Abstract

In order to carry out an open pit mining operation, planners must periodically prepare what is known as strategic mine plan. This is a tentative production schedule for the remaining life of the mine that defines which area of a mining reserve will be extracted, in what years this extraction will take place, which resources will be used for the extraction, and how the extracted material will be treated or processed. Given a discretized representation of the mining reserve, the problem of actually computing such a production schedule is known as the Open Pit Mine Production Scheduling Problem (OPM-PSP). OPM-PSP is widely acknowledged to be one of the most critical parts of a mine planning effort: Not only is it instrumental for investors looking to understand the expected cash flows of a project, but also, strategic decisions resulting from solving OPM-PSP can have binding consequences in the life of a mining project. An important limitation of traditional methodologies for solving OPM-PSP is that they fail to explicitly address the volatility of metal prices. In fact, these approaches typically assume a long-term fixed price for each metal, when in truth future prices are unknown. Though it is known that mine planning solutions are very sensitive to price volatility, we are not aware of any attempt to quantify this sensitivity, nor that try to deal with it. In this study, a mean-reverting stochastic process for modeling ore-price uncertainty is proposed. This model allows to analyze the sensitivity of mine planning solutions obtained by traditional mine planning optimization methods. Computational results confirm that solutions are extremely sensitive, and quantify the extent to which small price perturbations can result in tremendous losses of profits. Secondly, this paper pursues to determine if mine planning optimization methods can be modified (by explicitly taking into account price volatility) in order to produce solutions that are less sensitive. To this end, a robust optimization method is implemented and the solutions obtained are compared to those obtained by the traditional methods. Computational results suggest that there do not exist robust solutions that afford much protection against price volatility, thus raising the question: How should price volatility be dealt with in practice?