized examples.

Published in	Mathematics Letters (Volume 4, Issue 1)
DOI	10.11648/j.ml.20180401.11
Page(s)	1-5
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

TP, TT, TOT, RATOV, CATOV, IBFS

References

[1]	P. Pandian and G. Natarajan, ‘A New Approach for Solving Transportation Problems with Mixed Constraints’, Journal of Physical Sciences, Vol. 14, 2010, 53-61, 2010.
[2]	N. M. Deshmukh, ‘An Innovative Method for Solving Transportation Problem’, International Journal of Physics and Mathematical Sciences ISSN: 2277-2111 (Online), 2012.
[3]	N. Balakrishnan, ‘Modified Vogel’s Approximation Method for Unbalance Transportation Problem,’ Applied Mathematics Letters 3(2), 9,11,1990.
[4]	Serdar Korukoglu and Serkan Balli, ‘An Improved Vogel’s Approximation Method for the Transportation Problem’, Association for Scientific Research, Mathematical and Computational Application Vol. 16 No. 2, 370-381, 2011.
[5]	H. H. Shore, ‘The Transportation Problem and the Vogel’s Approximation Method’, Decision Science 1(3-4), 441-457, 1970.
[6]	D. G. Shimshak, J. A. Kaslik and T. D. Barelay, ‘A modification of Vogel’s Approximation Method through the use of Heuristics’, Infor 19,259-263, 1981.
[7]	Aminur Rahman Khan, ‘A Re-solution of the Transportation Problem: An Algorithmic Approach’ Jahangirnagar University Journal of Science, Vol. 34, No. 2, 49-62, 2011.
[8]	V. J. Sudhakar, N. Arunnsankar, T. Karpagam, ‘A new approach for find an Optimal Solution for Trasportation Problems’, European Journal of Scientific Research 68 254-257, 2012.
[9]	O. Kirca and A. Satir, ‘A Heuristic for Obtaining an Initial Solution for the Transportation Problem’, Journal of Operational Research Society, Vol. 41, No. 9, pp. 865-871, 1990.
[10]	Md. Amirul Islam et al., ‘Profit Maximization of a Manufacturing Company: An Algorithmic Approach’, J. J. Math. and Math. Sci., Vol. 28, 29-37, 2013.

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APA Style

Abul Kalam Azad, Mosharraf Hossain. (2018). An Innovative Algorithmic Approach for Solving Profit Maximization Problems. Mathematics Letters, 4(1), 1-5. https://doi.org/10.11648/j.ml.20180401.11

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ACS Style

Abul Kalam Azad; Mosharraf Hossain. An Innovative Algorithmic Approach for Solving Profit Maximization Problems. Math. Lett. 2018, 4(1), 1-5. doi: 10.11648/j.ml.20180401.11

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AMA Style

Abul Kalam Azad, Mosharraf Hossain. An Innovative Algorithmic Approach for Solving Profit Maximization Problems. Math Lett. 2018;4(1):1-5. doi: 10.11648/j.ml.20180401.11

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@article{10.11648/j.ml.20180401.11,
  author = {Abul Kalam Azad and Mosharraf Hossain},
  title = {An Innovative Algorithmic Approach for Solving Profit Maximization Problems},
  journal = {Mathematics Letters},
  volume = {4},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ml.20180401.11},
  url = {https://doi.org/10.11648/j.ml.20180401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180401.11},
  abstract = {The new algorithmic technique developed in this article to solve the profit maximization problems using transportation algorithm of Transportation Problem (TP) has three basic parts; first converting the maximization problem into the minimization problem, second formatting the Total Opportunity Table (TOT) from the converted Transportation Table (TT), and last allocations of profits using the Row Average Total Opportunity Value (RATOV) and Column Average Total Opportunity Value (CATOV). The current algorithm considers the average of the cell values of the TOT along each row identified as RATOV and the average of the cell values of the TOT along each column identified as CATOV. Allocations of profits are started in the cell along the row or column which has the highest RATOVs or CATOVs. The Initial Basic Feasible Solution (IBFS) obtained by the current method is better than some other familiar methods which is discussed in this paper with the three different sized examples.},
 year = {2018}
}

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TY  - JOUR
T1  - An Innovative Algorithmic Approach for Solving Profit Maximization Problems
AU  - Abul Kalam Azad
AU  - Mosharraf Hossain
Y1  - 2018/01/19
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180401.11
DO  - 10.11648/j.ml.20180401.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180401.11
AB  - The new algorithmic technique developed in this article to solve the profit maximization problems using transportation algorithm of Transportation Problem (TP) has three basic parts; first converting the maximization problem into the minimization problem, second formatting the Total Opportunity Table (TOT) from the converted Transportation Table (TT), and last allocations of profits using the Row Average Total Opportunity Value (RATOV) and Column Average Total Opportunity Value (CATOV). The current algorithm considers the average of the cell values of the TOT along each row identified as RATOV and the average of the cell values of the TOT along each column identified as CATOV. Allocations of profits are started in the cell along the row or column which has the highest RATOVs or CATOVs. The Initial Basic Feasible Solution (IBFS) obtained by the current method is better than some other familiar methods which is discussed in this paper with the three different sized examples.
VL  - 4
IS  - 1
ER  -

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Author Information

Abul Kalam Azad

Department of Mathematics, Rajshahi Government City College, Rajshahi, Bangladesh
Mosharraf Hossain

Department of IPE, Rajshahi University of Engineering and Technology, Rajshahi, Bangladesh

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APA Style

Abul Kalam Azad, Mosharraf Hossain. (2018). An Innovative Algorithmic Approach for Solving Profit Maximization Problems. Mathematics Letters, 4(1), 1-5. https://doi.org/10.11648/j.ml.20180401.11

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ACS Style

Abul Kalam Azad; Mosharraf Hossain. An Innovative Algorithmic Approach for Solving Profit Maximization Problems. Math. Lett. 2018, 4(1), 1-5. doi: 10.11648/j.ml.20180401.11

Copy | Download

AMA Style

Abul Kalam Azad, Mosharraf Hossain. An Innovative Algorithmic Approach for Solving Profit Maximization Problems. Math Lett. 2018;4(1):1-5. doi: 10.11648/j.ml.20180401.11

Copy | Download

@article{10.11648/j.ml.20180401.11,
  author = {Abul Kalam Azad and Mosharraf Hossain},
  title = {An Innovative Algorithmic Approach for Solving Profit Maximization Problems},
  journal = {Mathematics Letters},
  volume = {4},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ml.20180401.11},
  url = {https://doi.org/10.11648/j.ml.20180401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20180401.11},
  abstract = {The new algorithmic technique developed in this article to solve the profit maximization problems using transportation algorithm of Transportation Problem (TP) has three basic parts; first converting the maximization problem into the minimization problem, second formatting the Total Opportunity Table (TOT) from the converted Transportation Table (TT), and last allocations of profits using the Row Average Total Opportunity Value (RATOV) and Column Average Total Opportunity Value (CATOV). The current algorithm considers the average of the cell values of the TOT along each row identified as RATOV and the average of the cell values of the TOT along each column identified as CATOV. Allocations of profits are started in the cell along the row or column which has the highest RATOVs or CATOVs. The Initial Basic Feasible Solution (IBFS) obtained by the current method is better than some other familiar methods which is discussed in this paper with the three different sized examples.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - An Innovative Algorithmic Approach for Solving Profit Maximization Problems
AU  - Abul Kalam Azad
AU  - Mosharraf Hossain
Y1  - 2018/01/19
PY  - 2018
N1  - https://doi.org/10.11648/j.ml.20180401.11
DO  - 10.11648/j.ml.20180401.11
T2  - Mathematics Letters
JF  - Mathematics Letters
JO  - Mathematics Letters
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2575-5056
UR  - https://doi.org/10.11648/j.ml.20180401.11
AB  - The new algorithmic technique developed in this article to solve the profit maximization problems using transportation algorithm of Transportation Problem (TP) has three basic parts; first converting the maximization problem into the minimization problem, second formatting the Total Opportunity Table (TOT) from the converted Transportation Table (TT), and last allocations of profits using the Row Average Total Opportunity Value (RATOV) and Column Average Total Opportunity Value (CATOV). The current algorithm considers the average of the cell values of the TOT along each row identified as RATOV and the average of the cell values of the TOT along each column identified as CATOV. Allocations of profits are started in the cell along the row or column which has the highest RATOVs or CATOVs. The Initial Basic Feasible Solution (IBFS) obtained by the current method is better than some other familiar methods which is discussed in this paper with the three different sized examples.
VL  - 4
IS  - 1
ER  -

Copy | Download