Abstract
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.
Highlights
A fundamental problem in open-pit mine planning is the determination of the ultimate pit (UP), which consists of finding the contour of the mine that maximizes the difference between profits obtained from minerals minus extraction costs
Despite its popularity in finance and energy problems, we present somewhat surprising results that show that the conditional value-at-risk (CVaR) does not satisfy risk nestedness or additive consistency
These results show that the entropic risk measure is a good candidate to be utilized for solving the stochastic UP problem
Summary
A fundamental problem in open-pit mine planning is the determination of the ultimate pit (UP), which consists of finding the contour of the mine that maximizes the difference between profits obtained from minerals minus extraction costs. The most common technique is to extract samples from the deposit via drill holes, to infer the distribution of the ore grades based on those samples and to generate scenarios using techniques such as kriging (Cressie 1990). Most of this rich information about the deposit and its ore grades is not used on further steps of the mine planning process, and only one single grade value per block—in general, the average grade of each block—is utilized for solving the UP problem.
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