Reproduction of inequality constraint between iron and silica for accurate production scheduling

Abstract

Conventional geostatistical algorithms cannot reproduce bivariate complexities such as inequality constraint, nonlinearity and heteroscedasticity. Poor reproduction of these features may decrease the accuracy and reliability of mine planning results. For example, it is not unusual to have an inequality constraint between primary and disturbing elements in a metalliferous deposit. Implementation of traditional methodologies for such complex data sets can lead to the incorrect reproduction of a bivariate relationship, which will affect the validity of NPV results. In this paper, an iron data set containing iron and silica grades with an inequality constraint between variables is introduced as a case study. This study proposes an algorithm based on a hierarchical sequential Gaussian cosimulation integrated with inverse transform sampling. The proposed methodology considers the linear inequation between two variables in the hierarchical cosimulation process to reproduce an inequality constraint. As a comparison, conventional sequential Gaussian cosimulation is also applied to the same data set to demonstrate the difference in bivariate relationships from both models. Unlike the proposed algorithm, the conventional cosimulation cannot reproduce an inequality constraint and slightly overestimates silica grades. The modelled realisations are then used to assess the uncertainty of a plan and generate a stochastic strategy that adapts the destination of the blocks depending on the scenario. Two-stage stochastic long-term production scheduling takes extraction decisions using average information (ie e-type model) and ore/waste destinations based on geostatistical realisations. As a result, the proposed strategy is closer to the upper bound, highest possible NPV for each realisation, than to the lower bound, deterministic strategy that does not manage the risk of sending extracted material to wrong destinations. Furthermore, Comparing production schedules resulting from proposed and conventional geostatistical methodologies shows the importance of inequality constraint reproduction and more accurate long-term mine planning.