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Pit Optimization on the Efficient Frontier


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The mining industry has become increasingly concerned with the effects of uncertainty and risk in resource modeling. Some companies are moving away from deterministic geologic modeling techniques to approaches that quantify uncertainty. Stochastic modeling techniques produce multiple realizations of the geologic model to quantify uncertainty, but integrating these results into pit optimization is non-trivial. Conventional pit optimization calculates optimal pit limits from a block model of economic values and precedence rules for pit slopes. There are well established algorithms for this including Lerchs-Grossmann, push-relabel and pseudo-flow; however, these conventional optimizers have limited options for handling stochastic block models. The conventional optimizers could be modified to incorporate a block-by-block penalty based on uncertainty, but not uncertainty in the resource within the entire pit. There is a need for a new pit limit optimizing algorithm that would consider multiple block model realizations. To address risk management principles in the pit shell optimization stage, a novel approach is presented for optimizing pit shells over all realizations. The inclusion of multiple realizations provides access to summary statistics across the realizations such as the risk or uncertainty in the pit value. This permits an active risk management approach. A heuristic pit optimization algorithm is proposed to target the joint uncertainty between multiple input models. A practical framework is presented for actively managing the risk by adapting Harry Markowitz’s “Efficient Frontier” approach to pit shell optimization. Choosing the acceptable level of risk along the frontier can be subjective. A risk-rating modification is proposed to minimize some of the subjectivity in choosing the acceptable level of risk. The practical application of the framework using the heuristic pit optimization algorithm is demonstrated through multiple case studies.
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