Antithetic random fields applied to mine planning under uncertainty

Abstract

Traditional practice in mine planning often relies on estimation techniques that fail to account for the intrinsicuncertainty of geology and grades, which may have significant consequences in the mine operation. Dealing withthis uncertainty has been a major topic in the last years, where different algorithms and stochastic optimizationmodels have been proposed to tackle this issue. However, the increasing complexity of these stochastic modelsand the use of several simulations to represent the deposit variability impose a computational challenge in termsof resolution times, making them difficult to apply in large data or complex mining operations. In this paper weexplore the antithetic randomfields approach as a variance reduction technique, to solve a stochastic short-termmine planning problem, aiming to reduce the number of simulations required to obtain a reliable NPV value. Thereliability of the result is measured by the variance of the NPV when the problem is optimized with different setsof realizations. Our results show that this technique produces a significant variance reduction in the inference ofthe expected NPV value in the stochastic problem for a copper deposit application, generating a lower dispersionwith a smaller sample size, compared to traditional simulation techniques.