A fundamental problem in open pit mine planning is that of determining the optimum ultimate pit limits of the mine. These limits are that pit contour which is the result of extracting a volume of material which maximizes the difference between the value of extracted ore and the total extraction cost of ore and waste whilst satisfying certain practical operational requirements, such as. safe wall slopes. The determination of the optimum pit contour provides information which is essential in the evaluation of the economic potential of the mineral deposit.A number of optimization techniques have been proposed for determining the optimum pit contour. Of these techniques, those based on graph theory, linear programming and dynamic programming are mathematically rigorous, but only those based on graph theory are more suited to solving the three-dimensional problem. Unfortunately, direct application of these techniques to large ore- bodies may cause considerable difficulties because of the exceptionally high demand on computer storage and time requirements. Indeed, 25 years of research effort has not satisfactorily resolved these computational problems.A major contribution of the work presented in this thesis is the successful implementation of a system of techniques to solve the graph theoretic model, particularly when applied to large ore- bodies. A measure of this success is the fact that pits, as much as seven times larger may be designed with a given amount of computer storage, at a fraction of the time required by current software packages. The solution strategy presented involves the application of a modified Dinics Maximum Flow algorithm, together with an efficient data reducing technique. Computational results of these techniques applied on data from gold producing mines in Western Australia are used to demonstrate the success of this strategy.The relationships ++ / between the rigorous pit optimization techniques are also considered in this work. In particular, the Lerchs-Grossman graph-theoret ic method is shown to be stepwise equivalent to a modified version of the Dual-Simplex Linear Programming technique and not as efficient as the Network Flow method.

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. / Thesis (Master, Mining Engineering) -- Queen's University, 2010-02-08 22:07:52.331