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Comparison of Methods of Solving Transportation Problems (TP) and Resolving the Associated Variations

Received: 10 March 2022     Accepted: 14 May 2022     Published: 28 September 2022
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Abstract

Transportation Problem is a Linear Programming application to physical distribution of goods and services from various origins to several destinations such that the cost of transportation is minimal. In this study, five different methods were employed to solve transportation problems arising from unequal demand and supply of goods and variations. The methods considered in terms of North West Corner Rule, Least Cost Method, Vogel’s Approximation Method, Row Minima Method and Column Minima Method were compared. Necessary and sufficient condition for the existence of a feasible solution to the transportation problem was initiated and established. Unbalanced transportation problems were resolved using Vogel’s Approximation Method (VAM) and Modified Distribution (MODI) methods. The five methods compared produced different results with VAM generating the least transportation cost and better solution. The least value of the transportation costs obtained by the five methods is VAM with the most economical initial feasible solution. It was also established that, out of m + n constraint equations, only m + n-1 equations are linearly independent. With the MODI method, economic values were generated for the dual variables, uis and vjs associated with the source and demand points respectively.

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 5)
DOI 10.11648/j.ajtas.20221105.11
Page(s) 140-149
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), 2022. Published by Science Publishing Group

Keywords

Transportation Problems, Origins, Destinations, Unbalanced Transportation Problem, Optimal Solution, Optimality Test

References
[1] Abdallah, A. H. and Mohammad, A. A. (2012). Solving Transportation Problems using the Best Candidates Methods. Journal of Computer Science and Engineering, 2 (5), pp 23-30.
[2] Ahmed, M. M., Khan, A. R., Uddin, M. D. and Ahmed, F. (2016). A New Approach to Solving Transportation Problems. Open Journal of Optimization, 5 (3), pp 22-30.
[3] Farzana, S. R. and Safiqul, I. (2020). A Comparative Study of Solving Methods of Transportation Problem in Linear Programming Problem. British Journal of Mathematics and Computer Science, 35 (5), pp 45- 57.
[4] Funso, A. (1995). Practical Operational Research for Developing Countries (A Process Frame Work Approach. Panaf Press, Lagos, Nigeria.
[5] Hamdy, A. T. (2017). Operations Research, An Introduction. Pearson Education Limited, 10th ed., England.
[6] Joshi, R. V. (2015). Optimization Techniques for Transportation Problems of Three Variables. IOSR Journal of Mathematics, 9 (1), pp 46-50.
[7] Kalavathy, S. (2013). Operations Research. VIKAS Publishing House, PVT LTD.
[8] Mohammad, H. and Farzana, S. F. (2018). A New Method for Optimal Solutions of Transportation Problems in LPP. Journal of Mathematics, 10 (5), pp 60-75.
[9] Natarajan, A. M., Balasubramani, P. and Tamilarasi, A. (2005). Operations Research. Pearson Education, Singapore.
[10] Ocotlan, D. P., Jorge, A. R., Beatriz, B. L., Alejandro, F. P. and Richardo, A. B. C. (2013). A Survey of Transportation Problems. Journal of Applied Mathematics, 2014, pp 1-17.
[11] Richard, B. and Govindasami, N. (1997). Schaum’s Outline of Theory and Problems of Operations Research, McGraw Hill Co., Toronto.
[12] Sharma, J. K. (2017). Quantitative Techniques for Managerial Decisions. Macmillan Publishers, India.
[13] Shraddha, M. (2017). Solving Transportation Problems by Various Methods. International Journal of Mathematics Trends and Technology, 44 (4), pp 270-275.
[14] Ganesh, A. H., Suresh, M. and Sivakumar, G. (2020). On Solving Fuzzy Transportation Problem based on Distance based Defuzzification Method of Various Fuzzy Quantities using Centroid. Malaya Journal of Matematik, (1), pp 410-426.
[15] Havir, S. K. and Krishna, D. K. (2004). Introductory Operations Research. Springer Science and Business Media LLC.
Cite This Article
  • APA Style

    Awogbemi Clement Adeyeye, Alagbe Samson Adekola, Osamo Caleb Kehinde. (2022). Comparison of Methods of Solving Transportation Problems (TP) and Resolving the Associated Variations. American Journal of Theoretical and Applied Statistics, 11(5), 140-149. https://doi.org/10.11648/j.ajtas.20221105.11

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    ACS Style

    Awogbemi Clement Adeyeye; Alagbe Samson Adekola; Osamo Caleb Kehinde. Comparison of Methods of Solving Transportation Problems (TP) and Resolving the Associated Variations. Am. J. Theor. Appl. Stat. 2022, 11(5), 140-149. doi: 10.11648/j.ajtas.20221105.11

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    AMA Style

    Awogbemi Clement Adeyeye, Alagbe Samson Adekola, Osamo Caleb Kehinde. Comparison of Methods of Solving Transportation Problems (TP) and Resolving the Associated Variations. Am J Theor Appl Stat. 2022;11(5):140-149. doi: 10.11648/j.ajtas.20221105.11

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  • @article{10.11648/j.ajtas.20221105.11,
      author = {Awogbemi Clement Adeyeye and Alagbe Samson Adekola and Osamo Caleb Kehinde},
      title = {Comparison of Methods of Solving Transportation Problems (TP) and Resolving the Associated Variations},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {11},
      number = {5},
      pages = {140-149},
      doi = {10.11648/j.ajtas.20221105.11},
      url = {https://doi.org/10.11648/j.ajtas.20221105.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221105.11},
      abstract = {Transportation Problem is a Linear Programming application to physical distribution of goods and services from various origins to several destinations such that the cost of transportation is minimal. In this study, five different methods were employed to solve transportation problems arising from unequal demand and supply of goods and variations. The methods considered in terms of North West Corner Rule, Least Cost Method, Vogel’s Approximation Method, Row Minima Method and Column Minima Method were compared. Necessary and sufficient condition for the existence of a feasible solution to the transportation problem was initiated and established. Unbalanced transportation problems were resolved using Vogel’s Approximation Method (VAM) and Modified Distribution (MODI) methods. The five methods compared produced different results with VAM generating the least transportation cost and better solution. The least value of the transportation costs obtained by the five methods is VAM with the most economical initial feasible solution. It was also established that, out of m + n constraint equations, only m + n-1 equations are linearly independent. With the MODI method, economic values were generated for the dual variables, uis and vjs associated with the source and demand points respectively.},
     year = {2022}
    }
    

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    T1  - Comparison of Methods of Solving Transportation Problems (TP) and Resolving the Associated Variations
    AU  - Awogbemi Clement Adeyeye
    AU  - Alagbe Samson Adekola
    AU  - Osamo Caleb Kehinde
    Y1  - 2022/09/28
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    DO  - 10.11648/j.ajtas.20221105.11
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 140
    EP  - 149
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20221105.11
    AB  - Transportation Problem is a Linear Programming application to physical distribution of goods and services from various origins to several destinations such that the cost of transportation is minimal. In this study, five different methods were employed to solve transportation problems arising from unequal demand and supply of goods and variations. The methods considered in terms of North West Corner Rule, Least Cost Method, Vogel’s Approximation Method, Row Minima Method and Column Minima Method were compared. Necessary and sufficient condition for the existence of a feasible solution to the transportation problem was initiated and established. Unbalanced transportation problems were resolved using Vogel’s Approximation Method (VAM) and Modified Distribution (MODI) methods. The five methods compared produced different results with VAM generating the least transportation cost and better solution. The least value of the transportation costs obtained by the five methods is VAM with the most economical initial feasible solution. It was also established that, out of m + n constraint equations, only m + n-1 equations are linearly independent. With the MODI method, economic values were generated for the dual variables, uis and vjs associated with the source and demand points respectively.
    VL  - 11
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Author Information
  • Department of Statistics, National Mathematical Centre, Abuja, Nigeria

  • Department of Computer Science, Isaac Jasper Boro College of Education, Sagbama, Nigeria

  • Department of Banking and Finance, Veritas University, Abuja, Nigeria

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