Stochastic Dynamic Optimization of Cut-off Grade in Open Pit Mines
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Mining operations exploit mineral deposits, processing a portion of the extracted material to produce salable products. The concentration of valuable commodities within these deposits, or the grade, is heterogeneous. Not all material has sufficiently high grades to economically justify processing. Cut-off grade is the lowest grade at which material is considered ore and is processed to create a concentrated commodity product. The choice of cut-off grade at a mining project can be varied over time and dramatically impacts both the operation of the mine and the economics of the project. The majority of literature and the accepted industry practices focus on optimizing cut-off grade under known commodity prices. However, most mining operations sell their products into highly competitive global markets, which exhibit volatile commodity prices. Making planning decisions assuming that a given commodity price prediction is accurate can lead to sub-optimal cut-off grade strategies and inaccurate valuations. Some academic investigations have been conducted to optimize cut-off grade under stochastic or uncertain price conditions. These works made large simplifications in order to facilitate the computation of a solution. These simplifications mean that detailed mine planning data cannot be used and the complexities involved in many real world projects cannot be considered. A new method for optimizing cut-off grade under stochastic or uncertain prices is outlined and demonstrated. The model presented makes use of theory from the field of Real Options and is designed to incorporate real mine planning data. The model introduces two key innovations. The first is the method in which it handles the cut-off grade determination. The second innovation is the use of a stochastic price model of the entire futures curve and not simply a stocastic spot price model. The model is applied to two cases. The first uses public data from a National Instrument 43-101 report. The second case uses highly detailed, confidential data, provided by a mining company from one of their operating mines.