Stochastic Final Pit Limits: An Efficient Frontier Analysis under Geological Uncertainty in the Open-Pit Mining Industry

Enrique Jelvez,Julian M Ortiz,Nelson Morales

doi:10.3390/math10010100

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.

Highlights

The final pit limit problem is defined as determining the ultimate mining limits of an ore deposit exploited by the open-pit mining method such that a maximum undiscounted profit is obtained from its extraction, respecting the precedence constraints given by overall slope angles that ensure stable walls of the open-pit mine
The original samples are transformed to normal scores, and a standard Gaussian random variable is simulated in a spatial grid
Applying Procedure 1, Table 1 shows the main numerical results obtained: the parameter αα that determines the maximum risk μμ allowed according to Equation (18), value at risk (VaR), conditional value at risk (CVaR), expected profit, and the distance (Euclidean metric) to the ideal point (DIP), which is presented as a decision criterion

Summary

Introduction

The final pit limit plays a crucial role in long-term open-pit mine production planning It approximates the placement, size, shape, and depth of the mine at the end of its exploitation, determining important aspects for mine operation such as the layout of access roads, ramps, waste dumps, stockpiles, processing, and other facilities, as well as in developing a production schedule. An economic value that represents its profit is computed for each block This value depends on the estimated geological attributes and economic and operational parameters such as ore price, costs, and metallurgical recoveries.

Methods

Results

Discussion

Conclusion