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An Examination of Different Types of Transportation Problems and Mathematical Models

Received: 19 July 2022     Accepted: 31 August 2022     Published: 18 October 2022
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Abstract

Optimization processes in mathematics, computer science, and economics solve problems effectively by selecting the best element from a set of available alternatives. One of the most important and successful applications of optimization is the transportation problem (TP), which is a subclass of linear programming (LP) in operations research (OR). Its goal is to find shipping routes between supply and demand centers that will meet the demand for a given quantity of goods or services at each destination center while incurring the fewest transportation costs. Various transportation-related problems involving constraints, mixed constraints, intervals, bottlenecks, and uncertain quantities have recently received a great deal of attention. This relates to the transportation problem. In order to solve the TP, numerous researchers have proposed various exact, heuristic, and meta-heuristic strategies in the literature. Some strategies seek an initial, basic, feasible solution, whereas others seek the optimal way to solve the TP. Because it promotes economic and social activity, the transportation problem is important in operations research and management science. This research paper provides a high-level overview of various transportation-related issues and mathematical models. This can be used successfully to solve various business problems relating to the distribution of products, which are commonly referred to as transportation problems.

Published in American Journal of Mathematical and Computer Modelling (Volume 7, Issue 3)
DOI 10.11648/j.ajmcm.20220703.11
Page(s) 37-48
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

Classical Transportation Problems, Bottleneck Transportation Problems, Multi-objective Transportation Problems, Interval and Fuzzy Transportation Problems

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    Ekanayake Mudiyanselage Uthpala Senarath Bandara Ekanayake; Wasantha Bandara Daundasekara; Sattambirallage Pantaleon Chrysantha Perera. An Examination of Different Types of Transportation Problems and Mathematical Models. Am. J. Math. Comput. Model. 2022, 7(3), 37-48. doi: 10.11648/j.ajmcm.20220703.11

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    Ekanayake Mudiyanselage Uthpala Senarath Bandara Ekanayake, Wasantha Bandara Daundasekara, Sattambirallage Pantaleon Chrysantha Perera. An Examination of Different Types of Transportation Problems and Mathematical Models. Am J Math Comput Model. 2022;7(3):37-48. doi: 10.11648/j.ajmcm.20220703.11

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      title = {An Examination of Different Types of Transportation Problems and Mathematical Models},
      journal = {American Journal of Mathematical and Computer Modelling},
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      url = {https://doi.org/10.11648/j.ajmcm.20220703.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20220703.11},
      abstract = {Optimization processes in mathematics, computer science, and economics solve problems effectively by selecting the best element from a set of available alternatives. One of the most important and successful applications of optimization is the transportation problem (TP), which is a subclass of linear programming (LP) in operations research (OR). Its goal is to find shipping routes between supply and demand centers that will meet the demand for a given quantity of goods or services at each destination center while incurring the fewest transportation costs. Various transportation-related problems involving constraints, mixed constraints, intervals, bottlenecks, and uncertain quantities have recently received a great deal of attention. This relates to the transportation problem. In order to solve the TP, numerous researchers have proposed various exact, heuristic, and meta-heuristic strategies in the literature. Some strategies seek an initial, basic, feasible solution, whereas others seek the optimal way to solve the TP. Because it promotes economic and social activity, the transportation problem is important in operations research and management science. This research paper provides a high-level overview of various transportation-related issues and mathematical models. This can be used successfully to solve various business problems relating to the distribution of products, which are commonly referred to as transportation problems.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - An Examination of Different Types of Transportation Problems and Mathematical Models
    AU  - Ekanayake Mudiyanselage Uthpala Senarath Bandara Ekanayake
    AU  - Wasantha Bandara Daundasekara
    AU  - Sattambirallage Pantaleon Chrysantha Perera
    Y1  - 2022/10/18
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ajmcm.20220703.11
    DO  - 10.11648/j.ajmcm.20220703.11
    T2  - American Journal of Mathematical and Computer Modelling
    JF  - American Journal of Mathematical and Computer Modelling
    JO  - American Journal of Mathematical and Computer Modelling
    SP  - 37
    EP  - 48
    PB  - Science Publishing Group
    SN  - 2578-8280
    UR  - https://doi.org/10.11648/j.ajmcm.20220703.11
    AB  - Optimization processes in mathematics, computer science, and economics solve problems effectively by selecting the best element from a set of available alternatives. One of the most important and successful applications of optimization is the transportation problem (TP), which is a subclass of linear programming (LP) in operations research (OR). Its goal is to find shipping routes between supply and demand centers that will meet the demand for a given quantity of goods or services at each destination center while incurring the fewest transportation costs. Various transportation-related problems involving constraints, mixed constraints, intervals, bottlenecks, and uncertain quantities have recently received a great deal of attention. This relates to the transportation problem. In order to solve the TP, numerous researchers have proposed various exact, heuristic, and meta-heuristic strategies in the literature. Some strategies seek an initial, basic, feasible solution, whereas others seek the optimal way to solve the TP. Because it promotes economic and social activity, the transportation problem is important in operations research and management science. This research paper provides a high-level overview of various transportation-related issues and mathematical models. This can be used successfully to solve various business problems relating to the distribution of products, which are commonly referred to as transportation problems.
    VL  - 7
    IS  - 3
    ER  - 

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

  • Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka

  • Department of Engineering Mathematics, Faculty of Engineering, University of Peradeniya, Peradeniya, Sri Lanka

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