Mining Goes Digital – Mueller et al. (Eds)
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
300
Performance assessment of antithetic random fields in a stochastic
mine planning model
G. Nelis & N. Morales
Advanced Mining Technology Center and Department of Mining Engineering, University of Chile,
Santiago, Chile
J.M. Ortiz
The Robert M. Buchan Department of Mining, Queen’s University, Kingston, Canada
ABSTRACT: Conventional mine planning often relies on parameters estimation to obtain
a single production plan. There is no guarantee that these estimations will be accurate in
the long term, and this could lead to issues in the mine operation. To deal with this uncertainty, different optimization models have been proposed, which incorporate equally probable scenarios. Unfortunately, the incorporation of uncertainty also imposes a computational
challenge: a large number of scenarios is desirable to capture the variability of the uncertain parameters, but each additional scenario increases the computational complexity of the
mathematical problem, limiting the cases that can be addressed with stochastic optimization.
This paper implements a variance reduction technique in the sequential Gaussian simulation
algorithm, which generates grade scenarios with negative correlation, so fewer scenarios can
be used without compromising the representation of the grade variability. Our experiments
show that using these scenarios achieves the same precision in the objective value of a stochastic optimization problem, but using fewer simulations in the formulation compared with
the conventional gaussian algorithm.
Keywords: Antithetic Random Fields, Variance Reduction, Stochastic Optimization, Mine
Planning, Geoestatistics
1 INTRODUCTION
Uncertainty in Mine Planning has been a widely studied topic in the last decade. Several
works have stated the effect of uncertainty in production plans, and the difficulty in achieving the value predicted based on estimated models (Smith & Dimitrakopoulos 1999 and
Dimitrakopoulos et al. 2002). Given this scenario, different methodologies has been proposed to incorporate the uncertainty into the decision making process, using probable future
scenarios for the uncertain parameters (costs, prices, grades, etc.). Among these methodologies, several stochastic optimization models has been proposed in the literature, which aim to
obtain a production plan considering many scenarios in the formulation in order to obtain a
more profitable or robust production schedule. Regarding to geological uncertainty, geostatistics provides simulation techniques, which generates several possible geological scenarios,
which can be incorporated into stochastic optimization models. However, the optimization
models related to mine planning are often difficult to solve, and this issue is accentuated in
the stochastic framework with several scenarios. This poses a clear trade-off: a high number
of scenarios is needed to ensure a good representation of the true variability of the uncertain parameter. At the same time, each scenario makes the problem harder to solve, which
is a limiting factor to address complex and large mines. Given this scenario, in this paper we
evaluate the performance of the antithetic random fields technique, which aims to reduce
the number of grade scenarios needed in a optimization problem, without compromising
© 2019 Taylor & Francis Group, London, ISBN 978-0-367-33604-2
300
Performance assessment of antithetic random fields in a stochastic
mine planning model
G. Nelis & N. Morales
Advanced Mining Technology Center and Department of Mining Engineering, University of Chile,
Santiago, Chile
J.M. Ortiz
The Robert M. Buchan Department of Mining, Queen’s University, Kingston, Canada
ABSTRACT: Conventional mine planning often relies on parameters estimation to obtain
a single production plan. There is no guarantee that these estimations will be accurate in
the long term, and this could lead to issues in the mine operation. To deal with this uncertainty, different optimization models have been proposed, which incorporate equally probable scenarios. Unfortunately, the incorporation of uncertainty also imposes a computational
challenge: a large number of scenarios is desirable to capture the variability of the uncertain parameters, but each additional scenario increases the computational complexity of the
mathematical problem, limiting the cases that can be addressed with stochastic optimization.
This paper implements a variance reduction technique in the sequential Gaussian simulation
algorithm, which generates grade scenarios with negative correlation, so fewer scenarios can
be used without compromising the representation of the grade variability. Our experiments
show that using these scenarios achieves the same precision in the objective value of a stochastic optimization problem, but using fewer simulations in the formulation compared with
the conventional gaussian algorithm.
Keywords: Antithetic Random Fields, Variance Reduction, Stochastic Optimization, Mine
Planning, Geoestatistics
1 INTRODUCTION
Uncertainty in Mine Planning has been a widely studied topic in the last decade. Several
works have stated the effect of uncertainty in production plans, and the difficulty in achieving the value predicted based on estimated models (Smith & Dimitrakopoulos 1999 and
Dimitrakopoulos et al. 2002). Given this scenario, different methodologies has been proposed to incorporate the uncertainty into the decision making process, using probable future
scenarios for the uncertain parameters (costs, prices, grades, etc.). Among these methodologies, several stochastic optimization models has been proposed in the literature, which aim to
obtain a production plan considering many scenarios in the formulation in order to obtain a
more profitable or robust production schedule. Regarding to geological uncertainty, geostatistics provides simulation techniques, which generates several possible geological scenarios,
which can be incorporated into stochastic optimization models. However, the optimization
models related to mine planning are often difficult to solve, and this issue is accentuated in
the stochastic framework with several scenarios. This poses a clear trade-off: a high number
of scenarios is needed to ensure a good representation of the true variability of the uncertain parameter. At the same time, each scenario makes the problem harder to solve, which
is a limiting factor to address complex and large mines. Given this scenario, in this paper we
evaluate the performance of the antithetic random fields technique, which aims to reduce
the number of grade scenarios needed in a optimization problem, without compromising