Stope Sequencing Optimization for Underground Mines Through Chance-Constrained Programming

Underground mining operations are sensitive to price fluctuations because they usually perform with a narrow profit margin compared to open-pit mining. Furthermore, the economic evaluations regarding operation are based on estimated or simulated grades rather than actual values. These bring a high degree of uncertainty to the viability of an operation. Hence, mine planning that accounts for uncertainty is crucial for underground mining operations. As an underground mining technique, sublevel stoping has geotechnical, curing time, seismicity, cost minimization, and production requirements. A new mixed-integer linear program is proposed that considers the uncertainty associated with net present value using chance-constrained programming. The net present value (NPV) maximization objective is transformed into a multi-objective maximization problem where one objective is to maximize the mean NPV, and the other objective is to maximize the negative standard deviation multiplied by a scalar called risk or reliability level. The balance between the two objectives was maintained by this scalar and was selected based on the reliability level of the project. A case study was conducted with varying reliability levels, and sequences were generated. It was shown that the expected net present value increased at higher reliability levels, and the overall value of the objective function decreased as the reliability level increased. In other words, the variance component penalized the value of the objective function. Moreover, it was observed from the case study that at lower reliability levels, stope grade order bears similarity to the extraction order.