Optimisation of long-term production scheduling aims to define the extraction sequence of parts of the deposit over time and is used to maximise the global asset. Discrepancies between actual production and planned expectations in terms of tonnes and grades of multiple elements cause substantial loss of project value and are mainly caused by ignoring the in-situ grade variability and uncertainty. The ability to efficiently model grade uncertainty and variability as well as integrate these into production scheduling can considerably improve risk management and increase the project value. The first part of this thesis considers aspects of implementation and the practical application of the new and computationally efficient generalised sequential Gaussian simulation for modelling grade uncertainty. The second part focuses on long-term production scheduling of multi-element deposits under geological uncertainty and presents an application to the Yandi Central 1 iron ore deposit, located in the NW of Western Australia (WA).
The generalised sequential Gaussian simulation relies on sharing the neighbourhood of adjacent nodes and simulates groups of nodes simultaneously, instead of the traditional node-by-node simulation. A theoretical investigation prior to this thesis showed that the method is computationally efficient and suitable for simulation on large grids of nodes. Practical aspects of this method are investigated using the exhaustively known Walker Lake dataset and, subsequently, demonstrated in a case study on a porphyry copper deposit. The relationship between the size of the groups of nodes to be simulated simultaneously and the neighbourhood size used is found to be critical to both theoretical accuracy and computational efficiency. The theoretical accuracy of the method can be assessed using a general measure of accuracy, the relative screen-effect approximation loss, defined as the relative mean-square difference between the simulated value conditioned to the information in the local neighbourhood and the simulated value conditioned to all information. This measure may be used to calibrate the method to obtain results with an acceptable level of accuracy. Results show that relative small groups, such as 2x2x2 nodes or 3x3x3 nodes, substantially reduce computational costs while generating no artefacts and should thus be used in practical applications. Larger groups, such as 8x8x8 nodes, are computational inefficient and have the potential to produce artefacts in the realisations. Computational efficiency of the method is demonstrated in the case study involving orebody models with up to 14,000,000 grid nodes, where the method is up to 20 times faster than the well-established sequential Gaussian simulation when using relatively small group sizes. At the same time small group sizes ensure that the generalised sequential Gaussian simulation maintains a high level of accuracy.
Multiple simulated orebody models provide suitable input for the optimisation of production scheduling under uncertainty. A general stochastic integer programming (SIP) formulation for long-term production scheduling under geological uncertainty for single multi-element deposits is presented and applied to the Yandi Central 1 iron ore deposit, W A. The application is based on input parameter in terms of required ore tonnage and target grades per period derived from a global multi-pit scheduling approach and can thus represent an integrated part of a global asset optimisation approach. The ability of the stochastic scheduling approach to efficiently generate schedules that (i) are practical; (ii) are optimal for the local mine development; and (iii) have a desired level of risk for not meeting multiple production targets is demonstrated. Using manual open pit design and haul road construction, results obtained from the SIP formulation in this study can be converted to a mineable schedule without any practical loss of optimality. It is found that the goals of risk minimisation and practicality in the formulation are contradicting, since lower risk of not meeting production targets results in a more selective extraction sequence, which complicates equipment access. A fine-tuning of the risk controlling parameters in the formulation used results in a schedule that compromised both goals. The application to the Yandi Central 1 iron ore deposit, WA, demonstrates the computational efficiency of the formulation; schedules are generally generated in less than 20 hours (Pentium 4, 2 GHz processor). A further reduction of in computational costs may be achieved by taking the cross-correlation between the elements in the deposit into account. Results suggest that by controlling the risk of Al2O3 and SiO2, the element Fe is kept on line automatically and does not need to be considered in the scheduling formulation used. This simplification requires a reproduction of cross-correlations on a local scale and calls for joint-simulation of the multiple elements. A final comparison of the stochastic scheduling approach to a conventional approach based on a single estimated orebody model illustrates the benefit of the stochastic approach. Ignoring grade-uncertainty can cause substantial losses in profit. In this case study, losses due to not meeting production targets increased by 150% compared to the stochastic approach. This difference illustrates the value of stochastic modelling including both, modelling grade uncertainty and stochastic production scheduling.