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An Underground Mine Ore Pass System Optimization via Fuzzy 0–1 Linear Programming with Novel Torricelli–Simpson Ranking Function

Author

Listed:
  • Dževdet Halilović

    (Faculty of Mining and Geology, University of Belgrade, Đušina 7, 11000 Belgrade, Serbia)

  • Miloš Gligorić

    (Faculty of Mining and Geology, University of Belgrade, Đušina 7, 11000 Belgrade, Serbia)

  • Zoran Gligorić

    (Faculty of Mining and Geology, University of Belgrade, Đušina 7, 11000 Belgrade, Serbia)

  • Dragan Pamučar

    (Department of Operations Research and Statistic, Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000 Belgrade, Serbia
    College of Engineering, Yuan Ze University, No. 135, Yuandong Rd, Zhongli District, Taoyuan City 320, Taiwan)

Abstract

In this work, we propose a 3D dynamic optimization model that enables the design of an underground mine ore pass system with uncertainties. Ore transportation costs and ore pass development costs are quantified by triangular fuzzy numbers. Transportation costs are treated as production costs, and they vary over the duration of mining operation, while development costs of ore passes are treated as an investment, and they are treated as constant. The developed model belongs to the class of fuzzy 0–1 linear programming models, where the fuzzy objective cost function achieves a minimum value, with respect to given set of techno-dynamic constraints. Searching for optimal value in the fuzzy environment is a hard task, and because of that, we developed a new ranking function which transforms the fuzzy optimization model into a crisp one. A triangular fuzzy number can be presented as a triangular graph G(V,E) composed of vertices and edges. The x -coordinate of the Torricelli point of a triangular graph presents the crisp value of a triangular fuzzy number. The use of this model lets us know the optimal number of ore passes, optimal location of ore passes, and optimal dynamic ore transportation plan.

Suggested Citation

  • Dževdet Halilović & Miloš Gligorić & Zoran Gligorić & Dragan Pamučar, 2023. "An Underground Mine Ore Pass System Optimization via Fuzzy 0–1 Linear Programming with Novel Torricelli–Simpson Ranking Function," Mathematics, MDPI, vol. 11(13), pages 1-35, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2914-:d:1182362
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    References listed on IDEAS

    as
    1. Ning Li & Shuzhao Feng & Tao Lei & Haiwang Ye & Qizhou Wang & Liguan Wang & Mingtao Jia, 2022. "Rescheduling Plan Optimization of Underground Mine Haulage Equipment Based on Random Breakdown Simulation," Sustainability, MDPI, vol. 14(6), pages 1-18, March.
    2. Palash Dutta, 2021. "A Sophisticated Ranking Method of Fuzzy Numbers Based on the Concept of Exponential Area," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 303-318, July.
    3. He Chen & Shibo Yu & Zhixiu Wang & Ye Yuan, 2018. "A New Plugging Technology and Its Application for the Extensively Collapsed Ore Pass in the Non-Empty Condition," Energies, MDPI, vol. 11(6), pages 1-15, June.
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