Abstract
We present a mixed-integer programming model for solving the long-term planning problem of an underground mine. This model, which establishes the sequence of mining for a horizon of 20 years, determines which lens of the geological model will be mined and in what order, while respecting the operational constraints. For each lens to be mined, a specific cut-off grade has to be selected to maximize the net present value. The choice of a cut-off grade affects the volume and the average grade of each lens, which increases the size of problems to be solved. To reduce the computation time, different acceleration strategies and a Fix-and-Optimize heuristic are proposed. Computational experiments on instances of different sizes are performed to (1) assess the quality of the solution found by each method and (2) present the impact of the variable cut-off grade.
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Acknowledgements
This research was partially supported by the Fonds de recherche du Québec - Nature et technologies (FRQ-NT) and by the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), grants 313521/2017-4 and 425962/2016-4. All support is gratefully acknowledged. Computations were made on the supercomputer Mp2, managed by Calcul Québec and Compute Canada. The operation of this supercomputer is funded by the Canada Foundation for Innovation (CFI), the ministère de l’Économie, de la science et de l’innovation du Québec (MESI) and the Fonds de recherche du Québec - Nature et technologies (FRQ-NT). The authors would also like to thank the anonymous reviewers for their helpful and constructive comments that contributed to improve the final version of this paper, and Thibaut Vidal for helping with the figures.
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A Detailed Computational Experiments
A Detailed Computational Experiments
In this section, we present detailed information and results for all mine sizes and all approaches presented throughout the paper. Table 9 presents the number of lenses for each instance, in total and for each mine, and the number of variables, constraints, and non-zeros present in the MIP formulation. In Tables 10, 11, 12, 13, 14, 15, 16 and 17, we present the results for the original MIP formulation with the preprocessing procedure, for the Fix-and-Optimize Heuristic and for the MIP formulation using the Fix-and-Optimize heuristic solution as a hot-start. All results are presented using one thread and four threads, with a time limit of 12 hours for the MIP formulation.
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Martinelli, R., Collard, J. & Gamache, M. Strategic planning of an underground mine with variable cut-off grades. Optim Eng 21, 803–849 (2020). https://doi.org/10.1007/s11081-019-09479-6
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DOI: https://doi.org/10.1007/s11081-019-09479-6