Abstract
Long-term block scheduling is a challenging problem that involves determining the best extraction period for blocks to maximize the net present value of the open-pit mining business. This process involves multiple constraints, mainly ensuring safe pit walls and imposing maximum limits on operational resource consumption. However, most of the models proposed in the literature do not sufficiently consider geometric constraints that ensure a minimum space for mining equipment to operate safely. These models overlook practical and operational constraints and generate solutions that are difficult to implement. Consequently, the promised net present value cannot be achieved. In this paper, we propose an integer linear programming model that considers minimum mining width requirements along with a decomposition heuristic method to solve it.The proposed model determines which blocks should be mined and when to maximize net present value while ensuring safe pit walls and respecting limits on operational resources and geometric constraints. Geometric constraints require that the minimum operational distance be considered within each extraction period. Because the incorporation of geometric constraints in the proposed model makes it harder to solve, a time-space decomposition heuristic is implemented. This heuristic consists of successive time and space aggregation/disaggregation to generate simpler subproblems to be solved. This approach was applied on two case studies. The results show that the proposed methodology generates practical production plans that are more realistic to implement in mining operations, lowering the gap between factual and promised net present value.
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Abbreviations
- AGCPIT:
-
Aggregated geometric constrained pit limit problem
- CPIT:
-
Constrained pit limit problem
- DBS:
-
Direct block scheduling
- GCPIT:
-
Geometric constrained pit limit problem
- LG:
-
Lerchs & Grossmann (algorithm)
- NPV:
-
Net present value
- PCPSP:
-
Precedence constrained production scheduling problem
- STDH:
-
Space and time decomposition heuristic
- UPIT:
-
Ultimate pit limit problem
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We would like to express sincere thanks to Nick Sahinidis and the two anonymous reviewers whose comments/suggestions helped improve and clarify this manuscript.
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This research has been funded by the Chilean National Research and Development Agency ANID through the programs PIA/Basal Grants AFB180004 and AFB220002 (P.NP. and E.J.) and FONDECYT Iniciación Grant 11221352 (E.J.).
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Nancel-Penard, P., Jelvez, E. A direct block scheduling model considering operational space requirement for strategic open-pit mine production planning. Optim Eng (2023). https://doi.org/10.1007/s11081-023-09875-z
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DOI: https://doi.org/10.1007/s11081-023-09875-z