We present a mixed-integer programming model for solving the long-term planning problem of an underground mine. This model, which establishes the sequence of mining for a horizon of 20 years, determines which lens of the geological model will be mined and in what order, while respecting the operational constraints. For each lens to be mined, a specific cut-off grade has to be selected to maximize the net present value. The choice of a cut-off grade affects the volume and the average grade of each lens, which increases the size of problems to be solved. To reduce the computation time, different acceleration strategies and a Fix-and-Optimize heuristic are proposed. Computational experiments on instances of different sizes are performed to (1) assess the quality of the solution found by each method and (2) present the impact of the variable cut-off grade.

中文翻译：

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可变边界品位的地下矿山的战略规划

我们提出了一种混合整数规划模型，用于解决地下矿井的长期规划问题。该模型确定了20年的开采顺序，确定了要开采的地质模型的哪个镜头，以什么顺序开采，同时要考虑到操作上的限制。对于每个要开采的镜片，必须选择特定的截止等级，以使净现值最大化。截止等级的选择会影响每个镜片的体积和平均等级，从而增加了要解决的问题的大小。为了减少计算时间，提出了不同的加速策略和Fix-and-Optimize启发式算法。