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

Dževdet Halilović, Miloš Gligorić (), Zoran Gligorić and Dragan Pamučar
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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

Mathematics, 2023, vol. 11, issue 13, 1-35

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.

Keywords: ore pass; optimization; fuzzy linear programming; triangular graph; Torricelli point; ranking function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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