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Mathematical Programming and Solution Approaches for Transportation Optimisation in Supply Network

Author

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  • Joanna Szkutnik-Rogoż

    (Faculty of Mechanical Engineering, Institute of Mechanics and Computational Engineering, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland)

  • Jarosław Ziółkowski

    (Faculty of Mechanical Engineering, Institute of Mechanics and Computational Engineering, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland)

  • Jerzy Małachowski

    (Faculty of Mechanical Engineering, Institute of Mechanics and Computational Engineering, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland)

  • Mateusz Oszczypała

    (Faculty of Mechanical Engineering, Institute of Mechanics and Computational Engineering, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland)

Abstract

The problem of transport is a special type of mathematical programming designed to search for the optimal distribution network, taking into account the set of suppliers and the set of recipients. This article proposes an innovative approach to solving the transportation problem and devises source codes in GNU Octave (version 3.4.3) to avoid the necessity of carrying out enormous calculations in traditional methods and to minimize transportation costs, fuel consumption, and CO 2 emission. The paper presents a numerical example of a solution to the transportation problem using: the northwest corner, the least cost in the matrix, the row minimum, and Vogel’s Approximation Methods (VAM). The joint use of mathematical programming and optimization was applicable to real conditions. The transport was carried out with medium load trucks. Both suppliers and recipients of materials were located geographically within the territory of the Republic of Poland. The presented model was supported by a numerical example with interpretation and visualization of the obtained results. The implementation of the proposed solution enables the user to develop an optimal transport plan for individually defined criteria.

Suggested Citation

  • Joanna Szkutnik-Rogoż & Jarosław Ziółkowski & Jerzy Małachowski & Mateusz Oszczypała, 2021. "Mathematical Programming and Solution Approaches for Transportation Optimisation in Supply Network," Energies, MDPI, vol. 14(21), pages 1-32, October.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:21:p:7010-:d:664785
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    References listed on IDEAS

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    1. Angelelli, E. & Morandi, V. & Savelsbergh, M. & Speranza, M.G., 2021. "System optimal routing of traffic flows with user constraints using linear programming," European Journal of Operational Research, Elsevier, vol. 293(3), pages 863-879.
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    5. Juman, Z.A.M.S. & Hoque, M.A., 2014. "A heuristic solution technique to attain the minimal total cost bounds of transporting a homogeneous product with varying demands and supplies," European Journal of Operational Research, Elsevier, vol. 239(1), pages 146-156.
    6. Jarosław Ziółkowski & Mateusz Oszczypała & Jerzy Małachowski & Joanna Szkutnik-Rogoż, 2021. "Use of Artificial Neural Networks to Predict Fuel Consumption on the Basis of Technical Parameters of Vehicles," Energies, MDPI, vol. 14(9), pages 1-23, May.
    7. Kramer, Raphael & Maculan, Nelson & Subramanian, Anand & Vidal, Thibaut, 2015. "A speed and departure time optimization algorithm for the pollution-routing problem," European Journal of Operational Research, Elsevier, vol. 247(3), pages 782-787.
    8. Maria Cieśla & Aleksander Sobota & Marianna Jacyna, 2020. "Multi-Criteria Decision Making Process in Metropolitan Transport Means Selection Based on the Sharing Mobility Idea," Sustainability, MDPI, vol. 12(17), pages 1-21, September.
    9. M. Mathirajan & B. Meenakshi, 2004. "Experimental Analysis Of Some Variants Of Vogel'S Approximation Method," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 447-462.
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    Cited by:

    1. Jarosław Ziółkowski & Józef Żurek & Jerzy Małachowski & Mateusz Oszczypała & Joanna Szkutnik-Rogoż, 2022. "Method for Calculating the Required Number of Transport Vehicles Supplying Aviation Fuel to Aircraft during Combat Tasks," Sustainability, MDPI, vol. 14(3), pages 1-18, January.
    2. Jarosław Ziółkowski & Aleksandra Lęgas & Elżbieta Szymczyk & Jerzy Małachowski & Mateusz Oszczypała & Joanna Szkutnik-Rogoż, 2022. "Optimization of the Delivery Time within the Distribution Network, Taking into Account Fuel Consumption and the Level of Carbon Dioxide Emissions into the Atmosphere," Energies, MDPI, vol. 15(14), pages 1-22, July.

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