Optimisation of Mining Policy Under Diff erent Economical Conditions Using a Combination of Non-Linear Programming and Genetic Algorithm

摘要

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 infl uencing the fi nancial, technical, economic, legal, environmental, social and political issues in relation to mining operation. Choosing the optimum cut-off grade strategy that maximises the economic outcome has been a major topic of research workers for 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 non-linear mathematical programming for cut-off grade strategy optimisation is presented, considering the three main stages of mining operation introduced by K F Lane. In this model maximisation of net present value of mining operation, under the three constraints of mining stages’ capacities, considered as the optimisation criteria. Due to the discrete representation of the mining resource, the proposed non-linear formulation is approximated by a non-linear signomial geometric programming. According to non-convexity and the complexity of the proposed model, an augmented Lagrangian genetic algorithm was used to fi nd the optimum cut-off grade strategy under varying and fi xed price circumstances. To validate the proposed non-linear model effi ciency, the results were compared with the results obtained by the K F Lane methodology. It was found that the proposed non-linear model works effi ciently in the determination of cut-off grade strategy. According to the simplicity of the structure of non-linear programming modelling in comparison with dynamic programming it is hoped that, further development of this model would certainly provide the ability of considering managerial and technical fl exibilities as well as incorporating more real mining conditions in the determination of cut-off grade strategy optimisation.