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Letelier, O. R., Espinoza, D., Goycoolea, M., Moreno, E., & Munoz, G. (2020). Production Scheduling for Strategic Open Pit Mine Planning: A Mixed-Integer Programming Approach. Oper. Res., 68(5), 1425–1444.
Abstract: Given a discretized representation of an ore body known as a block model, the open pit mining production scheduling problem that we consider consists of defining which blocks to extract, when to extract them, and how or whether to process them, in such a way as to comply with operational constraints and maximize net present value. Although it has been established that this problem can be modeled with mixed-integer programming, the number of blocks used to represent real-world mines (millions) has made solving large instances nearly impossible in practice. In this article, we introduce a new methodology for tackling this problem and conduct computational tests using real problem sets ranging in size from 20,000 to 5,000,000 blocks and spanning 20 to 50 time periods. We consider both direct block scheduling and bench-phase scheduling problems, with capacity, blending, and minimum production constraints. Using new preprocessing and cutting planes techniques, we are able to reduce the linear programming relaxation value by up to 33%, depending on the instance. Then, using new heuristics, we are able to compute feasible solutions with an average gap of 1.52% relative to the previously computed bound. Moreover, after four hours of running a customized branch-and-bound algorithm on the problems with larger gaps, we are able to further reduce the average from 1.52% to 0.71%.
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Ogunmodede, O., Lamas, P., Brickey, A., Bogin, G., & Newman, A. (2022). Underground production scheduling with ventilation and refrigeration considerations. Optim. Eng., 23(3), 1677–1705.
Abstract: Underground mine production scheduling determines when, if ever, activities associated with the extraction of ore should be executed. The accumulation of heat in the mine where operators are working is a major concern. At the time of this writing, production scheduling and ventilation decisions are not made in concert. Correspondingly, heat limitations are largely ignored. Our mixed-integer program maximizes net present value subject to constraints on precedence, and mill and extraction capacities with the consideration of heat using thermodynamic principles, while affording the option of activating refrigeration to mitigate heat accumulation. In seconds to hours, depending on the problem size (up to thousands of activities and 900 daily time periods), a corresponding methodology that exploits the mathematical problem structure provides schedules that maintain a safe working environment for mine operators; optimality gaps are no more than 15% and average less than half that for otherwise-intractable instances.
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