Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem

Tuncay Can; Habip Koçak

doi:doi:10.11648/j.acm.20160502.17

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Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem

Tuncay Can, Habip Koçak

Published in Applied and Computational Mathematics (Volume 5, Issue 2)

Received: 14 April 2016 Accepted: 27 April 2016 Published: 12 May 2016

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Abstract

Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structure of the simplex method used when modelling with linear programming and located in a corner point sometimes at the optimal solution itself but mostly in close proximity to the optimal solution vector. One of the ways to eliminate this degenerated solution is to employ approximation methods. The main aim of this paper is to introduce Tuncay Can’s approximation method, which was developed as an alternative to the approximation methods in the literature for a balanced transport problem. Tuncay Can’s approximation method usually has less iterations than other approximation methods. In this paper, the Tuncay Can approximation method is introduced as an alternative to The North West Corner Rule, Minimum Cost Method, and the RAM and VAM methods.

Published in	Applied and Computational Mathematics (Volume 5, Issue 2)
DOI	10.11648/j.acm.20160502.17
Page(s)	78-82
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), 2016. Published by Science Publishing Group

Keywords

Basic Feasible Solution, Transportation Problems, Can Method, VAM, RAM

References

[1]	T. Can, “Yöneylem Araştırması, Nedensellik Üzerine Diyaloglar I”, Beta Publications, Istanbul, p. 396, 2015.
[2]	M., Kırca, A. Satır, “A Heuristic for Obtaining and Initial Solution for the Transportation Problem”, Journal of the Operational Research Society, Vol. 41, No. 9, pp. 865-871, 1990.
[3]	K. N., Krishnaswamy, A. I., Sivakumar, M., Mathirajan, Management Research Methodology, Dorling Kindersley Pvt. Ltd., p. 246, 2009.
[4]	S. Korukoğlu, S., Ballı, “An Improved Vogel’s Approximation Method for the Transportation Problem”, Mathematical and Computational Applications, Vol. 16, No. 2, pp. 370-381, 2011.
[5]	S., Sood, K., Jain, “The Maximum Difference Method to find Initial Basic Feasible Solution For Transportation Problem”, Asian Journal of Management Sciences, 03 (07), pp. 8-11, 2015.
[6]	S., Singh, G. C., Dubey, R., Shrivastava, R, “Optimization and Analysis of Some Variants Through Vogel’s Approximation Method (VAM)”, IOSR Journal of Engineering, Vol. 2, Issue 9, pp. 20-30, 2012.
[7]	N., Balakrishnan, “Modified Vogel’s Approximation Method for the Unbalanced Transportation Problem”, Applied Mathematics Letters, Vol. 3, Issue. 2, pp. 9-11, 1990.
[8]	Z. A. N. S., Juman, M. A., Hoque, “An Efficient Heuristic to Obtain a Better Initial Feasible Solution to the Transportation Problem”, Applied Soft Computing, Vol. 34, pp. 813-826, 2015.
[9]	B. G., Dantzig, N. M., Thapa, Linear Programming 1. Introduction, Springer-Verlag New York, p. 214, 1997.
[10]	M. Zangiabadi, T. Rabie,” A New Model for Transportation Problem with Qualitative Data”, Iran. Journal of Operations Research, 3 (2), pp. 33–46 (2012).
[11]	V. J. Sudhakar, N. Arunsankar, T. Karpagam, “A New Approach for Finding An Optimal Solution for Transportation Problems, Europan Journal of Sciences Research, 68 (2), pp. 254–257, 2012.
[12]	V. Srinivasan, G. L. Thompson, “Cost Operator Algorithms for the Transportation Problem”, Mathematical Programming, 12, pp. 372–391, 1977.
[13]	N. Sen, T. Som, B. Sinha, “A Study of Transportation Problem for an Essential Item of Southern Part of North Eastern Region of India as an OR Model and Use of Object Oriented Programming”, International Jorunal of Computation Sciences Network Security, 10 (4), pp. 78-86, 2010.
[14]	F. Pargar, N. Javadian, A. P. Ganji, “A Heuristic for Obtaining an Initial Solution for the Transportation Problem with Experimental Analysis”, in: The 6th International Industrial Engineering Conference, Sharif University of Technology, Tehran, Iran, 2009.
[15]	M. Mathirajan, B. Meenakshi, “Experimental Analysis of Some Variants of Vogel’s Approximation Method”, Asia-Pacian. Journal of Operations Research, 21 (4), p. 447–462, 2004.

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Tuncay Can, Habip Koçak. (2016). Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem. Applied and Computational Mathematics, 5(2), 78-82. https://doi.org/10.11648/j.acm.20160502.17

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ACS Style

Tuncay Can; Habip Koçak. Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem. Appl. Comput. Math. 2016, 5(2), 78-82. doi: 10.11648/j.acm.20160502.17

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AMA Style

Tuncay Can, Habip Koçak. Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem. Appl Comput Math. 2016;5(2):78-82. doi: 10.11648/j.acm.20160502.17

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@article{10.11648/j.acm.20160502.17,
  author = {Tuncay Can and Habip Koçak},
  title = {Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {2},
  pages = {78-82},
  doi = {10.11648/j.acm.20160502.17},
  url = {https://doi.org/10.11648/j.acm.20160502.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160502.17},
  abstract = {Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structure of the simplex method used when modelling with linear programming and located in a corner point sometimes at the optimal solution itself but mostly in close proximity to the optimal solution vector. One of the ways to eliminate this degenerated solution is to employ approximation methods. The main aim of this paper is to introduce Tuncay Can’s approximation method, which was developed as an alternative to the approximation methods in the literature for a balanced transport problem. Tuncay Can’s approximation method usually has less iterations than other approximation methods. In this paper, the Tuncay Can approximation method is introduced as an alternative to The North West Corner Rule, Minimum Cost Method, and the RAM and VAM methods.},
 year = {2016}
}

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TY  - JOUR
T1  - Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem
AU  - Tuncay Can
AU  - Habip Koçak
Y1  - 2016/05/12
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DO  - 10.11648/j.acm.20160502.17
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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AB  - Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structure of the simplex method used when modelling with linear programming and located in a corner point sometimes at the optimal solution itself but mostly in close proximity to the optimal solution vector. One of the ways to eliminate this degenerated solution is to employ approximation methods. The main aim of this paper is to introduce Tuncay Can’s approximation method, which was developed as an alternative to the approximation methods in the literature for a balanced transport problem. Tuncay Can’s approximation method usually has less iterations than other approximation methods. In this paper, the Tuncay Can approximation method is introduced as an alternative to The North West Corner Rule, Minimum Cost Method, and the RAM and VAM methods.
VL  - 5
IS  - 2
ER  -

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Author Information

Tuncay Can

Department of Econometrics, Faculty of Economics, Marmara University, Istanbul, Turkey
Habip Koçak

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APA Style

Tuncay Can, Habip Koçak. (2016). Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem. Applied and Computational Mathematics, 5(2), 78-82. https://doi.org/10.11648/j.acm.20160502.17

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ACS Style

Tuncay Can; Habip Koçak. Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem. Appl. Comput. Math. 2016, 5(2), 78-82. doi: 10.11648/j.acm.20160502.17

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AMA Style

Tuncay Can, Habip Koçak. Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem. Appl Comput Math. 2016;5(2):78-82. doi: 10.11648/j.acm.20160502.17

Copy | Download

@article{10.11648/j.acm.20160502.17,
  author = {Tuncay Can and Habip Koçak},
  title = {Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {2},
  pages = {78-82},
  doi = {10.11648/j.acm.20160502.17},
  url = {https://doi.org/10.11648/j.acm.20160502.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160502.17},
  abstract = {Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structure of the simplex method used when modelling with linear programming and located in a corner point sometimes at the optimal solution itself but mostly in close proximity to the optimal solution vector. One of the ways to eliminate this degenerated solution is to employ approximation methods. The main aim of this paper is to introduce Tuncay Can’s approximation method, which was developed as an alternative to the approximation methods in the literature for a balanced transport problem. Tuncay Can’s approximation method usually has less iterations than other approximation methods. In this paper, the Tuncay Can approximation method is introduced as an alternative to The North West Corner Rule, Minimum Cost Method, and the RAM and VAM methods.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Tuncay Can’s Approximation Method to Obtain Initial Basic Feasible Solution to Transport Problem
AU  - Tuncay Can
AU  - Habip Koçak
Y1  - 2016/05/12
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160502.17
DO  - 10.11648/j.acm.20160502.17
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 78
EP  - 82
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160502.17
AB  - Obtaining an initial basic feasible solution to a transport problem – or a corner point in the convex polytope region – is extremely important in terms of reaching the optimal solution to the problem in the shortest time. When a transport problem is basically accepted as a linear programming problem, a degenerated solution is caused by the structure of the simplex method used when modelling with linear programming and located in a corner point sometimes at the optimal solution itself but mostly in close proximity to the optimal solution vector. One of the ways to eliminate this degenerated solution is to employ approximation methods. The main aim of this paper is to introduce Tuncay Can’s approximation method, which was developed as an alternative to the approximation methods in the literature for a balanced transport problem. Tuncay Can’s approximation method usually has less iterations than other approximation methods. In this paper, the Tuncay Can approximation method is introduced as an alternative to The North West Corner Rule, Minimum Cost Method, and the RAM and VAM methods.
VL  - 5
IS  - 2
ER  -

Copy | Download