Risk in ultimate pit selection

The basis for the selection of the ultimate pit for an openpit mining operation is generally opaque. Some form of valuebased analysis will generally guide the final decision; however, the value will often gradually plateau while the ultimate pit size continues to increase. There is no established framework to guide specialists in the selection of the ultimate pit, with such decisions regularly made on a somewhat arbitrary basis. The key component that is missing from the analyses typically used to select the size of the ultimate pit is risk. Once risk is quantified within the analysis framework, the decision-making range is significantly reduced and the process for selecting the ultimate pit becomes more consistent, replicable and defensible. The technique outlined in this paper provides an approach to including risk in the process used to select the ultimate pit. Background The pit optimization process is widely used in the mining industry for the selection of both staging pits and the ultimate pit for deposits mined using openpit techniques. Pit optimization algorithms, referred to as maximum flow in optimization theory [1], provide essential guidance in terms of the high-level sequence that should be used to access the deposit, but the selection of the optimum ultimate pit remains subjective [2-6]. Methods The approach being outlined to incorporate risk quantification in the decision-making process is to calculate the value at risk (VAR) for the selected risk(s). In the case study presented in the full paper the commodity price risk was selected for analysis, being arguably the most obvious risk to consider. Other risks can be incorporated in this framework with appropriate adjustments to the modeling methodology. The variability in the future price environment is represented in the analyses by considering discretely two pricing points where there can be expected to be a disconnect: (1) the forecast price at which planning decisions must be made (the planning price environment), and (2) the price at which the operation must then deliver a result (the future operating price environment). The first dictates the planning decisions, and the second is what eventuates. Clearly, these will never be identical. This is recognized as a simplification, the discussion of which is expanded in the full paper. A summary of the methodology used is outlined below: Establish the range for commodity price analysis (including any correlations to other prices, costs and so on, and the probabilities for each price point). The analyses in this paper are based on 10 upside prices, 10 downside prices and the base case price, for a total of 21 macroeconomic input sets.Run 21 pit optimizations, one for each macroeconomic input set.Run a shell grouping algorithm to ensure unbiased and realistic stage sizes progress to the following steps.Run 441 schedule optimizations, one for each combination of the 21 pit optimizations (ranging ultimate pit size) and the 21 macroeconomic input sets (ranging the price).Calculate the value and VAR for each combination and probability, and adjust the results for the schedule price probability only. Results Figure 1 presents the VAR data after being adjusted for the probability of the schedule price environment and quantifies the VAR of selecting an ultimate pit that is either too small or too large as a function of the commodity price probability distribution used. A simplified and intuitive explanation of Fig. 1 is that the x-axis presents a transition of ultimate pit size from smaller ultimate pits on the left through to larger on the right, and then for each of the pit sizes the box and whisker data present the probability-adjusted VAR of the schedule results ranged from a low commodity price through to a high commodity price. The excess stripping VAR (indicating the ultimate pit is too large) increases from functionally zero in small ultimate pits to being significant as the ultimate pit increases in size. The residual resource VAR (indicating the ultimate pit is too small) logically displays the opposite trend. Discussion The VAR approach to the selection of the ultimate pit is different from the standard approach and can be expected to give different results. If it is assumed that the standard approach was to use a single optimization model and base the ultimate pit selection on the revenue factor 1.0 shell (this is not being advocated), which is one approach that is commonly cited and easy to understand, the following points summarize the differences between the RF1.0 and the VAR ultimate pits: 800 Mt larger, or increased the size of the ultimate pit by 102 percent.Value decreased by $115 million. This is within the accuracy of the model processes used and equates to a decrease of 2 percent; effectively, the value is the same.The value at risk is increased from $284 million to $807 million, an increase of 184 percent.The environmental risk profile is increased since the quantity of waste and tailings required to be stored is greater. While this could be quantified in this framework, it has not been to simplify the communication of the concept. It should be noted that the ultimate pit selection does not have to be based on the minimum VAR shell; however, using a VAR approach allows any deviations to be quantified to ensure alignment with the corporate strategy and associated risk appetite. Fig. 1 VAR analysis post price probability adjustments. (Note that the y-axis has been removed from this figure as it now represents a combination of VAR and probability, the chart should be interpreted by comparing the bars.) Conclusions If risk in the pit optimization process is not quantified it is possible to select an ultimate pit that is incorrectly sized. A VAR-based approach to ultimate pit selection has been demonstrated using commodity price risk as arguably the most obvious risk to consider; however, this is clearly not the only risk relevant to the selection of the ultimate pit. The results of the VAR analysis can be effectively used to guide the strategic planning process to select a base shell for the design of an ultimate pit that maximizes the potential NPV and minimizes the VAR as a function of the price probability distribution used. When value is maximized, and risk is either ignored or not quantified, the value is likely lower than the stated value and therefore may be potentially misleading. Strategic decision-making that does not incorporate risk is not very strategic. Concluding points are as follows: The selection of the ultimate pit should not be made based on financial value alone.Using a revenue factor assumption in isolation ignores risk.Considering risk in the selection of the ultimate pit can be expected to impact the outcome.Assuming that risk has been adequately modeled using a standard discount rate approach is flawed in this application.Risk can be endogenously incorporated into a pit optimization process. Selected references Hochbaum DS (2008) The pseudoflow algorithm: a new algorithm for the maximum flow problem. Oper Res 56(4):992–1009 Whittle J, Rozman L (1991) Open pit design in the 90s, in Mining Industry Optimisation Conference MINOPT 91, AusIMM, Sydney Elkington T, Durham R (2011) Integrated open pit pushback selection and production capacity optimization. J Min Sci 47(2):177–190 Breed MF, van Heerden D (2016) Post-pit optimization strategic alignment. J South Afr Inst Min Metall. 116(2):109–114 Abdel Sabour SA, Dimitrakopoulos RG, Kumral M (2008) Mine design selection under uncertainty. Mining Technology. 117(2):53–64 Hanson N, Hodson D, Mullins M (2001) Skin analysis in the selection of final pit limits. In: Strategic Mine Planning, A.I.o.M.a. Metallurgy, Australasian Institute of Mining and Metallurgy, Perth, Australia

Risk in ultimate pit selection

Authored by:
Edward Holloway

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