Test of an Innovative Stochastic Design System on an Open Pit
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Commodity markets are fundamentally cyclical, exposing mining companies to large swings in profitability during periods of economic boom and bust. Although this is well documented, companies continue to produce mine plans based on present market conditions that fail to acknowledge long-term metal price variability. The purpose of this thesis is to adapt McIsaac’s (2008) mathematical model for determining the most robust underground mining plan under conditions of metal price uncertainty for application in an open pit environment. An overview of conventional open pit algorithms is given to demonstrate that a circular analysis precludes the determination of an optimal solution when metal prices are uncertain. Under the proposed methodology, the optimal solution is achieved by selecting the cutoff grade and production rate under stochastic metal prices such that the net present value and probability of a positive net present value are maximized. The mathematical model was formulated with costs represented as a function of the level of production, rate of production or both. Revenues are achieved from either a mill, heap leach or stockpile process dependent on the level of production and metal price in the year of consideration. Metal prices are generated annually according to a stochastic model that balances short-term volatility with long-term trends. The compiled cash flow model determines the optimal net present value for a given production profile under input metal prices. The feasible area of production is established based on mine life, resource and financing constraints. Net present values are generated for a broad search grid, which converges towards a unimodal solution according to a golden search algorithm. The process is then repeated many times in order to identify the production profile at which the optimal solution is repeatedly reached. As a visual representation, the solutions are plotted on a bubble graph where the size of the bubble corresponds to the frequency of the solution; the largest bubble is associated with the optimal solution. The methodology is tested on two massive copper porphyry deposits, contained within a single claim, for which a Preliminary Economic Assessment has been completed.