Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems

Oshan Niluminda; Uthpala Ekanayake

doi:doi:10.11648/j.ajtte.20230806.12

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Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems

Oshan Niluminda^*, Uthpala Ekanayake

Published in American Journal of Traffic and Transportation Engineering (Volume 8, Issue 6)

Received: 5 October 2023 Accepted: 23 October 2023 Published: 11 November 2023

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Abstract

Transportation is one of the various worldwide challenges that organizations must tackle. The Transportation Problem (TP) is also an important topic in the subject of optimization, where the aim is to reduce the overall transportation cost of distributing from a particular number of sources to a specific number of destinations (locations). This paper aims to investigate the most effective way to solve the Transportation Problem (TP) using the line (edge) colouring of a bipartite network. To solve the TP, several solutions have been proposed in the literature. The Initial Basic Feasible Solution (IBFS) and the Optimal Solution are the two solutions of TP. The North-West Corner Method (NWCM), the Lowest Cost Method (LCM), Row Minima Method (RMM), Column Minima Method (CMM), and Vogel's Approximation Method (VAM) may be used to find an IBFS, while the Modified Distribution (MODI) Method and the Stepping Stone Method can be used to find an optimal solution for the TP In this paper, propose a new algorithmic technique that utilizes the line (edge) colouring of a bipartite network to obtain an optimal or nearly optimal solution to the TP. The proposed technique is applied to balanced and unbalanced TP and compared to other existing methods. Experimental results show that the line (edge) colouring algorithm requires fewer iterations to achieve optimality compared to other current methodologies. In conclusion, the line (edge) colouring algorithm is a highly effective method for solving TP. By representing the TP as a bipartite network and using the proposed algorithmic technique, the optimum or nearly optimum TP solution can be obtained quickly and efficiently. This approach has significant potential for optimizing transportation logistics in various industries.

Published in	American Journal of Traffic and Transportation Engineering (Volume 8, Issue 6)
DOI	10.11648/j.ajtte.20230806.12
Page(s)	135-144
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), 2023. Published by Science Publishing Group

Keywords

Column Minima Method, Graph Colouring, Modified Distribution, Optimization, Transportation Problem

References

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APA Style

Niluminda, O., Ekanayake, U. (2023). Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems. American Journal of Traffic and Transportation Engineering, 8(6), 135-144. https://doi.org/10.11648/j.ajtte.20230806.12

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ACS Style

Niluminda, O.; Ekanayake, U. Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems. Am. J. Traffic Transp. Eng. 2023, 8(6), 135-144. doi: 10.11648/j.ajtte.20230806.12

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AMA Style

Niluminda O, Ekanayake U. Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems. Am J Traffic Transp Eng. 2023;8(6):135-144. doi: 10.11648/j.ajtte.20230806.12

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@article{10.11648/j.ajtte.20230806.12,
  author = {Oshan Niluminda and Uthpala Ekanayake},
  title = {Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems},
  journal = {American Journal of Traffic and Transportation Engineering},
  volume = {8},
  number = {6},
  pages = {135-144},
  doi = {10.11648/j.ajtte.20230806.12},
  url = {https://doi.org/10.11648/j.ajtte.20230806.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtte.20230806.12},
  abstract = {Transportation is one of the various worldwide challenges that organizations must tackle. The Transportation Problem (TP) is also an important topic in the subject of optimization, where the aim is to reduce the overall transportation cost of distributing from a particular number of sources to a specific number of destinations (locations). This paper aims to investigate the most effective way to solve the Transportation Problem (TP) using the line (edge) colouring of a bipartite network. To solve the TP, several solutions have been proposed in the literature. The Initial Basic Feasible Solution (IBFS) and the Optimal Solution are the two solutions of TP. The North-West Corner Method (NWCM), the Lowest Cost Method (LCM), Row Minima Method (RMM), Column Minima Method (CMM), and Vogel's Approximation Method (VAM) may be used to find an IBFS, while the Modified Distribution (MODI) Method and the Stepping Stone Method can be used to find an optimal solution for the TP In this paper, propose a new algorithmic technique that utilizes the line (edge) colouring of a bipartite network to obtain an optimal or nearly optimal solution to the TP. The proposed technique is applied to balanced and unbalanced TP and compared to other existing methods. Experimental results show that the line (edge) colouring algorithm requires fewer iterations to achieve optimality compared to other current methodologies. In conclusion, the line (edge) colouring algorithm is a highly effective method for solving TP. By representing the TP as a bipartite network and using the proposed algorithmic technique, the optimum or nearly optimum TP solution can be obtained quickly and efficiently. This approach has significant potential for optimizing transportation logistics in various industries.
},
 year = {2023}
}

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TY  - JOUR
T1  - Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems
AU  - Oshan Niluminda
AU  - Uthpala Ekanayake
Y1  - 2023/11/11
PY  - 2023
N1  - https://doi.org/10.11648/j.ajtte.20230806.12
DO  - 10.11648/j.ajtte.20230806.12
T2  - American Journal of Traffic and Transportation Engineering
JF  - American Journal of Traffic and Transportation Engineering
JO  - American Journal of Traffic and Transportation Engineering
SP  - 135
EP  - 144
PB  - Science Publishing Group
SN  - 2578-8604
UR  - https://doi.org/10.11648/j.ajtte.20230806.12
AB  - Transportation is one of the various worldwide challenges that organizations must tackle. The Transportation Problem (TP) is also an important topic in the subject of optimization, where the aim is to reduce the overall transportation cost of distributing from a particular number of sources to a specific number of destinations (locations). This paper aims to investigate the most effective way to solve the Transportation Problem (TP) using the line (edge) colouring of a bipartite network. To solve the TP, several solutions have been proposed in the literature. The Initial Basic Feasible Solution (IBFS) and the Optimal Solution are the two solutions of TP. The North-West Corner Method (NWCM), the Lowest Cost Method (LCM), Row Minima Method (RMM), Column Minima Method (CMM), and Vogel's Approximation Method (VAM) may be used to find an IBFS, while the Modified Distribution (MODI) Method and the Stepping Stone Method can be used to find an optimal solution for the TP In this paper, propose a new algorithmic technique that utilizes the line (edge) colouring of a bipartite network to obtain an optimal or nearly optimal solution to the TP. The proposed technique is applied to balanced and unbalanced TP and compared to other existing methods. Experimental results show that the line (edge) colouring algorithm requires fewer iterations to achieve optimality compared to other current methodologies. In conclusion, the line (edge) colouring algorithm is a highly effective method for solving TP. By representing the TP as a bipartite network and using the proposed algorithmic technique, the optimum or nearly optimum TP solution can be obtained quickly and efficiently. This approach has significant potential for optimizing transportation logistics in various industries.

VL  - 8
IS  - 6
ER  -

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Author Information

Oshan Niluminda

Department of Physical Sciences, Faculty of Applied Sciences, Rajarata University of Sri Lanka, Mihinthale, Sri Lanka

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Uthpala Ekanayake

Department of Physical Sciences, Faculty of Applied Sciences, Rajarata University of Sri Lanka, Mihinthale, Sri Lanka

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APA Style

Niluminda, O., Ekanayake, U. (2023). Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems. American Journal of Traffic and Transportation Engineering, 8(6), 135-144. https://doi.org/10.11648/j.ajtte.20230806.12

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ACS Style

Niluminda, O.; Ekanayake, U. Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems. Am. J. Traffic Transp. Eng. 2023, 8(6), 135-144. doi: 10.11648/j.ajtte.20230806.12

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AMA Style

Niluminda O, Ekanayake U. Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems. Am J Traffic Transp Eng. 2023;8(6):135-144. doi: 10.11648/j.ajtte.20230806.12

Copy | Download

@article{10.11648/j.ajtte.20230806.12,
  author = {Oshan Niluminda and Uthpala Ekanayake},
  title = {Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems},
  journal = {American Journal of Traffic and Transportation Engineering},
  volume = {8},
  number = {6},
  pages = {135-144},
  doi = {10.11648/j.ajtte.20230806.12},
  url = {https://doi.org/10.11648/j.ajtte.20230806.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtte.20230806.12},
  abstract = {Transportation is one of the various worldwide challenges that organizations must tackle. The Transportation Problem (TP) is also an important topic in the subject of optimization, where the aim is to reduce the overall transportation cost of distributing from a particular number of sources to a specific number of destinations (locations). This paper aims to investigate the most effective way to solve the Transportation Problem (TP) using the line (edge) colouring of a bipartite network. To solve the TP, several solutions have been proposed in the literature. The Initial Basic Feasible Solution (IBFS) and the Optimal Solution are the two solutions of TP. The North-West Corner Method (NWCM), the Lowest Cost Method (LCM), Row Minima Method (RMM), Column Minima Method (CMM), and Vogel's Approximation Method (VAM) may be used to find an IBFS, while the Modified Distribution (MODI) Method and the Stepping Stone Method can be used to find an optimal solution for the TP In this paper, propose a new algorithmic technique that utilizes the line (edge) colouring of a bipartite network to obtain an optimal or nearly optimal solution to the TP. The proposed technique is applied to balanced and unbalanced TP and compared to other existing methods. Experimental results show that the line (edge) colouring algorithm requires fewer iterations to achieve optimality compared to other current methodologies. In conclusion, the line (edge) colouring algorithm is a highly effective method for solving TP. By representing the TP as a bipartite network and using the proposed algorithmic technique, the optimum or nearly optimum TP solution can be obtained quickly and efficiently. This approach has significant potential for optimizing transportation logistics in various industries.
},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Graph Colouring to Solve Both Balanced and Unbalanced Transportation Problems
AU  - Oshan Niluminda
AU  - Uthpala Ekanayake
Y1  - 2023/11/11
PY  - 2023
N1  - https://doi.org/10.11648/j.ajtte.20230806.12
DO  - 10.11648/j.ajtte.20230806.12
T2  - American Journal of Traffic and Transportation Engineering
JF  - American Journal of Traffic and Transportation Engineering
JO  - American Journal of Traffic and Transportation Engineering
SP  - 135
EP  - 144
PB  - Science Publishing Group
SN  - 2578-8604
UR  - https://doi.org/10.11648/j.ajtte.20230806.12
AB  - Transportation is one of the various worldwide challenges that organizations must tackle. The Transportation Problem (TP) is also an important topic in the subject of optimization, where the aim is to reduce the overall transportation cost of distributing from a particular number of sources to a specific number of destinations (locations). This paper aims to investigate the most effective way to solve the Transportation Problem (TP) using the line (edge) colouring of a bipartite network. To solve the TP, several solutions have been proposed in the literature. The Initial Basic Feasible Solution (IBFS) and the Optimal Solution are the two solutions of TP. The North-West Corner Method (NWCM), the Lowest Cost Method (LCM), Row Minima Method (RMM), Column Minima Method (CMM), and Vogel's Approximation Method (VAM) may be used to find an IBFS, while the Modified Distribution (MODI) Method and the Stepping Stone Method can be used to find an optimal solution for the TP In this paper, propose a new algorithmic technique that utilizes the line (edge) colouring of a bipartite network to obtain an optimal or nearly optimal solution to the TP. The proposed technique is applied to balanced and unbalanced TP and compared to other existing methods. Experimental results show that the line (edge) colouring algorithm requires fewer iterations to achieve optimality compared to other current methodologies. In conclusion, the line (edge) colouring algorithm is a highly effective method for solving TP. By representing the TP as a bipartite network and using the proposed algorithmic technique, the optimum or nearly optimum TP solution can be obtained quickly and efficiently. This approach has significant potential for optimizing transportation logistics in various industries.

VL  - 8
IS  - 6
ER  -

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