Ultimate open pit stochastic optimization

Marcotte, Denis; Caron, Josiane

doi:10.1016/j.cageo.2012.08.008

Cited by 24 publications

(10 citation statements)

References 7 publications

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“…If (⋅) is equal to the expected value [⋅] , then we fall into the risk-neutral case, which was extensively studied in Marcotte and Caron (2013). One of their main results is that the objective value of UP U is greater than or equal to the objective value of the deterministic problem when using the expected grade [g b ] of each block.…”

Section: Up With Uncertainty On Ore Gradesmentioning

confidence: 99%

“…In Leite and Dimitrakopoulos (2007) and Consuegra and Dimitrakopoulos (2010), the authors show how the net present value of a mine can be improved by using techniques based in stochastic programming. In Marcotte and Caron (2013), expected profits are considered in the objective function, and the authors conclude that larger profits can be obtained by incorporating uncertainty into the UP formulation with respect to the deterministic case and that the relative gains of the stochastic approach increase with the treatment costs. In Espinoza et al (2013), the authors move one step further and study the risk-averse UP problem, replacing the expected value by risk measures such as the conditional value-at-risk (CVaR) (Rockafellar and Uryasev 1997), which has been widely used in applications in finance and energy.…”

Section: Introductionmentioning

confidence: 99%

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The risk-averse ultimate pit problem

2020

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In this work, we consider a risk-averse ultimate pit problem where the grade of the mineral is uncertain. We derive conditions under which we can generate a set of nested pits by varying the risk level instead of using revenue factors. We propose two properties that we believe are desirable for the problem: risk nestedness, which means the pits generated for different risk aversion levels should be contained in one another, and additive consistency, which states that preferences in terms of order of extraction should not change if independent sectors of the mine are added as precedences. We show that only an entropic risk measure satisfies these properties and propose a two-stage stochastic programming formulation of the problem, including an efficient approximation scheme to solve it. We illustrate our approach in a small self-constructed example, and apply our approximation scheme to a real-world section of the Andina mine, in Chile.

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Section: Up With Uncertainty On Ore Gradesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The risk-averse ultimate pit problem

2020

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“…The block model is generated using exploration sample data and geostatistical modelling to estimate the block variables at unsampled locations (Chilès and Delfiner, 1999). The block model can be either deterministic, which reflects the best estimates, or stochastic, which provides possible alternative scenarios that reflect the uncertain geological and economic conditions (Marcotte and Caron, 2013).…”

Section: Pushbacks Geometric Constraints Bench Width Open Pit Planmentioning

confidence: 99%

Automatic generation of feasible mining pushbacks for open pit strategic planning

Bai¹,

Marcotte²,

Gamache³

et al. 2018

J. S. Afr. Inst. Min. Metall.

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“…In recent years, the study on production scheduling optimization has been focused on two aspects. On the one hand, the study is to solve the investment risk caused by the uncertainties of economic and geological environment (Ramazan and Dimitrakopoulos 2013, Marcotte and Caron 2010, Lamghari and Dimitrakopoulos 2012, Godoy and Dimitrakopoulos 2004, Benndorf and Shishvan 2014. On the other hand, the emphasis of the study was on reducing the problems for the optimization algorithm, to make it more efficient and practical (Cullenbine et al 2011, Shishvan and Sattarvand 2015, Askari-Nasab et al 2011, Nasab et al 2010.…”

Section: Introductionmentioning

confidence: 99%

Production Scheduling of Open Pit Metal Mine with Ecological Cost

Wang

et al. 2017

GREE

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：The ecological costs related to the various optimized production schemes were calculated based on the designed ultimate pit. Moreover, the influence of the ecological costs on the selection of production schemes was discussed. In one designed pit, a series of geologically optimum pushbacks with sufficiently small increment were produced using the floating cone method founded on the principle of the highest metal content. Then all the pushbacks were reordered by the dynamic network diagram. The production scheme with the maximum NPV route was considered as the optimum one. The ecological impacts produced by mining were quantified and the ecological cost calculation models, which contain the direct eco-value loss, the indirect eco-value loss, the eco-restoration cost and the carbon emission cost were proposed. In one big open pit mine case, various production schemes were optimized and the one with maximum NPV was selected without taking into account the eco-costs. The scheme with the maximum comprehensive profit was obtained by calculating the eco-cost of each scheme. The results showed that the best scheme considered with the eco-cost was not the scheme with the maximum NPV. Therefore, the eco-cost presents the effect on the selection of the best production scheme.

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Ultimate open pit stochastic optimization

Cited by 24 publications

References 7 publications

The risk-averse ultimate pit problem

The risk-averse ultimate pit problem

Automatic generation of feasible mining pushbacks for open pit strategic planning

Production Scheduling of Open Pit Metal Mine with Ecological Cost

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