Determination of Open Pit Mining Cut-Off Grade Strategy Using Combination of Nonlinear Programming and Genetic Algorithm

Determination of cut-off grade strategy is one of the most important stages of open pit mine planning and design. It is the parameter directly influencing the financial, technical, economic, legal, environmental, social and political issues in relation to mining operation. Choosing the optimum cut-off grade strategy (COGS) that maximizes the economic outcome has been a major topic for research workers of nearly one century. Many researchers have contributed in devising methods and algorithms, such as dynamic programming, linear programming, optimal control and so on for various aspects of its determination. In this paper, a nonlinear mathematical programming for cut-off grade strategy optimization is presented considering the three main stages of mining operation introduced by K.F. Lane. In this model maximization of net present value of mining operation, under the three constraints of mining stages’ capacities, considered as the optimization criteria. Due to the discrete representation of the mining resource, the proposed nonlinear formulation is approximated by a nonlinear signomial geometric programming. According to nonconvexity and the complexity of the proposed model, an augmented Lagrangian genetic algorithm was used to find the optimum cut-off grade strategy under varying and fixed price circumstances. To validate the proposed nonlinear model efficiency, their results were compared with the results obtained by the K.F. Lane methodology. It was found that the proposed nonlinear model works efficiently in the determination of cut-off grade strategy. According to the simplicity of the structure of nonlinear programming modeling in comparison with dynamic programming it is hoped that, further development of this model would certainly provide the ability of considering managerial and technical flexibilities as well as incorporating more real mining conditions in the determination of cut-off grade strategy optimization.

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