Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry
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Bibliographic record
Abstract
In the context of planning the exploitation of an open-pit mine, the final pit limit problem consists of finding the volume to be extracted so that it maximizes the total profit of exploitation subject to overall slope angles to keep pit walls stable. To address this problem, the ore deposit is discretized as a block model, and efficient algorithms are used to find the optimal final pit. However, this methodology assumes a deterministic scenario, i.e., it does not consider that information, such as ore grades, is subject to several sources of uncertainty. This paper presents a model based on stochastic programming, seeking a balance between conflicting objectives: on the one hand, it maximizes the expected value of the open-pit mining business and simultaneously minimizes the risk of losses, measured as conditional value at risk, associated with the uncertainty in the estimation of the mineral content found in the deposit, which is characterized by a set of conditional simulations. This allows generating a set of optimal solutions in the expected return vs. risk space, forming the Pareto front or efficient frontier of final pit alternatives under geological uncertainty. In addition, some criteria are proposed that can be used by the decision maker of the mining company to choose which final pit best fits the return/risk trade off according to its objectives. This methodology was applied on a real case study, making a comparison with other proposals in the literature. The results show that our proposal better manages the relationship in controlling the risk of suffering economic losses without renouncing high expected profit.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it