American Journal of Mathematical and Computer Modelling

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The Novel Efficient Method to Solve Balanced and Unbalanced Profit Maximization in Transportation Problems

Received: Sep. 27, 2023    Accepted: Oct. 16, 2023    Published: Oct. 31, 2023
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Abstract

Organizations must plan how to get their commodities from production centers to consumers' homes with the least amount of transportation expense to maximize profit. The Transportation Problem (TP) approach is used to evaluate and reduce the cost of transportation. There are two types of TPs. Such as cost minimization TP and profit maximization TP. Typically, the transportation technique is employed for minimization but the objective function should be maximized rather than minimized in several categories of TPs. By changing the maximizing problem into the minimization problem, these types of issues may be resolved in literature. By deducting the unit costs from the table's greatest unit cost, maximizing is changed into minimization. The first step in achieving an optimal solution is to find the initial basic feasible solution (IBFS). North-West Conner, Least Cost, and Vogel’s Approximation Methods can be used to find IBFS. The optimal solution can be obtained by using only Modified Distribution (MODI) and Stepping Stone Methods. This study proposes a novel direct method to find an optimal or near-optimal solution to profit maximization TPs. In this proposed method, maximization TP is not needed to convert minimization TP. This method is very easy and it has less implementation. In the end, by solving several illustrative examples, we compare the proposed method’s results with other existing methods.

DOI 10.11648/j.ajmcm.20230802.11
Published in American Journal of Mathematical and Computer Modelling ( Volume 8, Issue 2, June 2023 )
Page(s) 17-24
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

Cost Minimization, Profit Maximization, Unit Cost, Optimal Solution, Transportation Problem

References
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  • APA Style

    Oshan Niluminda, Uthpala Ekanayake. (2023). The Novel Efficient Method to Solve Balanced and Unbalanced Profit Maximization in Transportation Problems. American Journal of Mathematical and Computer Modelling, 8(2), 17-24. https://doi.org/10.11648/j.ajmcm.20230802.11

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    ACS Style

    Oshan Niluminda; Uthpala Ekanayake. The Novel Efficient Method to Solve Balanced and Unbalanced Profit Maximization in Transportation Problems. Am. J. Math. Comput. Model. 2023, 8(2), 17-24. doi: 10.11648/j.ajmcm.20230802.11

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    AMA Style

    Oshan Niluminda, Uthpala Ekanayake. The Novel Efficient Method to Solve Balanced and Unbalanced Profit Maximization in Transportation Problems. Am J Math Comput Model. 2023;8(2):17-24. doi: 10.11648/j.ajmcm.20230802.11

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  • @article{10.11648/j.ajmcm.20230802.11,
      author = {Oshan Niluminda and Uthpala Ekanayake},
      title = {The Novel Efficient Method to Solve Balanced and Unbalanced Profit Maximization in Transportation Problems},
      journal = {American Journal of Mathematical and Computer Modelling},
      volume = {8},
      number = {2},
      pages = {17-24},
      doi = {10.11648/j.ajmcm.20230802.11},
      url = {https://doi.org/10.11648/j.ajmcm.20230802.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajmcm.20230802.11},
      abstract = {Organizations must plan how to get their commodities from production centers to consumers' homes with the least amount of transportation expense to maximize profit. The Transportation Problem (TP) approach is used to evaluate and reduce the cost of transportation. There are two types of TPs. Such as cost minimization TP and profit maximization TP. Typically, the transportation technique is employed for minimization but the objective function should be maximized rather than minimized in several categories of TPs. By changing the maximizing problem into the minimization problem, these types of issues may be resolved in literature. By deducting the unit costs from the table's greatest unit cost, maximizing is changed into minimization. The first step in achieving an optimal solution is to find the initial basic feasible solution (IBFS). North-West Conner, Least Cost, and Vogel’s Approximation Methods can be used to find IBFS. The optimal solution can be obtained by using only Modified Distribution (MODI) and Stepping Stone Methods. This study proposes a novel direct method to find an optimal or near-optimal solution to profit maximization TPs. In this proposed method, maximization TP is not needed to convert minimization TP. This method is very easy and it has less implementation. In the end, by solving several illustrative examples, we compare the proposed method’s results with other existing methods.},
     year = {2023}
    }
    

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    AU  - Oshan Niluminda
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    T2  - American Journal of Mathematical and Computer Modelling
    JF  - American Journal of Mathematical and Computer Modelling
    JO  - American Journal of Mathematical and Computer Modelling
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    AB  - Organizations must plan how to get their commodities from production centers to consumers' homes with the least amount of transportation expense to maximize profit. The Transportation Problem (TP) approach is used to evaluate and reduce the cost of transportation. There are two types of TPs. Such as cost minimization TP and profit maximization TP. Typically, the transportation technique is employed for minimization but the objective function should be maximized rather than minimized in several categories of TPs. By changing the maximizing problem into the minimization problem, these types of issues may be resolved in literature. By deducting the unit costs from the table's greatest unit cost, maximizing is changed into minimization. The first step in achieving an optimal solution is to find the initial basic feasible solution (IBFS). North-West Conner, Least Cost, and Vogel’s Approximation Methods can be used to find IBFS. The optimal solution can be obtained by using only Modified Distribution (MODI) and Stepping Stone Methods. This study proposes a novel direct method to find an optimal or near-optimal solution to profit maximization TPs. In this proposed method, maximization TP is not needed to convert minimization TP. This method is very easy and it has less implementation. In the end, by solving several illustrative examples, we compare the proposed method’s results with other existing methods.
    VL  - 8
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Author Information
  • Department of Physical Sciences, Faculty of Applied Sciences, Rajarata University of Sri Lanka, Mihinthale, Sri Lanka

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

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